%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG153+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.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 18:30:36 EDT 2022 % Result : Unsatisfiable 21.42s 21.66s % Output : Proof 22.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG153+1 : TPTP v8.1.0. Released v2.7.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n018.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Wed Jun 8 18:37:52 EDT 2022 % 0.13/0.35 % CPUTime : % 21.42/21.66 (* PROOF-FOUND *) % 21.42/21.66 % SZS status Unsatisfiable % 21.42/21.66 (* BEGIN-PROOF *) % 21.42/21.66 % SZS output start Proof % 21.42/21.66 Theorem zenon_thm : False. % 21.42/21.66 Proof. % 21.42/21.66 assert (zenon_L1_ : ((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 21.42/21.66 do 0 intro. intros zenon_H1d zenon_H1e. % 21.42/21.66 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 21.42/21.66 exact (zenon_H1f zenon_H1e). % 21.42/21.66 exact (zenon_H1f zenon_H1e). % 21.42/21.66 (* end of lemma zenon_L1_ *) % 21.42/21.66 assert (zenon_L2_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> False). % 21.42/21.66 do 0 intro. intros zenon_H20. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H1e. zenon_intro zenon_H21. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H1e. zenon_intro zenon_H22. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.42/21.66 apply (zenon_L1_); trivial. % 21.42/21.66 (* end of lemma zenon_L2_ *) % 21.42/21.66 assert (zenon_L3_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> False). % 21.42/21.66 do 0 intro. intros zenon_H24 zenon_H1e zenon_H25. % 21.42/21.66 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H24. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H1e. % 21.42/21.66 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 21.42/21.66 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 21.42/21.66 congruence. % 21.42/21.66 apply zenon_H27. apply refl_equal. % 21.42/21.66 apply zenon_H26. apply sym_equal. exact zenon_H25. % 21.42/21.66 (* end of lemma zenon_L3_ *) % 21.42/21.66 assert (zenon_L4_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 21.42/21.66 do 0 intro. intros zenon_H28 zenon_H24 zenon_H1e. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 21.42/21.66 apply (zenon_L3_); trivial. % 21.42/21.66 (* end of lemma zenon_L4_ *) % 21.42/21.66 assert (zenon_L5_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> False). % 21.42/21.66 do 0 intro. intros zenon_H2c zenon_H1e zenon_H2d. % 21.42/21.66 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H2c. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H1e. % 21.42/21.66 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 21.42/21.66 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 21.42/21.66 congruence. % 21.42/21.66 apply zenon_H27. apply refl_equal. % 21.42/21.66 apply zenon_H2e. apply sym_equal. exact zenon_H2d. % 21.42/21.66 (* end of lemma zenon_L5_ *) % 21.42/21.66 assert (zenon_L6_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 21.42/21.66 do 0 intro. intros zenon_H2f zenon_H2c zenon_H1e. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 21.42/21.66 apply (zenon_L5_); trivial. % 21.42/21.66 (* end of lemma zenon_L6_ *) % 21.42/21.66 assert (zenon_L7_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> False). % 21.42/21.66 do 0 intro. intros zenon_H33 zenon_H1e zenon_H34. % 21.42/21.66 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H33. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H1e. % 21.42/21.66 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 21.42/21.66 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 21.42/21.66 congruence. % 21.42/21.66 apply zenon_H27. apply refl_equal. % 21.42/21.66 apply zenon_H35. apply sym_equal. exact zenon_H34. % 21.42/21.66 (* end of lemma zenon_L7_ *) % 21.42/21.66 assert (zenon_L8_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 21.42/21.66 do 0 intro. intros zenon_H36 zenon_H33 zenon_H1e. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 21.42/21.66 apply (zenon_L7_); trivial. % 21.42/21.66 (* end of lemma zenon_L8_ *) % 21.42/21.66 assert (zenon_L9_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e0)) = (e0)) -> False). % 21.42/21.66 do 0 intro. intros zenon_H3a zenon_H1e. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.42/21.66 apply (zenon_L1_); trivial. % 21.42/21.66 (* end of lemma zenon_L9_ *) % 21.42/21.66 assert (zenon_L10_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((op (e1) (e1)) = (e1)) -> False). % 21.42/21.66 do 0 intro. intros zenon_H3e zenon_H3f. % 21.42/21.66 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 21.42/21.66 exact (zenon_H40 zenon_H3f). % 21.42/21.66 exact (zenon_H40 zenon_H3f). % 21.42/21.66 (* end of lemma zenon_L10_ *) % 21.42/21.66 assert (zenon_L11_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> False). % 21.42/21.66 do 0 intro. intros zenon_H41. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H3f. zenon_intro zenon_H42. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H3f. zenon_intro zenon_H2b. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.42/21.66 apply (zenon_L10_); trivial. % 21.42/21.66 (* end of lemma zenon_L11_ *) % 21.42/21.66 assert (zenon_L12_ : (~((e0) = (e0))) -> False). % 21.42/21.66 do 0 intro. intros zenon_H46. % 21.42/21.66 apply zenon_H46. apply refl_equal. % 21.42/21.66 (* end of lemma zenon_L12_ *) % 21.42/21.66 assert (zenon_L13_ : ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.42/21.66 do 0 intro. intros zenon_H1e zenon_H47 zenon_H48. % 21.42/21.66 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H49 | zenon_intro zenon_H4a ]. % 21.42/21.66 cut (((e1) = (e1)) = ((e0) = (e1))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H48. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H49. % 21.42/21.66 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.66 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 21.42/21.66 congruence. % 21.42/21.66 cut (((op (e0) (e0)) = (e0)) = ((e1) = (e0))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H4b. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H1e. % 21.42/21.66 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.42/21.66 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 21.42/21.66 congruence. % 21.42/21.66 exact (zenon_H4c zenon_H47). % 21.42/21.66 apply zenon_H46. apply refl_equal. % 21.42/21.66 apply zenon_H4a. apply refl_equal. % 21.42/21.66 apply zenon_H4a. apply refl_equal. % 21.42/21.66 (* end of lemma zenon_L13_ *) % 21.42/21.66 assert (zenon_L14_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 21.42/21.66 do 0 intro. intros zenon_H4d zenon_H3c zenon_H4e. % 21.42/21.66 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H4f | zenon_intro zenon_H50 ]. % 21.42/21.66 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e0)) = (op (e1) (e2)))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H4e. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H4f. % 21.42/21.66 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.42/21.66 cut (((op (e1) (e2)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 21.42/21.66 congruence. % 21.42/21.66 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e0)))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H51. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H4d. % 21.42/21.66 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 21.42/21.66 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.42/21.66 congruence. % 21.42/21.66 apply zenon_H50. apply refl_equal. % 21.42/21.66 apply zenon_H52. apply sym_equal. exact zenon_H3c. % 21.42/21.66 apply zenon_H50. apply refl_equal. % 21.42/21.66 apply zenon_H50. apply refl_equal. % 21.42/21.66 (* end of lemma zenon_L14_ *) % 21.42/21.66 assert (zenon_L15_ : ((op (e2) (e1)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 21.42/21.66 do 0 intro. intros zenon_H53 zenon_H54 zenon_H55. % 21.42/21.66 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ]. % 21.42/21.66 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (e0)) = (op (e2) (e1)))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H55. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H56. % 21.42/21.66 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 21.42/21.66 cut (((op (e2) (e1)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 21.42/21.66 congruence. % 21.42/21.66 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (e1)) = (op (e2) (e0)))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H58. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H53. % 21.42/21.66 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 21.42/21.66 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 21.42/21.66 congruence. % 21.42/21.66 apply zenon_H57. apply refl_equal. % 21.42/21.66 apply zenon_H59. apply sym_equal. exact zenon_H54. % 21.42/21.66 apply zenon_H57. apply refl_equal. % 21.42/21.66 apply zenon_H57. apply refl_equal. % 21.42/21.66 (* end of lemma zenon_L15_ *) % 21.42/21.66 assert (zenon_L16_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 21.42/21.66 do 0 intro. intros zenon_H5a zenon_H3c zenon_H4e. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.42/21.66 apply (zenon_L14_); trivial. % 21.42/21.66 (* end of lemma zenon_L16_ *) % 21.42/21.66 assert (zenon_L17_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 21.42/21.66 do 0 intro. intros zenon_H5c zenon_H3c zenon_H5d. % 21.42/21.66 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H5e | zenon_intro zenon_H5f ]. % 21.42/21.66 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e0)) = (op (e1) (e3)))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H5d. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H5e. % 21.42/21.66 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.42/21.66 cut (((op (e1) (e3)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 21.42/21.66 congruence. % 21.42/21.66 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e0)))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H60. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H5c. % 21.42/21.66 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 21.42/21.66 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.42/21.66 congruence. % 21.42/21.66 apply zenon_H5f. apply refl_equal. % 21.42/21.66 apply zenon_H52. apply sym_equal. exact zenon_H3c. % 21.42/21.66 apply zenon_H5f. apply refl_equal. % 21.42/21.66 apply zenon_H5f. apply refl_equal. % 21.42/21.66 (* end of lemma zenon_L17_ *) % 21.42/21.66 assert (zenon_L18_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 21.42/21.66 do 0 intro. intros zenon_H61 zenon_H3c zenon_H5d. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.42/21.66 apply (zenon_L17_); trivial. % 21.42/21.66 (* end of lemma zenon_L18_ *) % 21.42/21.66 assert (zenon_L19_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e0)) = (e0)) -> False). % 21.42/21.66 do 0 intro. intros zenon_H63 zenon_H1e. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 21.42/21.66 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.42/21.66 apply (zenon_L1_); trivial. % 21.42/21.66 (* end of lemma zenon_L19_ *) % 21.42/21.66 assert (zenon_L20_ : ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 21.42/21.66 do 0 intro. intros zenon_H1e zenon_H67 zenon_H68. % 21.42/21.66 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.42/21.66 cut (((e2) = (e2)) = ((e0) = (e2))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H68. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H69. % 21.42/21.66 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.66 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 21.42/21.66 congruence. % 21.42/21.66 cut (((op (e0) (e0)) = (e0)) = ((e2) = (e0))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H6b. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H1e. % 21.42/21.66 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.42/21.66 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 21.42/21.66 congruence. % 21.42/21.66 exact (zenon_H6c zenon_H67). % 21.42/21.66 apply zenon_H46. apply refl_equal. % 21.42/21.66 apply zenon_H6a. apply refl_equal. % 21.42/21.66 apply zenon_H6a. apply refl_equal. % 21.42/21.66 (* end of lemma zenon_L20_ *) % 21.42/21.66 assert (zenon_L21_ : ((op (e2) (e1)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> False). % 21.42/21.66 do 0 intro. intros zenon_H6d zenon_H6e zenon_H6f. % 21.42/21.66 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ]. % 21.42/21.66 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e0) (e1)) = (op (e2) (e1)))). % 21.42/21.66 intro zenon_D_pnotp. % 21.42/21.66 apply zenon_H6f. % 21.42/21.66 rewrite <- zenon_D_pnotp. % 21.42/21.66 exact zenon_H56. % 21.42/21.67 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 21.42/21.67 cut (((op (e2) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e0) (e1)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H70. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H6d. % 21.42/21.67 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 21.42/21.67 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H57. apply refl_equal. % 21.42/21.67 apply zenon_H71. apply sym_equal. exact zenon_H6e. % 21.42/21.67 apply zenon_H57. apply refl_equal. % 21.42/21.67 apply zenon_H57. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L21_ *) % 21.42/21.67 assert (zenon_L22_ : ((op (e1) (e2)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H72 zenon_H66 zenon_H73. % 21.42/21.67 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H4f | zenon_intro zenon_H50 ]. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e0) (e2)) = (op (e1) (e2)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H73. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H4f. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e0) (e2)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H74. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H72. % 21.42/21.67 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H50. apply refl_equal. % 21.42/21.67 apply zenon_H75. apply sym_equal. exact zenon_H66. % 21.42/21.67 apply zenon_H50. apply refl_equal. % 21.42/21.67 apply zenon_H50. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L22_ *) % 21.42/21.67 assert (zenon_L23_ : (~((e1) = (e1))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H4a. % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L23_ *) % 21.42/21.67 assert (zenon_L24_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H3c zenon_H76 zenon_H77. % 21.42/21.67 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.42/21.67 cut (((e2) = (e2)) = ((e1) = (e2))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H77. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H69. % 21.42/21.67 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.67 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e1) (e0)) = (e1)) = ((e2) = (e1))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H78. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H3c. % 21.42/21.67 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.67 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H79 zenon_H76). % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L24_ *) % 21.42/21.67 assert (zenon_L25_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H25 zenon_H3c zenon_H48. % 21.42/21.67 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H49 | zenon_intro zenon_H4a ]. % 21.42/21.67 cut (((e1) = (e1)) = ((e0) = (e1))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H48. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H49. % 21.42/21.67 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.67 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e1) (e0)) = (e0)) = ((e1) = (e0))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H4b. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H25. % 21.42/21.67 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.42/21.67 cut (((op (e1) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H7a zenon_H3c). % 21.42/21.67 apply zenon_H46. apply refl_equal. % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L25_ *) % 21.42/21.67 assert (zenon_L26_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H28 zenon_H3c zenon_H48. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 21.42/21.67 apply (zenon_L25_); trivial. % 21.42/21.67 (* end of lemma zenon_L26_ *) % 21.42/21.67 assert (zenon_L27_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H2d zenon_H65 zenon_H68. % 21.42/21.67 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.42/21.67 cut (((e2) = (e2)) = ((e0) = (e2))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H68. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H69. % 21.42/21.67 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.67 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e2) (e0)) = (e0)) = ((e2) = (e0))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H6b. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H2d. % 21.42/21.67 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.42/21.67 cut (((op (e2) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H7b zenon_H65). % 21.42/21.67 apply zenon_H46. apply refl_equal. % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L27_ *) % 21.42/21.67 assert (zenon_L28_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H2f zenon_H65 zenon_H68. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 21.42/21.67 apply (zenon_L27_); trivial. % 21.42/21.67 (* end of lemma zenon_L28_ *) % 21.42/21.67 assert (zenon_L29_ : (~((e2) = (e2))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H6a. % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L29_ *) % 21.42/21.67 assert (zenon_L30_ : (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H77 zenon_H65 zenon_H54. % 21.42/21.67 cut (((op (e2) (e0)) = (e2)) = ((e1) = (e2))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H77. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H65. % 21.42/21.67 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.67 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H7c zenon_H54). % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L30_ *) % 21.42/21.67 assert (zenon_L31_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H7d zenon_H7e zenon_H7f. % 21.42/21.67 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H7d. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H7e. % 21.42/21.67 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 21.42/21.67 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H81. apply refl_equal. % 21.42/21.67 apply zenon_H80. apply sym_equal. exact zenon_H7f. % 21.42/21.67 (* end of lemma zenon_L31_ *) % 21.42/21.67 assert (zenon_L32_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H82 zenon_H48 zenon_H1e zenon_H5d zenon_H5c zenon_H65 zenon_H77 zenon_H7d zenon_H7f. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.42/21.67 apply (zenon_L13_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.42/21.67 apply (zenon_L17_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.42/21.67 apply (zenon_L30_); trivial. % 21.42/21.67 apply (zenon_L31_); trivial. % 21.42/21.67 (* end of lemma zenon_L32_ *) % 21.42/21.67 assert (zenon_L33_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H61 zenon_H82 zenon_H48 zenon_H1e zenon_H5d zenon_H65 zenon_H77 zenon_H7d. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 21.42/21.67 apply (zenon_L32_); trivial. % 21.42/21.67 (* end of lemma zenon_L33_ *) % 21.42/21.67 assert (zenon_L34_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H55 zenon_H65 zenon_H6d. % 21.42/21.67 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H55. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H65. % 21.42/21.67 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 21.42/21.67 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H86. apply refl_equal. % 21.42/21.67 apply zenon_H85. apply sym_equal. exact zenon_H6d. % 21.42/21.67 (* end of lemma zenon_L34_ *) % 21.42/21.67 assert (zenon_L35_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H87 zenon_H55 zenon_H65. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.42/21.67 apply (zenon_L34_); trivial. % 21.42/21.67 (* end of lemma zenon_L35_ *) % 21.42/21.67 assert (zenon_L36_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H89 zenon_H8a. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.42/21.67 exact (zenon_H8b zenon_H8a). % 21.42/21.67 exact (zenon_H8b zenon_H8a). % 21.42/21.67 (* end of lemma zenon_L36_ *) % 21.42/21.67 assert (zenon_L37_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H8c. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8a. zenon_intro zenon_H8d. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H8a. zenon_intro zenon_H32. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.42/21.67 apply (zenon_L36_); trivial. % 21.42/21.67 (* end of lemma zenon_L37_ *) % 21.42/21.67 assert (zenon_L38_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H93 zenon_H65 zenon_H94. % 21.42/21.67 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 21.42/21.67 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e0)) = (op (e2) (e3)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H94. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H95. % 21.42/21.67 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.42/21.67 cut (((op (e2) (e3)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e0)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H97. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H93. % 21.42/21.67 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 21.42/21.67 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H96. apply refl_equal. % 21.42/21.67 apply zenon_H98. apply sym_equal. exact zenon_H65. % 21.42/21.67 apply zenon_H96. apply refl_equal. % 21.42/21.67 apply zenon_H96. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L38_ *) % 21.42/21.67 assert (zenon_L39_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H99 zenon_H65 zenon_H94. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.42/21.67 apply (zenon_L38_); trivial. % 21.42/21.67 (* end of lemma zenon_L39_ *) % 21.42/21.67 assert (zenon_L40_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e0)) = (e0)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H9b zenon_H1e. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.42/21.67 apply (zenon_L1_); trivial. % 21.42/21.67 (* end of lemma zenon_L40_ *) % 21.42/21.67 assert (zenon_L41_ : ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H1e zenon_H9f zenon_Ha0. % 21.42/21.67 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.42/21.67 cut (((e3) = (e3)) = ((e0) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha0. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Ha1. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e0) (e0)) = (e0)) = ((e3) = (e0))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha3. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H1e. % 21.42/21.67 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.42/21.67 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Ha4 zenon_H9f). % 21.42/21.67 apply zenon_H46. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L41_ *) % 21.42/21.67 assert (zenon_L42_ : ((op (e1) (e3)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Ha5 zenon_Ha6 zenon_H5d. % 21.42/21.67 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H5e | zenon_intro zenon_H5f ]. % 21.42/21.67 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e0)) = (op (e1) (e3)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H5d. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H5e. % 21.42/21.67 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.42/21.67 cut (((op (e1) (e3)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e1) (e0)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H60. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Ha5. % 21.42/21.67 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 21.42/21.67 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H5f. apply refl_equal. % 21.42/21.67 apply zenon_Ha7. apply sym_equal. exact zenon_Ha6. % 21.42/21.67 apply zenon_H5f. apply refl_equal. % 21.42/21.67 apply zenon_H5f. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L42_ *) % 21.42/21.67 assert (zenon_L43_ : ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H65 zenon_Ha8 zenon_Ha9. % 21.42/21.67 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.42/21.67 cut (((e3) = (e3)) = ((e2) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha9. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Ha1. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e2) (e0)) = (e2)) = ((e3) = (e2))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Haa. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H65. % 21.42/21.67 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.67 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Hab zenon_Ha8). % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L43_ *) % 21.42/21.67 assert (zenon_L44_ : ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hac zenon_H9d zenon_H7d. % 21.42/21.67 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_Had | zenon_intro zenon_Hae ]. % 21.42/21.67 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (e0)) = (op (e3) (e1)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H7d. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Had. % 21.42/21.67 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 21.42/21.67 cut (((op (e3) (e1)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e0)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Haf. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hac. % 21.42/21.67 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 21.42/21.67 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_Hae. apply refl_equal. % 21.42/21.67 apply zenon_Hb0. apply sym_equal. exact zenon_H9d. % 21.42/21.67 apply zenon_Hae. apply refl_equal. % 21.42/21.67 apply zenon_Hae. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L44_ *) % 21.42/21.67 assert (zenon_L45_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hb1 zenon_Hb2 zenon_Ha0 zenon_H1e zenon_H5d zenon_Ha9 zenon_H65 zenon_H7d. % 21.42/21.67 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.42/21.67 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.42/21.67 apply (zenon_L41_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.42/21.67 apply (zenon_L42_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.42/21.67 apply (zenon_L43_); trivial. % 21.42/21.67 apply (zenon_L44_); trivial. % 21.42/21.67 (* end of lemma zenon_L45_ *) % 21.42/21.67 assert (zenon_L46_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H3c zenon_Ha6 zenon_Hb6. % 21.42/21.67 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.42/21.67 cut (((e3) = (e3)) = ((e1) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hb6. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Ha1. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e1) (e0)) = (e1)) = ((e3) = (e1))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hb7. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H3c. % 21.42/21.67 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.67 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb8]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Hb8 zenon_Ha6). % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L46_ *) % 21.42/21.67 assert (zenon_L47_ : ((op (e2) (e3)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hb9 zenon_Ha8 zenon_H94. % 21.42/21.67 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 21.42/21.67 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e0)) = (op (e2) (e3)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H94. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H95. % 21.42/21.67 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.42/21.67 cut (((op (e2) (e3)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e2) (e0)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H97. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hb9. % 21.42/21.67 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 21.42/21.67 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H96. apply refl_equal. % 21.42/21.67 apply zenon_Hba. apply sym_equal. exact zenon_Ha8. % 21.42/21.67 apply zenon_H96. apply refl_equal. % 21.42/21.67 apply zenon_H96. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L47_ *) % 21.42/21.67 assert (zenon_L48_ : ((op (e3) (e2)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hbb zenon_H9d zenon_Hbc. % 21.42/21.67 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 21.42/21.67 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e0)) = (op (e3) (e2)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hbc. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hbd. % 21.42/21.67 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.42/21.67 cut (((op (e3) (e2)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e0)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hbf. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hbb. % 21.42/21.67 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 21.42/21.67 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_Hbe. apply refl_equal. % 21.42/21.67 apply zenon_Hb0. apply sym_equal. exact zenon_H9d. % 21.42/21.67 apply zenon_Hbe. apply refl_equal. % 21.42/21.67 apply zenon_Hbe. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L48_ *) % 21.42/21.67 assert (zenon_L49_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hc0 zenon_Hb2 zenon_Ha0 zenon_H1e zenon_Hb6 zenon_H3c zenon_H94 zenon_Hbc. % 21.42/21.67 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.42/21.67 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.42/21.67 apply (zenon_L41_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.42/21.67 apply (zenon_L46_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.42/21.67 apply (zenon_L47_); trivial. % 21.42/21.67 apply (zenon_L48_); trivial. % 21.42/21.67 (* end of lemma zenon_L49_ *) % 21.42/21.67 assert (zenon_L50_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hc2 zenon_Hc3. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.42/21.67 exact (zenon_Hc4 zenon_Hc3). % 21.42/21.67 exact (zenon_Hc4 zenon_Hc3). % 21.42/21.67 (* end of lemma zenon_L50_ *) % 21.42/21.67 assert (zenon_L51_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hc5. % 21.42/21.67 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_Hc3. zenon_intro zenon_Hc6. % 21.42/21.67 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc3. zenon_intro zenon_H39. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.42/21.67 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.42/21.67 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.42/21.67 apply (zenon_L50_); trivial. % 21.42/21.67 (* end of lemma zenon_L51_ *) % 21.42/21.67 assert (zenon_L52_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hcc zenon_H68 zenon_H33 zenon_H4e zenon_H77 zenon_H48 zenon_H82 zenon_H55 zenon_H7d zenon_H65 zenon_Ha9 zenon_H5d zenon_Hbc zenon_H94 zenon_H3c zenon_Hb6 zenon_H1e zenon_Ha0 zenon_Hb2. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.42/21.67 apply (zenon_L2_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.42/21.67 apply (zenon_L26_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.42/21.67 apply (zenon_L28_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.42/21.67 apply (zenon_L8_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.42/21.67 apply (zenon_L9_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.42/21.67 apply (zenon_L11_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.42/21.67 apply (zenon_L16_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.42/21.67 apply (zenon_L33_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.42/21.67 apply (zenon_L19_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.42/21.67 apply (zenon_L35_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.42/21.67 apply (zenon_L37_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.42/21.67 apply (zenon_L39_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.42/21.67 apply (zenon_L40_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.42/21.67 apply (zenon_L45_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.42/21.67 apply (zenon_L49_); trivial. % 21.42/21.67 apply (zenon_L51_); trivial. % 21.42/21.67 (* end of lemma zenon_L52_ *) % 21.42/21.67 assert (zenon_L53_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H2a zenon_Hdb zenon_Ha0. % 21.42/21.67 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.42/21.67 cut (((e3) = (e3)) = ((e0) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha0. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Ha1. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e0) (e1)) = (e0)) = ((e3) = (e0))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha3. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H2a. % 21.42/21.67 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.42/21.67 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Hdc zenon_Hdb). % 21.42/21.67 apply zenon_H46. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L53_ *) % 21.42/21.67 assert (zenon_L54_ : (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H68 zenon_H6d zenon_Hdd. % 21.42/21.67 cut (((op (e2) (e1)) = (e2)) = ((e0) = (e2))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H68. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H6d. % 21.42/21.67 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.67 cut (((op (e2) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Hde zenon_Hdd). % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L54_ *) % 21.42/21.67 assert (zenon_L55_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H3d zenon_Hdb zenon_Hb6. % 21.42/21.67 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.42/21.67 cut (((e3) = (e3)) = ((e1) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hb6. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Ha1. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e0) (e1)) = (e1)) = ((e3) = (e1))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hb7. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H3d. % 21.42/21.67 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.67 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Hdc zenon_Hdb). % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L55_ *) % 21.42/21.67 assert (zenon_L56_ : (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H77 zenon_H6d zenon_H53. % 21.42/21.67 cut (((op (e2) (e1)) = (e2)) = ((e1) = (e2))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H77. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H6d. % 21.42/21.67 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.67 cut (((op (e2) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Hdf zenon_H53). % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L56_ *) % 21.42/21.67 assert (zenon_L57_ : (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H48 zenon_H7f zenon_He0. % 21.42/21.67 cut (((op (e3) (e1)) = (e1)) = ((e0) = (e1))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H48. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H7f. % 21.42/21.67 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.67 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_He1 zenon_He0). % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L57_ *) % 21.42/21.67 assert (zenon_L58_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> False). % 21.42/21.67 do 0 intro. intros zenon_He2 zenon_Ha0 zenon_He3 zenon_H68 zenon_He4 zenon_Hb6 zenon_Hdb zenon_H40 zenon_H6d zenon_H77 zenon_H48. % 21.42/21.67 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.42/21.67 apply (zenon_L53_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.42/21.67 exact (zenon_He3 zenon_He7). % 21.42/21.67 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.42/21.67 apply (zenon_L54_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.42/21.67 apply (zenon_L55_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.42/21.67 exact (zenon_H40 zenon_H3f). % 21.42/21.67 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.42/21.67 apply (zenon_L56_); trivial. % 21.42/21.67 apply (zenon_L57_); trivial. % 21.42/21.67 (* end of lemma zenon_L58_ *) % 21.42/21.67 assert (zenon_L59_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H4d zenon_H72 zenon_H77. % 21.42/21.67 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.42/21.67 cut (((e2) = (e2)) = ((e1) = (e2))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H77. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H69. % 21.42/21.67 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.67 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e1) (e2)) = (e1)) = ((e2) = (e1))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H78. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H4d. % 21.42/21.67 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.67 cut (((op (e1) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Hea zenon_H72). % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L59_ *) % 21.42/21.67 assert (zenon_L60_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Heb zenon_H48 zenon_H25 zenon_H40 zenon_H77 zenon_H72 zenon_Hec. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.42/21.67 apply (zenon_L25_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.42/21.67 exact (zenon_H40 zenon_H3f). % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.42/21.67 apply (zenon_L59_); trivial. % 21.42/21.67 exact (zenon_Hec zenon_H5c). % 21.42/21.67 (* end of lemma zenon_L60_ *) % 21.42/21.67 assert (zenon_L61_ : ((op (e2) (e1)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H6d zenon_Hef zenon_Hf0. % 21.42/21.67 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ]. % 21.42/21.67 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e1) (e1)) = (op (e2) (e1)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hf0. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H56. % 21.42/21.67 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 21.42/21.67 cut (((op (e2) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf1]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e1) (e1)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hf1. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H6d. % 21.42/21.67 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 21.42/21.67 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H57. apply refl_equal. % 21.42/21.67 apply zenon_Hf2. apply sym_equal. exact zenon_Hef. % 21.42/21.67 apply zenon_H57. apply refl_equal. % 21.42/21.67 apply zenon_H57. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L61_ *) % 21.42/21.67 assert (zenon_L62_ : (~((e0) = (e2))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H68 zenon_H72 zenon_Hf3. % 21.42/21.67 cut (((op (e1) (e2)) = (e2)) = ((e0) = (e2))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H68. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H72. % 21.42/21.67 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.67 cut (((op (e1) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Hf4 zenon_Hf3). % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L62_ *) % 21.42/21.67 assert (zenon_L63_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hf5 zenon_Hf6 zenon_Hf7. % 21.42/21.67 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hf5. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hf6. % 21.42/21.67 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 21.42/21.67 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_Hf9. apply refl_equal. % 21.42/21.67 apply zenon_Hf8. apply sym_equal. exact zenon_Hf7. % 21.42/21.67 (* end of lemma zenon_L63_ *) % 21.42/21.67 assert (zenon_L64_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hfa zenon_H77 zenon_H3c zenon_Hf0 zenon_H6d zenon_Hf3 zenon_H68 zenon_Hf5 zenon_Hf6. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.42/21.67 apply (zenon_L24_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.42/21.67 apply (zenon_L61_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.42/21.67 apply (zenon_L62_); trivial. % 21.42/21.67 apply (zenon_L63_); trivial. % 21.42/21.67 (* end of lemma zenon_L64_ *) % 21.42/21.67 assert (zenon_L65_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H2a zenon_H3d zenon_H48. % 21.42/21.67 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H49 | zenon_intro zenon_H4a ]. % 21.42/21.67 cut (((e1) = (e1)) = ((e0) = (e1))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H48. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H49. % 21.42/21.67 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.67 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e0) (e1)) = (e0)) = ((e1) = (e0))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H4b. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H2a. % 21.42/21.67 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.42/21.67 cut (((op (e0) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Hfd zenon_H3d). % 21.42/21.67 apply zenon_H46. apply refl_equal. % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L65_ *) % 21.42/21.67 assert (zenon_L66_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Heb zenon_Hb6 zenon_Ha6 zenon_H40 zenon_H77 zenon_H72 zenon_Hec. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.42/21.67 apply (zenon_L46_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.42/21.67 exact (zenon_H40 zenon_H3f). % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.42/21.67 apply (zenon_L59_); trivial. % 21.42/21.67 exact (zenon_Hec zenon_H5c). % 21.42/21.67 (* end of lemma zenon_L66_ *) % 21.42/21.67 assert (zenon_L67_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H2d zenon_Ha8 zenon_Ha0. % 21.42/21.67 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.42/21.67 cut (((e3) = (e3)) = ((e0) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha0. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Ha1. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e2) (e0)) = (e0)) = ((e3) = (e0))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha3. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H2d. % 21.42/21.67 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.42/21.67 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Hab zenon_Ha8). % 21.42/21.67 apply zenon_H46. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L67_ *) % 21.42/21.67 assert (zenon_L68_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H31 zenon_Hfe zenon_Ha0. % 21.42/21.67 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.42/21.67 cut (((e3) = (e3)) = ((e0) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha0. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Ha1. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e0) (e2)) = (e0)) = ((e3) = (e0))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha3. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H31. % 21.42/21.67 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.42/21.67 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Hff zenon_Hfe). % 21.42/21.67 apply zenon_H46. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L68_ *) % 21.42/21.67 assert (zenon_L69_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H100 zenon_H3c zenon_H54. % 21.42/21.67 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e2) (e0)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H100. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H3c. % 21.42/21.67 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 21.42/21.67 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H101]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H101. apply refl_equal. % 21.42/21.67 apply zenon_H59. apply sym_equal. exact zenon_H54. % 21.42/21.67 (* end of lemma zenon_L69_ *) % 21.42/21.67 assert (zenon_L70_ : (((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))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Heb zenon_H54 zenon_H100 zenon_H40 zenon_H77 zenon_H72 zenon_Hec. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.42/21.67 apply (zenon_L69_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.42/21.67 exact (zenon_H40 zenon_H3f). % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.42/21.67 apply (zenon_L59_); trivial. % 21.42/21.67 exact (zenon_Hec zenon_H5c). % 21.42/21.67 (* end of lemma zenon_L70_ *) % 21.42/21.67 assert (zenon_L71_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H7e zenon_H102 zenon_H77. % 21.42/21.67 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.42/21.67 cut (((e2) = (e2)) = ((e1) = (e2))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H77. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H69. % 21.42/21.67 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.67 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e3) (e0)) = (e1)) = ((e2) = (e1))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H78. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H7e. % 21.42/21.67 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.67 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H103 zenon_H102). % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L71_ *) % 21.42/21.67 assert (zenon_L72_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H104 zenon_H105 zenon_H106. % 21.42/21.67 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H104. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H105. % 21.42/21.67 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 21.42/21.67 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H108. apply refl_equal. % 21.42/21.67 apply zenon_H107. apply sym_equal. exact zenon_H106. % 21.42/21.67 (* end of lemma zenon_L72_ *) % 21.42/21.67 assert (zenon_L73_ : ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H9d zenon_Ha8 zenon_H109. % 21.42/21.67 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H10a | zenon_intro zenon_H81 ]. % 21.42/21.67 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H109. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H10a. % 21.42/21.67 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 21.42/21.67 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H10b]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H10b. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H9d. % 21.42/21.67 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 21.42/21.67 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H81. apply refl_equal. % 21.42/21.67 apply zenon_Hba. apply sym_equal. exact zenon_Ha8. % 21.42/21.67 apply zenon_H81. apply refl_equal. % 21.42/21.67 apply zenon_H81. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L73_ *) % 21.42/21.67 assert (zenon_L74_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hf0 zenon_H10c zenon_H10d. % 21.42/21.67 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hf0. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H10c. % 21.42/21.67 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 21.42/21.67 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H10f. apply refl_equal. % 21.42/21.67 apply zenon_H10e. apply sym_equal. exact zenon_H10d. % 21.42/21.67 (* end of lemma zenon_L74_ *) % 21.42/21.67 assert (zenon_L75_ : ((op (e2) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H110 zenon_Hfe zenon_H111. % 21.42/21.67 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H112 | zenon_intro zenon_H108 ]. % 21.42/21.67 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H111. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H112. % 21.42/21.67 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.42/21.67 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H113. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H110. % 21.42/21.67 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 21.42/21.67 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H108. apply refl_equal. % 21.42/21.67 apply zenon_H114. apply sym_equal. exact zenon_Hfe. % 21.42/21.67 apply zenon_H108. apply refl_equal. % 21.42/21.67 apply zenon_H108. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L75_ *) % 21.42/21.67 assert (zenon_L76_ : (~((e3) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Ha2. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L76_ *) % 21.42/21.67 assert (zenon_L77_ : (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (e3)) = (e0)) -> False). % 21.42/21.67 do 0 intro. intros zenon_Ha0 zenon_Hb9 zenon_H115. % 21.42/21.67 cut (((op (e2) (e3)) = (e3)) = ((e0) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha0. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hb9. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H116 zenon_H115). % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L77_ *) % 21.42/21.67 assert (zenon_L78_ : (((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) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H117 zenon_H109 zenon_H9d zenon_H10c zenon_Hf0 zenon_H111 zenon_Hfe zenon_Ha0 zenon_H115. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.42/21.67 apply (zenon_L73_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.42/21.67 apply (zenon_L74_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.42/21.67 apply (zenon_L75_); trivial. % 21.42/21.67 apply (zenon_L77_); trivial. % 21.42/21.67 (* end of lemma zenon_L78_ *) % 21.42/21.67 assert (zenon_L79_ : ((op (e3) (e1)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hac zenon_H10c zenon_H11a. % 21.42/21.67 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_Had | zenon_intro zenon_Hae ]. % 21.42/21.67 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e1) (e1)) = (op (e3) (e1)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H11a. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Had. % 21.42/21.67 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 21.42/21.67 cut (((op (e3) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e1) (e1)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H11b. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hac. % 21.42/21.67 cut (((e3) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 21.42/21.67 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_Hae. apply refl_equal. % 21.42/21.67 apply zenon_H11c. apply sym_equal. exact zenon_H10c. % 21.42/21.67 apply zenon_Hae. apply refl_equal. % 21.42/21.67 apply zenon_Hae. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L79_ *) % 21.42/21.67 assert (zenon_L80_ : (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> False). % 21.42/21.67 do 0 intro. intros zenon_Ha0 zenon_Hbb zenon_H11d. % 21.42/21.67 cut (((op (e3) (e2)) = (e3)) = ((e0) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha0. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hbb. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H11e zenon_H11d). % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L80_ *) % 21.42/21.67 assert (zenon_L81_ : (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> False). % 21.42/21.67 do 0 intro. intros zenon_Hb6 zenon_Hc3 zenon_H11f. % 21.42/21.67 cut (((op (e3) (e3)) = (e3)) = ((e1) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hb6. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hc3. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H120 zenon_H11f). % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L81_ *) % 21.42/21.67 assert (zenon_L82_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (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) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e1)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H121 zenon_H115 zenon_Hfe zenon_H111 zenon_Hf0 zenon_H109 zenon_H117 zenon_H11a zenon_H10c zenon_H11d zenon_Ha0 zenon_Hb6 zenon_H11f. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.42/21.67 apply (zenon_L78_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.42/21.67 apply (zenon_L79_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.42/21.67 apply (zenon_L80_); trivial. % 21.42/21.67 apply (zenon_L81_); trivial. % 21.42/21.67 (* end of lemma zenon_L82_ *) % 21.42/21.67 assert (zenon_L83_ : ((op (e1) (e2)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H72 zenon_H76 zenon_H4e. % 21.42/21.67 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H4f | zenon_intro zenon_H50 ]. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e0)) = (op (e1) (e2)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H4e. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H4f. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e1) (e0)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H51. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H72. % 21.42/21.67 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H50. apply refl_equal. % 21.42/21.67 apply zenon_H124. apply sym_equal. exact zenon_H76. % 21.42/21.67 apply zenon_H50. apply refl_equal. % 21.42/21.67 apply zenon_H50. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L83_ *) % 21.42/21.67 assert (zenon_L84_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H125 zenon_H68 zenon_H1e zenon_H4e zenon_H72 zenon_H55 zenon_H87 zenon_H7e zenon_H77. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.42/21.67 apply (zenon_L20_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.42/21.67 apply (zenon_L83_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.42/21.67 apply (zenon_L35_); trivial. % 21.42/21.67 apply (zenon_L71_); trivial. % 21.42/21.67 (* end of lemma zenon_L84_ *) % 21.42/21.67 assert (zenon_L85_ : ((op (e3) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H11f zenon_H128 zenon_H129. % 21.42/21.67 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.42/21.67 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H129. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H12a. % 21.42/21.67 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.42/21.67 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H12c. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H11f. % 21.42/21.67 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 21.42/21.67 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H12b. apply refl_equal. % 21.42/21.67 apply zenon_H12d. apply sym_equal. exact zenon_H128. % 21.42/21.67 apply zenon_H12b. apply refl_equal. % 21.42/21.67 apply zenon_H12b. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L85_ *) % 21.42/21.67 assert (zenon_L86_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H12e zenon_H77 zenon_H87 zenon_H55 zenon_H72 zenon_H4e zenon_H1e zenon_H68 zenon_H125 zenon_He0 zenon_H48 zenon_H105 zenon_H104 zenon_H128 zenon_H129. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.42/21.67 apply (zenon_L84_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.42/21.67 apply (zenon_L57_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.42/21.67 apply (zenon_L72_); trivial. % 21.42/21.67 apply (zenon_L85_); trivial. % 21.42/21.67 (* end of lemma zenon_L86_ *) % 21.42/21.67 assert (zenon_L87_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H131 zenon_H72 zenon_H8a. % 21.42/21.67 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H131. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H72. % 21.42/21.67 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H50. apply refl_equal. % 21.42/21.67 apply zenon_H132. apply sym_equal. exact zenon_H8a. % 21.42/21.67 (* end of lemma zenon_L87_ *) % 21.42/21.67 assert (zenon_L88_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H87 zenon_H131 zenon_H8a. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 21.42/21.67 apply (zenon_L87_); trivial. % 21.42/21.67 (* end of lemma zenon_L88_ *) % 21.42/21.67 assert (zenon_L89_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H73 zenon_Hfe zenon_H133. % 21.42/21.67 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H73. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hfe. % 21.42/21.67 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 21.42/21.67 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H135. apply refl_equal. % 21.42/21.67 apply zenon_H134. apply sym_equal. exact zenon_H133. % 21.42/21.67 (* end of lemma zenon_L89_ *) % 21.42/21.67 assert (zenon_L90_ : (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> False). % 21.42/21.67 do 0 intro. intros zenon_Ha0 zenon_Ha5 zenon_H136. % 21.42/21.67 cut (((op (e1) (e3)) = (e3)) = ((e0) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha0. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Ha5. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H137 zenon_H136). % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L90_ *) % 21.42/21.67 assert (zenon_L91_ : (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> False). % 21.42/21.67 do 0 intro. intros zenon_Ha9 zenon_H9d zenon_H102. % 21.42/21.67 cut (((op (e3) (e0)) = (e3)) = ((e2) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha9. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H9d. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H103 zenon_H102). % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L91_ *) % 21.42/21.67 assert (zenon_L92_ : (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> False). % 21.42/21.67 do 0 intro. intros zenon_Ha9 zenon_H9e zenon_Hf6. % 21.42/21.67 cut (((op (e0) (e3)) = (e3)) = ((e2) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha9. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H9e. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H138]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H138 zenon_Hf6). % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L92_ *) % 21.42/21.67 assert (zenon_L93_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (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) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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) (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)))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H139 zenon_H6f zenon_H94 zenon_Hbc zenon_H5d zenon_H7d zenon_H82 zenon_H33 zenon_Hcc zenon_H13a zenon_He4 zenon_H13b zenon_He2 zenon_H3d zenon_He3 zenon_H13c zenon_H111 zenon_H87 zenon_H131 zenon_H12e zenon_H77 zenon_H55 zenon_H72 zenon_H4e zenon_H1e zenon_H68 zenon_H125 zenon_H48 zenon_H104 zenon_H129 zenon_H13d zenon_H13e zenon_H121 zenon_Hf0 zenon_H109 zenon_H117 zenon_H11a zenon_Hb6 zenon_H6d zenon_Heb zenon_H100 zenon_H40 zenon_Hec zenon_H13f zenon_Hfa zenon_H3c zenon_Hf5 zenon_H140 zenon_H141 zenon_H73 zenon_Ha0 zenon_Hb2 zenon_Ha9. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.42/21.67 apply (zenon_L20_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.42/21.67 apply (zenon_L21_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.42/21.67 apply (zenon_L22_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.42/21.67 apply (zenon_L20_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.42/21.67 apply (zenon_L24_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.42/21.67 apply (zenon_L52_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.42/21.67 apply (zenon_L41_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.42/21.67 apply (zenon_L58_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.42/21.67 apply (zenon_L41_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.42/21.67 apply (zenon_L46_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.42/21.67 apply (zenon_L60_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.42/21.67 exact (zenon_He3 zenon_He7). % 21.42/21.67 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.42/21.67 apply (zenon_L64_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.42/21.67 apply (zenon_L65_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.42/21.67 exact (zenon_He3 zenon_He7). % 21.42/21.67 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.42/21.67 apply (zenon_L54_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.42/21.67 apply (zenon_L66_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.42/21.67 apply (zenon_L67_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.42/21.67 apply (zenon_L54_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.42/21.67 exact (zenon_H13d zenon_H14c). % 21.42/21.67 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.42/21.67 apply (zenon_L68_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.42/21.67 apply (zenon_L64_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.42/21.67 exact (zenon_H13d zenon_H14c). % 21.42/21.67 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.42/21.67 apply (zenon_L70_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.42/21.67 apply (zenon_L56_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.42/21.67 apply (zenon_L71_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.42/21.67 apply (zenon_L57_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.42/21.67 apply (zenon_L72_); trivial. % 21.42/21.67 apply (zenon_L82_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H14c | zenon_intro zenon_H151 ]. % 21.42/21.67 exact (zenon_H13d zenon_H14c). % 21.42/21.67 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H105 | zenon_intro zenon_H152 ]. % 21.42/21.67 apply (zenon_L86_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H8a | zenon_intro zenon_H110 ]. % 21.42/21.67 apply (zenon_L88_); trivial. % 21.42/21.67 apply (zenon_L75_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.42/21.67 apply (zenon_L89_); trivial. % 21.42/21.67 apply (zenon_L90_); trivial. % 21.42/21.67 apply (zenon_L91_); trivial. % 21.42/21.67 apply (zenon_L92_); trivial. % 21.42/21.67 (* end of lemma zenon_L93_ *) % 21.42/21.67 assert (zenon_L94_ : (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H77 zenon_H66 zenon_H153. % 21.42/21.67 cut (((op (e0) (e2)) = (e2)) = ((e1) = (e2))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H77. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H66. % 21.42/21.67 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.67 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H154 zenon_H153). % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L94_ *) % 21.42/21.67 assert (zenon_L95_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H153 zenon_Hfe zenon_Hb6. % 21.42/21.67 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.42/21.67 cut (((e3) = (e3)) = ((e1) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hb6. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Ha1. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e0) (e2)) = (e1)) = ((e3) = (e1))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hb7. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H153. % 21.42/21.67 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.67 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_Hff zenon_Hfe). % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L95_ *) % 21.42/21.67 assert (zenon_L96_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H13a zenon_H1e zenon_H48 zenon_H77 zenon_H6d zenon_H40 zenon_He4 zenon_H68 zenon_He3 zenon_Ha0 zenon_He2 zenon_Hb6 zenon_H153 zenon_Ha9 zenon_Hf6. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.42/21.67 apply (zenon_L41_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.42/21.67 apply (zenon_L58_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.42/21.67 apply (zenon_L95_); trivial. % 21.42/21.67 apply (zenon_L92_); trivial. % 21.42/21.67 (* end of lemma zenon_L96_ *) % 21.42/21.67 assert (zenon_L97_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H139 zenon_H6f zenon_H13a zenon_H1e zenon_H48 zenon_H77 zenon_H6d zenon_H40 zenon_He4 zenon_H68 zenon_He3 zenon_Ha0 zenon_He2 zenon_Hb6 zenon_H153 zenon_Ha9. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.42/21.67 apply (zenon_L20_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.42/21.67 apply (zenon_L21_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.42/21.67 apply (zenon_L94_); trivial. % 21.42/21.67 apply (zenon_L96_); trivial. % 21.42/21.67 (* end of lemma zenon_L97_ *) % 21.42/21.67 assert (zenon_L98_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H155 zenon_Hf6 zenon_H77. % 21.42/21.67 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.42/21.67 cut (((e2) = (e2)) = ((e1) = (e2))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H77. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H69. % 21.42/21.67 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.67 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e0) (e3)) = (e1)) = ((e2) = (e1))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H78. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H155. % 21.42/21.67 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.67 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H138]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_H138 zenon_Hf6). % 21.42/21.67 apply zenon_H4a. apply refl_equal. % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 apply zenon_H6a. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L98_ *) % 21.42/21.67 assert (zenon_L99_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H139 zenon_H68 zenon_H1e zenon_H6f zenon_H6d zenon_H73 zenon_H72 zenon_H155 zenon_H77. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.42/21.67 apply (zenon_L20_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.42/21.67 apply (zenon_L21_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.42/21.67 apply (zenon_L22_); trivial. % 21.42/21.67 apply (zenon_L98_); trivial. % 21.42/21.67 (* end of lemma zenon_L99_ *) % 21.42/21.67 assert (zenon_L100_ : ((op (e1) (e2)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H72 zenon_Hef zenon_H156. % 21.42/21.67 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H4f | zenon_intro zenon_H50 ]. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e1)) = (op (e1) (e2)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H156. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H4f. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H157]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e1) (e1)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H157. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H72. % 21.42/21.67 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H50. apply refl_equal. % 21.42/21.67 apply zenon_Hf2. apply sym_equal. exact zenon_Hef. % 21.42/21.67 apply zenon_H50. apply refl_equal. % 21.42/21.67 apply zenon_H50. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L100_ *) % 21.42/21.67 assert (zenon_L101_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H158 zenon_He3 zenon_H40 zenon_H156 zenon_H72 zenon_H159. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 21.42/21.67 exact (zenon_He3 zenon_He7). % 21.42/21.67 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 21.42/21.67 exact (zenon_H40 zenon_H3f). % 21.42/21.67 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 21.42/21.67 apply (zenon_L100_); trivial. % 21.42/21.67 exact (zenon_H159 zenon_H10c). % 21.42/21.67 (* end of lemma zenon_L101_ *) % 21.42/21.67 assert (zenon_L102_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H3e zenon_He3 zenon_H156 zenon_H72 zenon_H159 zenon_H158. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 21.42/21.67 apply (zenon_L101_); trivial. % 21.42/21.67 apply (zenon_L101_); trivial. % 21.42/21.67 (* end of lemma zenon_L102_ *) % 21.42/21.67 assert (zenon_L103_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (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)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (((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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (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 (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 (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H15c zenon_H158 zenon_H156 zenon_H3e zenon_H48 zenon_H1e zenon_H139 zenon_H77 zenon_H3c zenon_Hcc zenon_Hbc zenon_Hb6 zenon_Hb2 zenon_Ha9 zenon_Ha0 zenon_H94 zenon_H55 zenon_H82 zenon_H7d zenon_H5d zenon_H4e zenon_H33 zenon_H13a zenon_H13b zenon_H13c zenon_H13d zenon_H140 zenon_H100 zenon_H12e zenon_H117 zenon_H111 zenon_H109 zenon_H11a zenon_H121 zenon_H104 zenon_H13e zenon_H131 zenon_H125 zenon_H87 zenon_H129 zenon_H13f zenon_H141 zenon_Hf0 zenon_Hf5 zenon_Hfa zenon_Heb zenon_He3 zenon_He4 zenon_H40 zenon_He2 zenon_H72 zenon_H73 zenon_H6d zenon_H6f zenon_H68 zenon_H15d. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.42/21.67 apply (zenon_L13_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.42/21.67 apply (zenon_L93_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.42/21.67 apply (zenon_L97_); trivial. % 21.42/21.67 apply (zenon_L99_); trivial. % 21.42/21.67 apply (zenon_L102_); trivial. % 21.42/21.67 (* end of lemma zenon_L103_ *) % 21.42/21.67 assert (zenon_L104_ : ((op (e3) (e2)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H160 zenon_H102 zenon_Hbc. % 21.42/21.67 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 21.42/21.67 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e0)) = (op (e3) (e2)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hbc. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hbd. % 21.42/21.67 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.42/21.67 cut (((op (e3) (e2)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 21.42/21.67 congruence. % 21.42/21.67 cut (((op (e3) (e2)) = (e2)) = ((op (e3) (e2)) = (op (e3) (e0)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Hbf. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_H160. % 21.42/21.67 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 21.42/21.67 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_Hbe. apply refl_equal. % 21.42/21.67 apply zenon_H161. apply sym_equal. exact zenon_H102. % 21.42/21.67 apply zenon_Hbe. apply refl_equal. % 21.42/21.67 apply zenon_Hbe. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L104_ *) % 21.42/21.67 assert (zenon_L105_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H125 zenon_H68 zenon_H1e zenon_H77 zenon_H3c zenon_H94 zenon_H93 zenon_H160 zenon_Hbc. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.42/21.67 apply (zenon_L20_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.42/21.67 apply (zenon_L24_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.42/21.67 apply (zenon_L38_); trivial. % 21.42/21.67 apply (zenon_L104_); trivial. % 21.42/21.67 (* end of lemma zenon_L105_ *) % 21.42/21.67 assert (zenon_L106_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((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) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H99 zenon_H125 zenon_H68 zenon_H1e zenon_H77 zenon_H3c zenon_H94 zenon_Hbc. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.42/21.67 apply (zenon_L105_); trivial. % 21.42/21.67 (* end of lemma zenon_L106_ *) % 21.42/21.67 assert (zenon_L107_ : (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> False). % 21.42/21.67 do 0 intro. intros zenon_Ha0 zenon_Hac zenon_He0. % 21.42/21.67 cut (((op (e3) (e1)) = (e3)) = ((e0) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha0. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hac. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.67 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 21.42/21.67 congruence. % 21.42/21.67 exact (zenon_He1 zenon_He0). % 21.42/21.67 apply zenon_Ha2. apply refl_equal. % 21.42/21.67 (* end of lemma zenon_L107_ *) % 21.42/21.67 assert (zenon_L108_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 21.42/21.67 do 0 intro. intros zenon_H13b zenon_H24 zenon_He3 zenon_H162 zenon_H163 zenon_Hac zenon_H33 zenon_H1e zenon_H164 zenon_Ha0 zenon_Ha5. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.42/21.67 apply (zenon_L3_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.42/21.67 exact (zenon_He3 zenon_He7). % 21.42/21.67 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.42/21.67 apply (zenon_L7_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.42/21.67 apply (zenon_L107_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.42/21.67 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_H163. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Hf3. % 21.42/21.67 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 21.42/21.67 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.42/21.67 congruence. % 21.42/21.67 apply zenon_H50. apply refl_equal. % 21.42/21.67 apply zenon_H168. apply sym_equal. exact zenon_H11d. % 21.42/21.67 exact (zenon_H162 zenon_H167). % 21.42/21.67 apply (zenon_L90_); trivial. % 21.42/21.67 (* end of lemma zenon_L108_ *) % 21.42/21.67 assert (zenon_L109_ : (~((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)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((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 (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 (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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)) = (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (~((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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H2c zenon_H15d zenon_H6f zenon_H73 zenon_He2 zenon_He4 zenon_Heb zenon_Hfa zenon_Hf5 zenon_Hf0 zenon_H141 zenon_H13f zenon_H129 zenon_H131 zenon_H13e zenon_H104 zenon_H121 zenon_H11a zenon_H109 zenon_H111 zenon_H117 zenon_H12e zenon_H100 zenon_H140 zenon_H13d zenon_H13c zenon_H13a zenon_H4e zenon_H5d zenon_H7d zenon_H82 zenon_H55 zenon_Ha9 zenon_Hcc zenon_H139 zenon_H48 zenon_H156 zenon_H158 zenon_H77 zenon_H68 zenon_H125 zenon_H13b zenon_H33 zenon_H163 zenon_H162 zenon_H164 zenon_H24 zenon_Hbc zenon_H94 zenon_H3c zenon_Hb6 zenon_H1e zenon_Ha0 zenon_Hb2. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.42/21.67 apply (zenon_L2_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.42/21.67 apply (zenon_L4_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.42/21.67 apply (zenon_L6_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.42/21.67 apply (zenon_L8_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.42/21.67 apply (zenon_L9_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.42/21.67 apply (zenon_L11_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.42/21.67 apply (zenon_L16_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.42/21.67 apply (zenon_L18_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.42/21.67 apply (zenon_L19_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 21.42/21.67 exact (zenon_H7a zenon_H3c). % 21.42/21.67 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 21.42/21.67 apply (zenon_L103_); trivial. % 21.42/21.67 apply (zenon_L103_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.42/21.67 apply (zenon_L37_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.42/21.67 apply (zenon_L106_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.42/21.67 apply (zenon_L40_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.42/21.67 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.42/21.67 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 21.42/21.67 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.42/21.67 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 21.42/21.67 exact (zenon_H7a zenon_H3c). % 21.42/21.67 apply (zenon_L108_); trivial. % 21.42/21.67 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.42/21.67 apply (zenon_L49_); trivial. % 21.42/21.67 apply (zenon_L51_); trivial. % 21.42/21.67 (* end of lemma zenon_L109_ *) % 21.42/21.67 assert (zenon_L110_ : ((op (e0) (e1)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 21.42/21.67 do 0 intro. intros zenon_H6e zenon_Hdb zenon_Ha9. % 21.42/21.67 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.42/21.67 cut (((e3) = (e3)) = ((e2) = (e3))). % 21.42/21.67 intro zenon_D_pnotp. % 21.42/21.67 apply zenon_Ha9. % 21.42/21.67 rewrite <- zenon_D_pnotp. % 21.42/21.67 exact zenon_Ha1. % 21.42/21.67 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.68 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 21.42/21.68 congruence. % 21.42/21.68 cut (((op (e0) (e1)) = (e2)) = ((e3) = (e2))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_Haa. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H6e. % 21.42/21.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.42/21.68 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 21.42/21.68 congruence. % 21.42/21.68 exact (zenon_Hdc zenon_Hdb). % 21.42/21.68 apply zenon_H6a. apply refl_equal. % 21.42/21.68 apply zenon_Ha2. apply refl_equal. % 21.42/21.68 apply zenon_Ha2. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L110_ *) % 21.42/21.68 assert (zenon_L111_ : (~((e0) = (e1))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> False). % 21.42/21.68 do 0 intro. intros zenon_H48 zenon_H53 zenon_Hdd. % 21.42/21.68 cut (((op (e2) (e1)) = (e1)) = ((e0) = (e1))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H48. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H53. % 21.42/21.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.68 cut (((op (e2) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 21.42/21.68 congruence. % 21.42/21.68 exact (zenon_Hde zenon_Hdd). % 21.42/21.68 apply zenon_H4a. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L111_ *) % 21.42/21.68 assert (zenon_L112_ : (((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))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H16a zenon_Ha9 zenon_Ha8 zenon_H53 zenon_H77 zenon_H8b zenon_H16b. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.42/21.68 apply (zenon_L43_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.42/21.68 apply (zenon_L56_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.42/21.68 exact (zenon_H8b zenon_H8a). % 21.42/21.68 exact (zenon_H16b zenon_H93). % 21.42/21.68 (* end of lemma zenon_L112_ *) % 21.42/21.68 assert (zenon_L113_ : ((op (e2) (e1)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H53 zenon_H10d zenon_Hb6. % 21.42/21.68 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.42/21.68 cut (((e3) = (e3)) = ((e1) = (e3))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_Hb6. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_Ha1. % 21.42/21.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.68 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 21.42/21.68 congruence. % 21.42/21.68 cut (((op (e2) (e1)) = (e1)) = ((e3) = (e1))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_Hb7. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H53. % 21.42/21.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.68 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 21.42/21.68 congruence. % 21.42/21.68 exact (zenon_H16e zenon_H10d). % 21.42/21.68 apply zenon_H4a. apply refl_equal. % 21.42/21.68 apply zenon_Ha2. apply refl_equal. % 21.42/21.68 apply zenon_Ha2. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L113_ *) % 21.42/21.68 assert (zenon_L114_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H141 zenon_H1e zenon_H2c zenon_H48 zenon_H13d zenon_H117 zenon_H16b zenon_H8b zenon_H77 zenon_Ha9 zenon_H16a zenon_Hb6 zenon_H53 zenon_H111 zenon_Hfe zenon_Ha0. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.42/21.68 apply (zenon_L5_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.42/21.68 apply (zenon_L111_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.42/21.68 exact (zenon_H13d zenon_H14c). % 21.42/21.68 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.42/21.68 apply (zenon_L112_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.42/21.68 apply (zenon_L113_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.42/21.68 apply (zenon_L75_); trivial. % 21.42/21.68 apply (zenon_L77_); trivial. % 21.42/21.68 (* end of lemma zenon_L114_ *) % 21.42/21.68 assert (zenon_L115_ : (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> False). % 21.42/21.68 do 0 intro. intros zenon_Hb6 zenon_H9e zenon_H155. % 21.42/21.68 cut (((op (e0) (e3)) = (e3)) = ((e1) = (e3))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_Hb6. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H9e. % 21.42/21.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.68 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H16f]. % 21.42/21.68 congruence. % 21.42/21.68 exact (zenon_H16f zenon_H155). % 21.42/21.68 apply zenon_Ha2. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L115_ *) % 21.42/21.68 assert (zenon_L116_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H25 zenon_Ha6 zenon_Ha0. % 21.42/21.68 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.42/21.68 cut (((e3) = (e3)) = ((e0) = (e3))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_Ha0. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_Ha1. % 21.42/21.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.68 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 21.42/21.68 congruence. % 21.42/21.68 cut (((op (e1) (e0)) = (e0)) = ((e3) = (e0))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_Ha3. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H25. % 21.42/21.68 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.42/21.68 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb8]. % 21.42/21.68 congruence. % 21.42/21.68 exact (zenon_Hb8 zenon_Ha6). % 21.42/21.68 apply zenon_H46. apply refl_equal. % 21.42/21.68 apply zenon_Ha2. apply refl_equal. % 21.42/21.68 apply zenon_Ha2. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L116_ *) % 21.42/21.68 assert (zenon_L117_ : (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> False). % 21.42/21.68 do 0 intro. intros zenon_H48 zenon_H4d zenon_Hf3. % 21.42/21.68 cut (((op (e1) (e2)) = (e1)) = ((e0) = (e1))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H48. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H4d. % 21.42/21.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.68 cut (((op (e1) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 21.42/21.68 congruence. % 21.42/21.68 exact (zenon_Hf4 zenon_Hf3). % 21.42/21.68 apply zenon_H4a. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L117_ *) % 21.42/21.68 assert (zenon_L118_ : ((op (e2) (e1)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H53 zenon_H3f zenon_Hf0. % 21.42/21.68 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ]. % 21.42/21.68 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e1) (e1)) = (op (e2) (e1)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_Hf0. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H56. % 21.42/21.68 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 21.42/21.68 cut (((op (e2) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf1]. % 21.42/21.68 congruence. % 21.42/21.68 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (e1)) = (op (e1) (e1)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_Hf1. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H53. % 21.42/21.68 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H170]. % 21.42/21.68 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 21.42/21.68 congruence. % 21.42/21.68 apply zenon_H57. apply refl_equal. % 21.42/21.68 apply zenon_H170. apply sym_equal. exact zenon_H3f. % 21.42/21.68 apply zenon_H57. apply refl_equal. % 21.42/21.68 apply zenon_H57. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L118_ *) % 21.42/21.68 assert (zenon_L119_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 21.42/21.68 do 0 intro. intros zenon_H11a zenon_Hef zenon_H171. % 21.42/21.68 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H11a. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_Hef. % 21.42/21.68 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 21.42/21.68 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 21.42/21.68 congruence. % 21.42/21.68 apply zenon_H10f. apply refl_equal. % 21.42/21.68 apply zenon_H172. apply sym_equal. exact zenon_H171. % 21.42/21.68 (* end of lemma zenon_L119_ *) % 21.42/21.68 assert (zenon_L120_ : ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H10c zenon_Hdb zenon_H173. % 21.42/21.68 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H174 | zenon_intro zenon_H10f ]. % 21.42/21.68 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H173. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H174. % 21.42/21.68 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 21.42/21.68 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H175]. % 21.42/21.68 congruence. % 21.42/21.68 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H175. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H10c. % 21.42/21.68 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 21.42/21.68 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 21.42/21.68 congruence. % 21.42/21.68 apply zenon_H10f. apply refl_equal. % 21.42/21.68 apply zenon_H176. apply sym_equal. exact zenon_Hdb. % 21.42/21.68 apply zenon_H10f. apply refl_equal. % 21.42/21.68 apply zenon_H10f. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L120_ *) % 21.42/21.68 assert (zenon_L121_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H158 zenon_He3 zenon_Hf0 zenon_H53 zenon_H171 zenon_H11a zenon_Hdb zenon_H173. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 21.42/21.68 exact (zenon_He3 zenon_He7). % 21.42/21.68 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 21.42/21.68 apply (zenon_L118_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 21.42/21.68 apply (zenon_L119_); trivial. % 21.42/21.68 apply (zenon_L120_); trivial. % 21.42/21.68 (* end of lemma zenon_L121_ *) % 21.42/21.68 assert (zenon_L122_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 21.42/21.68 do 0 intro. intros zenon_H177 zenon_H66 zenon_H160. % 21.42/21.68 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H177. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H66. % 21.42/21.68 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 21.42/21.68 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 21.42/21.68 congruence. % 21.42/21.68 apply zenon_H135. apply refl_equal. % 21.42/21.68 apply zenon_H178. apply sym_equal. exact zenon_H160. % 21.42/21.68 (* end of lemma zenon_L122_ *) % 21.42/21.68 assert (zenon_L123_ : ((op (e3) (e0)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H9d zenon_Ha6 zenon_H179. % 21.42/21.68 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H10a | zenon_intro zenon_H81 ]. % 21.42/21.68 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e1) (e0)) = (op (e3) (e0)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H179. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H10a. % 21.42/21.68 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 21.42/21.68 cut (((op (e3) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 21.42/21.68 congruence. % 21.42/21.68 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e1) (e0)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H17a. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H9d. % 21.42/21.68 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 21.42/21.68 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 21.42/21.68 congruence. % 21.42/21.68 apply zenon_H81. apply refl_equal. % 21.42/21.68 apply zenon_Ha7. apply sym_equal. exact zenon_Ha6. % 21.42/21.68 apply zenon_H81. apply refl_equal. % 21.42/21.68 apply zenon_H81. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L123_ *) % 21.42/21.68 assert (zenon_L124_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H4d zenon_H133 zenon_Hb6. % 21.42/21.68 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.42/21.68 cut (((e3) = (e3)) = ((e1) = (e3))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_Hb6. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_Ha1. % 21.42/21.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.68 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 21.42/21.68 congruence. % 21.42/21.68 cut (((op (e1) (e2)) = (e1)) = ((e3) = (e1))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_Hb7. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H4d. % 21.42/21.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.42/21.68 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 21.42/21.68 congruence. % 21.42/21.68 exact (zenon_H17b zenon_H133). % 21.42/21.68 apply zenon_H4a. apply refl_equal. % 21.42/21.68 apply zenon_Ha2. apply refl_equal. % 21.42/21.68 apply zenon_Ha2. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L124_ *) % 21.42/21.68 assert (zenon_L125_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e0)) -> False). % 21.42/21.68 do 0 intro. intros zenon_H13c zenon_H179 zenon_H9d zenon_H173 zenon_Hdb zenon_Hb6 zenon_H4d zenon_Ha0 zenon_H136. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.42/21.68 apply (zenon_L123_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.42/21.68 apply (zenon_L120_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.42/21.68 apply (zenon_L124_); trivial. % 21.42/21.68 apply (zenon_L90_); trivial. % 21.42/21.68 (* end of lemma zenon_L125_ *) % 21.42/21.68 assert (zenon_L126_ : ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H17c zenon_H93 zenon_H129. % 21.42/21.68 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.42/21.68 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H129. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H12a. % 21.42/21.68 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.42/21.68 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 21.42/21.68 congruence. % 21.42/21.68 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H12c. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H17c. % 21.42/21.68 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17d]. % 21.42/21.68 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.42/21.68 congruence. % 21.42/21.68 apply zenon_H12b. apply refl_equal. % 21.42/21.68 apply zenon_H17d. apply sym_equal. exact zenon_H93. % 21.42/21.68 apply zenon_H12b. apply refl_equal. % 21.42/21.68 apply zenon_H12b. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L126_ *) % 21.42/21.68 assert (zenon_L127_ : (((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))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H16a zenon_H7b zenon_H53 zenon_H77 zenon_H8b zenon_H17c zenon_H129. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.42/21.68 exact (zenon_H7b zenon_H65). % 21.42/21.68 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.42/21.68 apply (zenon_L56_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.42/21.68 exact (zenon_H8b zenon_H8a). % 21.42/21.68 apply (zenon_L126_); trivial. % 21.42/21.68 (* end of lemma zenon_L127_ *) % 21.42/21.68 assert (zenon_L128_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 21.42/21.68 do 0 intro. intros zenon_H131 zenon_H4d zenon_H105. % 21.42/21.68 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H131. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H4d. % 21.42/21.68 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 21.42/21.68 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.42/21.68 congruence. % 21.42/21.68 apply zenon_H50. apply refl_equal. % 21.42/21.68 apply zenon_H17e. apply sym_equal. exact zenon_H105. % 21.42/21.68 (* end of lemma zenon_L128_ *) % 21.42/21.68 assert (zenon_L129_ : ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 21.42/21.68 do 0 intro. intros zenon_Hbb zenon_H110 zenon_H104. % 21.42/21.68 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 21.42/21.68 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e2) (e2)) = (op (e3) (e2)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H104. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_Hbd. % 21.42/21.68 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.42/21.68 cut (((op (e3) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 21.42/21.68 congruence. % 21.42/21.68 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e2) (e2)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H17f. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_Hbb. % 21.42/21.68 cut (((e3) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 21.42/21.68 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.42/21.68 congruence. % 21.42/21.68 apply zenon_Hbe. apply refl_equal. % 21.42/21.68 apply zenon_H180. apply sym_equal. exact zenon_H110. % 21.42/21.68 apply zenon_Hbe. apply refl_equal. % 21.42/21.68 apply zenon_Hbe. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L129_ *) % 21.42/21.68 assert (zenon_L130_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H13e zenon_H13d zenon_H4d zenon_H131 zenon_H8b zenon_Hbb zenon_H104. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H14c | zenon_intro zenon_H151 ]. % 21.42/21.68 exact (zenon_H13d zenon_H14c). % 21.42/21.68 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H105 | zenon_intro zenon_H152 ]. % 21.42/21.68 apply (zenon_L128_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H8a | zenon_intro zenon_H110 ]. % 21.42/21.68 exact (zenon_H8b zenon_H8a). % 21.42/21.68 apply (zenon_L129_); trivial. % 21.42/21.68 (* end of lemma zenon_L130_ *) % 21.42/21.68 assert (zenon_L131_ : ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (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))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H8f zenon_H131 zenon_H4d zenon_H104 zenon_Hbb zenon_H13e zenon_H77 zenon_H53 zenon_H8b zenon_H129 zenon_H17c zenon_H16a. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.42/21.68 apply (zenon_L127_); trivial. % 21.42/21.68 apply (zenon_L130_); trivial. % 21.42/21.68 (* end of lemma zenon_L131_ *) % 21.42/21.68 assert (zenon_L132_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H5a zenon_H131 zenon_H104 zenon_Hbb zenon_H13e zenon_H77 zenon_H8b zenon_H129 zenon_H17c zenon_H16a. % 21.42/21.68 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.42/21.68 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.42/21.68 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.42/21.68 apply (zenon_L131_); trivial. % 21.42/21.68 (* end of lemma zenon_L132_ *) % 21.42/21.68 assert (zenon_L133_ : (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> False). % 21.42/21.68 do 0 intro. intros zenon_Ha9 zenon_Hc3 zenon_H17c. % 21.42/21.68 cut (((op (e3) (e3)) = (e3)) = ((e2) = (e3))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_Ha9. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_Hc3. % 21.42/21.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.68 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 21.42/21.68 congruence. % 21.42/21.68 exact (zenon_H181 zenon_H17c). % 21.42/21.68 apply zenon_Ha2. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L133_ *) % 21.42/21.68 assert (zenon_L134_ : (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.42/21.68 do 0 intro. intros zenon_Hb6 zenon_H9d zenon_H7e. % 21.42/21.68 cut (((op (e3) (e0)) = (e3)) = ((e1) = (e3))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_Hb6. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H9d. % 21.42/21.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.42/21.68 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 21.42/21.68 congruence. % 21.42/21.68 exact (zenon_H182 zenon_H7e). % 21.42/21.68 apply zenon_Ha2. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L134_ *) % 21.42/21.68 assert (zenon_L135_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 21.42/21.68 do 0 intro. intros zenon_H82 zenon_H48 zenon_H1e zenon_H4e zenon_H4d zenon_H55 zenon_H53 zenon_Hb6 zenon_H9d. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.42/21.68 apply (zenon_L13_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.42/21.68 apply (zenon_L14_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.42/21.68 apply (zenon_L15_); trivial. % 21.42/21.68 apply (zenon_L134_); trivial. % 21.42/21.68 (* end of lemma zenon_L135_ *) % 21.42/21.68 assert (zenon_L136_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((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)) = (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (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 (e2) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((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 (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.42/21.68 do 0 intro. intros zenon_H13a zenon_H55 zenon_H4d zenon_H4e zenon_H82 zenon_H13b zenon_He2 zenon_H183 zenon_H7e zenon_H11a zenon_Hf0 zenon_He3 zenon_H158 zenon_H66 zenon_H177 zenon_H121 zenon_H173 zenon_H179 zenon_H13c zenon_H129 zenon_H13e zenon_H104 zenon_H131 zenon_H5a zenon_Hb2 zenon_Ha0 zenon_H111 zenon_H53 zenon_H16a zenon_Ha9 zenon_H77 zenon_H8b zenon_H16b zenon_H117 zenon_H13d zenon_H48 zenon_H2c zenon_H1e zenon_H141 zenon_Hb6 zenon_H155. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.42/21.68 apply (zenon_L41_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.42/21.68 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.42/21.68 apply (zenon_L41_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.42/21.68 apply (zenon_L116_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.42/21.68 exact (zenon_He3 zenon_He7). % 21.42/21.68 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.42/21.68 apply (zenon_L117_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.42/21.68 apply (zenon_L53_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.42/21.68 exact (zenon_He3 zenon_He7). % 21.42/21.68 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.42/21.68 apply (zenon_L111_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.42/21.68 apply (zenon_L71_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.42/21.68 apply (zenon_L121_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.42/21.68 apply (zenon_L122_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.42/21.68 apply (zenon_L125_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.42/21.68 apply (zenon_L107_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.42/21.68 apply (zenon_L132_); trivial. % 21.42/21.68 apply (zenon_L133_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.42/21.68 apply (zenon_L112_); trivial. % 21.42/21.68 apply (zenon_L135_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.42/21.68 apply (zenon_L114_); trivial. % 21.42/21.68 apply (zenon_L115_); trivial. % 21.42/21.68 (* end of lemma zenon_L136_ *) % 21.42/21.68 assert (zenon_L137_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (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) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (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)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (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 (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e2)) = (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 (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 (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((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 (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 (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H94 zenon_Hbc zenon_H24 zenon_H164 zenon_H162 zenon_H163 zenon_H33 zenon_H125 zenon_H156 zenon_Hcc zenon_H7d zenon_H5d zenon_H140 zenon_H100 zenon_H12e zenon_H109 zenon_H13f zenon_Hf5 zenon_Hfa zenon_Heb zenon_He4 zenon_H73 zenon_H6f zenon_H15d zenon_H139 zenon_H68 zenon_Hb6 zenon_H141 zenon_H1e zenon_H2c zenon_H48 zenon_H13d zenon_H117 zenon_H16b zenon_H8b zenon_Ha9 zenon_H16a zenon_H53 zenon_H111 zenon_Ha0 zenon_Hb2 zenon_H5a zenon_H131 zenon_H104 zenon_H13e zenon_H129 zenon_H13c zenon_H179 zenon_H173 zenon_H121 zenon_H177 zenon_H158 zenon_He3 zenon_Hf0 zenon_H11a zenon_H183 zenon_He2 zenon_H13b zenon_H82 zenon_H4e zenon_H4d zenon_H55 zenon_H13a zenon_H155 zenon_H77. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.42/21.68 apply (zenon_L13_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.42/21.68 apply (zenon_L109_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.42/21.68 apply (zenon_L15_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.42/21.68 apply (zenon_L20_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.42/21.68 apply (zenon_L41_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.42/21.68 apply (zenon_L110_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.42/21.68 apply (zenon_L114_); trivial. % 21.42/21.68 apply (zenon_L115_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.42/21.68 apply (zenon_L136_); trivial. % 21.42/21.68 apply (zenon_L98_); trivial. % 21.42/21.68 (* end of lemma zenon_L137_ *) % 21.42/21.68 assert (zenon_L138_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H5c zenon_H4d zenon_H186. % 21.42/21.68 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H5e | zenon_intro zenon_H5f ]. % 21.42/21.68 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e2)) = (op (e1) (e3)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H186. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H5e. % 21.42/21.68 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.42/21.68 cut (((op (e1) (e3)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 21.42/21.68 congruence. % 21.42/21.68 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e2)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H187. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H5c. % 21.42/21.68 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 21.42/21.68 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.42/21.68 congruence. % 21.42/21.68 apply zenon_H5f. apply refl_equal. % 21.42/21.68 apply zenon_H188. apply sym_equal. exact zenon_H4d. % 21.42/21.68 apply zenon_H5f. apply refl_equal. % 21.42/21.68 apply zenon_H5f. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L138_ *) % 21.42/21.68 assert (zenon_L139_ : (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 21.42/21.68 do 0 intro. intros zenon_H189 zenon_H53 zenon_H128. % 21.42/21.68 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (e1)) = (op (e2) (e3)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H189. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H53. % 21.42/21.68 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 21.42/21.68 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 21.42/21.68 congruence. % 21.42/21.68 apply zenon_H57. apply refl_equal. % 21.42/21.68 apply zenon_H12d. apply sym_equal. exact zenon_H128. % 21.42/21.68 (* end of lemma zenon_L139_ *) % 21.42/21.68 assert (zenon_L140_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H11f zenon_H7e zenon_H18a. % 21.42/21.68 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.42/21.68 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H18a. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H12a. % 21.42/21.68 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.42/21.68 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 21.42/21.68 congruence. % 21.42/21.68 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 21.42/21.68 intro zenon_D_pnotp. % 21.42/21.68 apply zenon_H18b. % 21.42/21.68 rewrite <- zenon_D_pnotp. % 21.42/21.68 exact zenon_H11f. % 21.42/21.68 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 21.42/21.68 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.42/21.68 congruence. % 21.42/21.68 apply zenon_H12b. apply refl_equal. % 21.42/21.68 apply zenon_H18c. apply sym_equal. exact zenon_H7e. % 21.42/21.68 apply zenon_H12b. apply refl_equal. % 21.42/21.68 apply zenon_H12b. apply refl_equal. % 21.42/21.68 (* end of lemma zenon_L140_ *) % 21.42/21.68 assert (zenon_L141_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((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)) = (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((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 (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (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) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H18d zenon_H77 zenon_H13a zenon_H55 zenon_H4e zenon_H82 zenon_H13b zenon_He2 zenon_H183 zenon_H11a zenon_Hf0 zenon_He3 zenon_H158 zenon_H177 zenon_H121 zenon_H173 zenon_H179 zenon_H13c zenon_H129 zenon_H13e zenon_H104 zenon_H131 zenon_H5a zenon_Hb2 zenon_Ha0 zenon_H111 zenon_H16a zenon_Ha9 zenon_H8b zenon_H16b zenon_H117 zenon_H13d zenon_H48 zenon_H2c zenon_H1e zenon_H141 zenon_Hb6 zenon_H68 zenon_H139 zenon_H15d zenon_H6f zenon_H73 zenon_He4 zenon_Heb zenon_Hfa zenon_Hf5 zenon_H13f zenon_H109 zenon_H12e zenon_H100 zenon_H140 zenon_H5d zenon_H7d zenon_Hcc zenon_H156 zenon_H125 zenon_H33 zenon_H163 zenon_H162 zenon_H164 zenon_H24 zenon_Hbc zenon_H94 zenon_H186 zenon_H4d zenon_H53 zenon_H189 zenon_H7e zenon_H18a. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.42/21.68 apply (zenon_L137_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.42/21.68 apply (zenon_L138_); trivial. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.42/21.68 apply (zenon_L139_); trivial. % 21.42/21.68 apply (zenon_L140_); trivial. % 21.42/21.68 (* end of lemma zenon_L141_ *) % 21.42/21.68 assert (zenon_L142_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((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)) = (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((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 (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (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) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.42/21.68 do 0 intro. intros zenon_H18d zenon_H77 zenon_H13a zenon_H55 zenon_H4e zenon_H82 zenon_H13b zenon_He2 zenon_H183 zenon_H11a zenon_Hf0 zenon_He3 zenon_H158 zenon_H177 zenon_H121 zenon_H173 zenon_H179 zenon_H13c zenon_H129 zenon_H13e zenon_H104 zenon_H131 zenon_H5a zenon_Hb2 zenon_Ha0 zenon_H111 zenon_H16a zenon_Ha9 zenon_H8b zenon_H16b zenon_H117 zenon_H13d zenon_H48 zenon_H2c zenon_H1e zenon_H141 zenon_Hb6 zenon_H68 zenon_H139 zenon_H15d zenon_H6f zenon_H73 zenon_He4 zenon_Heb zenon_Hfa zenon_Hf5 zenon_H13f zenon_H109 zenon_H12e zenon_H100 zenon_H140 zenon_H5d zenon_H7d zenon_Hcc zenon_H156 zenon_H125 zenon_H33 zenon_H163 zenon_H162 zenon_H164 zenon_H24 zenon_Hbc zenon_H94 zenon_H186 zenon_H4d zenon_H53 zenon_H189 zenon_H18a. % 21.42/21.68 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.51/21.69 apply (zenon_L13_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.51/21.69 apply (zenon_L14_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.51/21.69 apply (zenon_L15_); trivial. % 21.51/21.69 apply (zenon_L141_); trivial. % 21.51/21.69 (* end of lemma zenon_L142_ *) % 21.51/21.69 assert (zenon_L143_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H190 zenon_H53 zenon_H105. % 21.51/21.69 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (e1)) = (op (e2) (e2)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H190. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H53. % 21.51/21.69 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 21.51/21.69 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H57. apply refl_equal. % 21.51/21.69 apply zenon_H17e. apply sym_equal. exact zenon_H105. % 21.51/21.69 (* end of lemma zenon_L143_ *) % 21.51/21.69 assert (zenon_L144_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H13e zenon_H13d zenon_H53 zenon_H190 zenon_H8b zenon_H191. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H14c | zenon_intro zenon_H151 ]. % 21.51/21.69 exact (zenon_H13d zenon_H14c). % 21.51/21.69 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H105 | zenon_intro zenon_H152 ]. % 21.51/21.69 apply (zenon_L143_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H8a | zenon_intro zenon_H110 ]. % 21.51/21.69 exact (zenon_H8b zenon_H8a). % 21.51/21.69 exact (zenon_H191 zenon_H110). % 21.51/21.69 (* end of lemma zenon_L144_ *) % 21.51/21.69 assert (zenon_L145_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (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) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (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 (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (((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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (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 (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 (e2) (e2)))) -> (((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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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) (e2)) = (e2))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H92 zenon_H190 zenon_H48 zenon_H1e zenon_H4e zenon_H4d zenon_H55 zenon_H53 zenon_H18d zenon_H18a zenon_H189 zenon_H186 zenon_H164 zenon_H162 zenon_H163 zenon_H158 zenon_H156 zenon_H139 zenon_H77 zenon_Hcc zenon_Hbc zenon_Hb6 zenon_Hb2 zenon_Ha9 zenon_Ha0 zenon_H94 zenon_H82 zenon_H7d zenon_H13a zenon_H13b zenon_H13c zenon_H13d zenon_H140 zenon_H100 zenon_H12e zenon_H117 zenon_H111 zenon_H109 zenon_H11a zenon_H121 zenon_H104 zenon_H13e zenon_H131 zenon_H125 zenon_H129 zenon_H13f zenon_H141 zenon_Hf0 zenon_Hf5 zenon_Hfa zenon_Heb zenon_He4 zenon_He2 zenon_H73 zenon_H6f zenon_H68 zenon_H15d zenon_H5d zenon_H33 zenon_H2c zenon_H24 zenon_He3 zenon_H173 zenon_H177 zenon_H5a zenon_H179 zenon_H183 zenon_H16a zenon_H8b. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.51/21.69 apply (zenon_L142_); trivial. % 21.51/21.69 apply (zenon_L144_); trivial. % 21.51/21.69 (* end of lemma zenon_L145_ *) % 21.51/21.69 assert (zenon_L146_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H192 zenon_H3d zenon_H7f. % 21.51/21.69 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H192. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H3d. % 21.51/21.69 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 21.51/21.69 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H193. apply refl_equal. % 21.51/21.69 apply zenon_H80. apply sym_equal. exact zenon_H7f. % 21.51/21.69 (* end of lemma zenon_L146_ *) % 21.51/21.69 assert (zenon_L147_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H2a zenon_H6e zenon_H68. % 21.51/21.69 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.51/21.69 cut (((e2) = (e2)) = ((e0) = (e2))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H68. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H69. % 21.51/21.69 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.51/21.69 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e0) (e1)) = (e0)) = ((e2) = (e0))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H6b. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H2a. % 21.51/21.69 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.51/21.69 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_H194 zenon_H6e). % 21.51/21.69 apply zenon_H46. apply refl_equal. % 21.51/21.69 apply zenon_H6a. apply refl_equal. % 21.51/21.69 apply zenon_H6a. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L147_ *) % 21.51/21.69 assert (zenon_L148_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H111 zenon_H153 zenon_H105. % 21.51/21.69 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H111. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H153. % 21.51/21.69 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 21.51/21.69 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H135. apply refl_equal. % 21.51/21.69 apply zenon_H17e. apply sym_equal. exact zenon_H105. % 21.51/21.69 (* end of lemma zenon_L148_ *) % 21.51/21.69 assert (zenon_L149_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H195 zenon_H5c zenon_H128. % 21.51/21.69 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H195. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H5c. % 21.51/21.69 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 21.51/21.69 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H5f. apply refl_equal. % 21.51/21.69 apply zenon_H12d. apply sym_equal. exact zenon_H128. % 21.51/21.69 (* end of lemma zenon_L149_ *) % 21.51/21.69 assert (zenon_L150_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H13f zenon_H65 zenon_H77 zenon_Hdd zenon_H48 zenon_H153 zenon_H111 zenon_H195 zenon_H5c. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.51/21.69 apply (zenon_L30_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.51/21.69 apply (zenon_L111_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.51/21.69 apply (zenon_L148_); trivial. % 21.51/21.69 apply (zenon_L149_); trivial. % 21.51/21.69 (* end of lemma zenon_L150_ *) % 21.51/21.69 assert (zenon_L151_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H54 zenon_Ha8 zenon_Hb6. % 21.51/21.69 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.51/21.69 cut (((e3) = (e3)) = ((e1) = (e3))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Hb6. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Ha1. % 21.51/21.69 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.51/21.69 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e2) (e0)) = (e1)) = ((e3) = (e1))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Hb7. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H54. % 21.51/21.69 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.51/21.69 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_Hab zenon_Ha8). % 21.51/21.69 apply zenon_H4a. apply refl_equal. % 21.51/21.69 apply zenon_Ha2. apply refl_equal. % 21.51/21.69 apply zenon_Ha2. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L151_ *) % 21.51/21.69 assert (zenon_L152_ : ((op (e2) (e1)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 21.51/21.69 do 0 intro. intros zenon_Hdd zenon_H10d zenon_Ha0. % 21.51/21.69 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.51/21.69 cut (((e3) = (e3)) = ((e0) = (e3))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Ha0. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Ha1. % 21.51/21.69 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.51/21.69 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e2) (e1)) = (e0)) = ((e3) = (e0))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Ha3. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Hdd. % 21.51/21.69 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.51/21.69 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_H16e zenon_H10d). % 21.51/21.69 apply zenon_H46. apply refl_equal. % 21.51/21.69 apply zenon_Ha2. apply refl_equal. % 21.51/21.69 apply zenon_Ha2. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L152_ *) % 21.51/21.69 assert (zenon_L153_ : (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> False). % 21.51/21.69 do 0 intro. intros zenon_Ha9 zenon_H110 zenon_H8a. % 21.51/21.69 cut (((op (e2) (e2)) = (e3)) = ((e2) = (e3))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Ha9. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H110. % 21.51/21.69 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.51/21.69 cut (((op (e2) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_H8b zenon_H8a). % 21.51/21.69 apply zenon_Ha2. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L153_ *) % 21.51/21.69 assert (zenon_L154_ : ((op (e2) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_Hb9 zenon_H9e zenon_H196. % 21.51/21.69 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 21.51/21.69 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H196. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H95. % 21.51/21.69 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.51/21.69 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H197. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Hb9. % 21.51/21.69 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 21.51/21.69 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H96. apply refl_equal. % 21.51/21.69 apply zenon_H198. apply sym_equal. exact zenon_H9e. % 21.51/21.69 apply zenon_H96. apply refl_equal. % 21.51/21.69 apply zenon_H96. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L154_ *) % 21.51/21.69 assert (zenon_L155_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha0 zenon_Hdd zenon_H8a zenon_Ha9 zenon_H9e zenon_H196. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.51/21.69 apply (zenon_L151_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.51/21.69 apply (zenon_L152_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.51/21.69 apply (zenon_L153_); trivial. % 21.51/21.69 apply (zenon_L154_); trivial. % 21.51/21.69 (* end of lemma zenon_L155_ *) % 21.51/21.69 assert (zenon_L156_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H38 zenon_H9e zenon_Ha0. % 21.51/21.69 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.51/21.69 cut (((e3) = (e3)) = ((e0) = (e3))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Ha0. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Ha1. % 21.51/21.69 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.51/21.69 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e0) (e3)) = (e0)) = ((e3) = (e0))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Ha3. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H38. % 21.51/21.69 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.51/21.69 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_H199 zenon_H9e). % 21.51/21.69 apply zenon_H46. apply refl_equal. % 21.51/21.69 apply zenon_Ha2. apply refl_equal. % 21.51/21.69 apply zenon_Ha2. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L156_ *) % 21.51/21.69 assert (zenon_L157_ : (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H48 zenon_H5c zenon_H136. % 21.51/21.69 cut (((op (e1) (e3)) = (e1)) = ((e0) = (e1))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H48. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H5c. % 21.51/21.69 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.51/21.69 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_H137 zenon_H136). % 21.51/21.69 apply zenon_H4a. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L157_ *) % 21.51/21.69 assert (zenon_L158_ : (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e0)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H68 zenon_H93 zenon_H115. % 21.51/21.69 cut (((op (e2) (e3)) = (e2)) = ((e0) = (e2))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H68. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H93. % 21.51/21.69 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.51/21.69 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_H116 zenon_H115). % 21.51/21.69 apply zenon_H6a. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L158_ *) % 21.51/21.69 assert (zenon_L159_ : (((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)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H19a zenon_Ha0 zenon_H9e zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H162. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.51/21.69 apply (zenon_L156_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.51/21.69 apply (zenon_L157_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.51/21.69 apply (zenon_L158_); trivial. % 21.51/21.69 exact (zenon_H162 zenon_H167). % 21.51/21.69 (* end of lemma zenon_L159_ *) % 21.51/21.69 assert (zenon_L160_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (((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))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (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) = (e1))) -> ((op (e3) (e1)) = (e1)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H13a zenon_H1e zenon_He2 zenon_H6e zenon_He3 zenon_H162 zenon_H68 zenon_H5c zenon_Ha0 zenon_H19a zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_H196 zenon_H13f zenon_H77 zenon_H153 zenon_H111 zenon_H195 zenon_H16a zenon_H48 zenon_H7f. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.51/21.69 apply (zenon_L41_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.51/21.69 apply (zenon_L110_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.51/21.69 apply (zenon_L95_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.51/21.69 apply (zenon_L147_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.51/21.69 exact (zenon_He3 zenon_He7). % 21.51/21.69 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.51/21.69 apply (zenon_L150_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.51/21.69 apply (zenon_L54_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.51/21.69 apply (zenon_L155_); trivial. % 21.51/21.69 apply (zenon_L159_); trivial. % 21.51/21.69 apply (zenon_L57_); trivial. % 21.51/21.69 (* end of lemma zenon_L160_ *) % 21.51/21.69 assert (zenon_L161_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H2a zenon_H1e zenon_H19d. % 21.51/21.69 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H19e | zenon_intro zenon_H193 ]. % 21.51/21.69 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (e0)) = (op (e0) (e1)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H19d. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H19e. % 21.51/21.69 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 21.51/21.69 cut (((op (e0) (e1)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e0)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H19f. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H2a. % 21.51/21.69 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 21.51/21.69 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H193. apply refl_equal. % 21.51/21.69 apply zenon_H1a0. apply sym_equal. exact zenon_H1e. % 21.51/21.69 apply zenon_H193. apply refl_equal. % 21.51/21.69 apply zenon_H193. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L161_ *) % 21.51/21.69 assert (zenon_L162_ : ((op (e1) (e2)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 21.51/21.69 do 0 intro. intros zenon_Hf3 zenon_H133 zenon_Ha0. % 21.51/21.69 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.51/21.69 cut (((e3) = (e3)) = ((e0) = (e3))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Ha0. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Ha1. % 21.51/21.69 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.51/21.69 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e1) (e2)) = (e0)) = ((e3) = (e0))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Ha3. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Hf3. % 21.51/21.69 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.51/21.69 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_H17b zenon_H133). % 21.51/21.69 apply zenon_H46. apply refl_equal. % 21.51/21.69 apply zenon_Ha2. apply refl_equal. % 21.51/21.69 apply zenon_Ha2. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L162_ *) % 21.51/21.69 assert (zenon_L163_ : ((op (e2) (e2)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H110 zenon_H10d zenon_H190. % 21.51/21.69 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H112 | zenon_intro zenon_H108 ]. % 21.51/21.69 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H190. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H112. % 21.51/21.69 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.51/21.69 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H1a1. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H110. % 21.51/21.69 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 21.51/21.69 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H108. apply refl_equal. % 21.51/21.69 apply zenon_H10e. apply sym_equal. exact zenon_H10d. % 21.51/21.69 apply zenon_H108. apply refl_equal. % 21.51/21.69 apply zenon_H108. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L163_ *) % 21.51/21.69 assert (zenon_L164_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Ha0 zenon_Hf3 zenon_H190 zenon_H10d zenon_H1a3. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.51/21.69 apply (zenon_L95_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.51/21.69 apply (zenon_L162_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.51/21.69 apply (zenon_L163_); trivial. % 21.51/21.69 exact (zenon_H1a3 zenon_Hbb). % 21.51/21.69 (* end of lemma zenon_L164_ *) % 21.51/21.69 assert (zenon_L165_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H38 zenon_Hf6 zenon_H68. % 21.51/21.69 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.51/21.69 cut (((e2) = (e2)) = ((e0) = (e2))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H68. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H69. % 21.51/21.69 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.51/21.69 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e0) (e3)) = (e0)) = ((e2) = (e0))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H6b. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H38. % 21.51/21.69 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.51/21.69 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H138]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_H138 zenon_Hf6). % 21.51/21.69 apply zenon_H46. apply refl_equal. % 21.51/21.69 apply zenon_H6a. apply refl_equal. % 21.51/21.69 apply zenon_H6a. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L165_ *) % 21.51/21.69 assert (zenon_L166_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H19a zenon_H68 zenon_Hf6 zenon_H5c zenon_H48 zenon_Hb9 zenon_Ha0 zenon_H162. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.51/21.69 apply (zenon_L165_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.51/21.69 apply (zenon_L157_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.51/21.69 apply (zenon_L77_); trivial. % 21.51/21.69 exact (zenon_H162 zenon_H167). % 21.51/21.69 (* end of lemma zenon_L166_ *) % 21.51/21.69 assert (zenon_L167_ : ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H93 zenon_Hf6 zenon_H196. % 21.51/21.69 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 21.51/21.69 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H196. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H95. % 21.51/21.69 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.51/21.69 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H197. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H93. % 21.51/21.69 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1a6]. % 21.51/21.69 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H96. apply refl_equal. % 21.51/21.69 apply zenon_H1a6. apply sym_equal. exact zenon_Hf6. % 21.51/21.69 apply zenon_H96. apply refl_equal. % 21.51/21.69 apply zenon_H96. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L167_ *) % 21.51/21.69 assert (zenon_L168_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H16a zenon_H195 zenon_H111 zenon_Hdd zenon_H77 zenon_H13f zenon_Hf0 zenon_Hef zenon_H162 zenon_Ha0 zenon_H48 zenon_H5c zenon_H68 zenon_H19a zenon_Ha9 zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Hf3 zenon_H190 zenon_H1a3 zenon_H54 zenon_H117 zenon_Hf6 zenon_H196. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.51/21.69 apply (zenon_L150_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.51/21.69 apply (zenon_L61_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.51/21.69 apply (zenon_L151_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.51/21.69 apply (zenon_L164_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.51/21.69 apply (zenon_L153_); trivial. % 21.51/21.69 apply (zenon_L166_); trivial. % 21.51/21.69 apply (zenon_L167_); trivial. % 21.51/21.69 (* end of lemma zenon_L168_ *) % 21.51/21.69 assert (zenon_L169_ : ((op (e3) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H7f zenon_H171 zenon_H77. % 21.51/21.69 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.51/21.69 cut (((e2) = (e2)) = ((e1) = (e2))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H77. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H69. % 21.51/21.69 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.51/21.69 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e3) (e1)) = (e1)) = ((e2) = (e1))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H78. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H7f. % 21.51/21.69 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.51/21.69 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_H1a7 zenon_H171). % 21.51/21.69 apply zenon_H4a. apply refl_equal. % 21.51/21.69 apply zenon_H6a. apply refl_equal. % 21.51/21.69 apply zenon_H6a. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L169_ *) % 21.51/21.69 assert (zenon_L170_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (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 (e0) (e2)) = (op (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))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H13b zenon_Ha6 zenon_H7f zenon_H1a8 zenon_He3 zenon_He2 zenon_H1e zenon_H13a zenon_H196 zenon_Hf6 zenon_H117 zenon_H54 zenon_H1a3 zenon_H190 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_Ha9 zenon_H19a zenon_Ha0 zenon_H162 zenon_Hf0 zenon_H13f zenon_H111 zenon_H195 zenon_H16a zenon_H68 zenon_H77 zenon_H19d zenon_H48 zenon_H5c. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.51/21.69 apply (zenon_L116_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.51/21.69 exact (zenon_He3 zenon_He7). % 21.51/21.69 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.51/21.69 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.51/21.69 apply (zenon_L161_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.51/21.69 exact (zenon_He3 zenon_He7). % 21.51/21.69 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.51/21.69 apply (zenon_L160_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.51/21.69 apply (zenon_L168_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.51/21.69 apply (zenon_L54_); trivial. % 21.51/21.69 apply (zenon_L169_); trivial. % 21.51/21.69 apply (zenon_L57_); trivial. % 21.51/21.69 apply (zenon_L157_); trivial. % 21.51/21.69 (* end of lemma zenon_L170_ *) % 21.51/21.69 assert (zenon_L171_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H25 zenon_H76 zenon_H68. % 21.51/21.69 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.51/21.69 cut (((e2) = (e2)) = ((e0) = (e2))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H68. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H69. % 21.51/21.69 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.51/21.69 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e1) (e0)) = (e0)) = ((e2) = (e0))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H6b. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H25. % 21.51/21.69 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.51/21.69 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_H79 zenon_H76). % 21.51/21.69 apply zenon_H46. apply refl_equal. % 21.51/21.69 apply zenon_H6a. apply refl_equal. % 21.51/21.69 apply zenon_H6a. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L171_ *) % 21.51/21.69 assert (zenon_L172_ : ((op (e2) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_Hb9 zenon_Ha5 zenon_H195. % 21.51/21.69 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 21.51/21.69 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H195. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H95. % 21.51/21.69 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.51/21.69 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H1ab. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Hb9. % 21.51/21.69 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 21.51/21.69 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H96. apply refl_equal. % 21.51/21.69 apply zenon_H1ac. apply sym_equal. exact zenon_Ha5. % 21.51/21.69 apply zenon_H96. apply refl_equal. % 21.51/21.69 apply zenon_H96. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L172_ *) % 21.51/21.69 assert (zenon_L173_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha0 zenon_Hdd zenon_H8a zenon_Ha9 zenon_Ha5 zenon_H195. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.51/21.69 apply (zenon_L151_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.51/21.69 apply (zenon_L152_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.51/21.69 apply (zenon_L153_); trivial. % 21.51/21.69 apply (zenon_L172_); trivial. % 21.51/21.69 (* end of lemma zenon_L173_ *) % 21.51/21.69 assert (zenon_L174_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (((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)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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)) = (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)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H13b zenon_H76 zenon_H7f zenon_H1a8 zenon_H196 zenon_Hf6 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha0 zenon_Ha9 zenon_H195 zenon_Hf0 zenon_H13f zenon_H153 zenon_H111 zenon_H16a zenon_Hdb zenon_H173 zenon_H9d zenon_H179 zenon_H13c zenon_H68 zenon_H77 zenon_He3 zenon_He2 zenon_H48 zenon_H5c. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.51/21.69 apply (zenon_L171_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.51/21.69 exact (zenon_He3 zenon_He7). % 21.51/21.69 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.51/21.69 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.51/21.69 apply (zenon_L53_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.51/21.69 exact (zenon_He3 zenon_He7). % 21.51/21.69 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.51/21.69 apply (zenon_L110_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.51/21.69 apply (zenon_L123_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.51/21.69 apply (zenon_L120_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.51/21.69 apply (zenon_L162_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.51/21.69 apply (zenon_L150_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.51/21.69 apply (zenon_L61_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.51/21.69 apply (zenon_L173_); trivial. % 21.51/21.69 apply (zenon_L167_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.51/21.69 apply (zenon_L54_); trivial. % 21.51/21.69 apply (zenon_L169_); trivial. % 21.51/21.69 apply (zenon_L57_); trivial. % 21.51/21.69 apply (zenon_L157_); trivial. % 21.51/21.69 (* end of lemma zenon_L174_ *) % 21.51/21.69 assert (zenon_L175_ : ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((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)) = (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((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 (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (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) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H65 zenon_H18d zenon_H77 zenon_H13a zenon_H55 zenon_H4e zenon_H82 zenon_H13b zenon_He2 zenon_H183 zenon_H11a zenon_Hf0 zenon_He3 zenon_H158 zenon_H177 zenon_H121 zenon_H173 zenon_H179 zenon_H13c zenon_H129 zenon_H13e zenon_H104 zenon_H131 zenon_H5a zenon_Hb2 zenon_Ha0 zenon_H111 zenon_H16a zenon_Ha9 zenon_H8b zenon_H16b zenon_H117 zenon_H13d zenon_H48 zenon_H2c zenon_H1e zenon_H141 zenon_Hb6 zenon_H68 zenon_H139 zenon_H15d zenon_H6f zenon_H73 zenon_He4 zenon_Heb zenon_Hfa zenon_Hf5 zenon_H13f zenon_H109 zenon_H12e zenon_H100 zenon_H140 zenon_H5d zenon_H7d zenon_Hcc zenon_H156 zenon_H125 zenon_H33 zenon_H163 zenon_H162 zenon_H164 zenon_H24 zenon_Hbc zenon_H94 zenon_H186 zenon_H4d zenon_H53 zenon_H189 zenon_H18a. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.51/21.69 apply (zenon_L13_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.51/21.69 apply (zenon_L16_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.51/21.69 apply (zenon_L30_); trivial. % 21.51/21.69 apply (zenon_L141_); trivial. % 21.51/21.69 (* end of lemma zenon_L175_ *) % 21.51/21.69 assert (zenon_L176_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H89 zenon_H13d zenon_H190 zenon_H53 zenon_H191 zenon_H13e. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.51/21.69 apply (zenon_L144_); trivial. % 21.51/21.69 apply (zenon_L144_); trivial. % 21.51/21.69 (* end of lemma zenon_L176_ *) % 21.51/21.69 assert (zenon_L177_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (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) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (((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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (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 (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 (e2) (e2)))) -> (((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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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) (e2)) = (e2))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H92 zenon_H190 zenon_H89 zenon_H48 zenon_H1e zenon_H5a zenon_H4e zenon_H77 zenon_H65 zenon_H18d zenon_H18a zenon_H189 zenon_H186 zenon_H164 zenon_H162 zenon_H163 zenon_H158 zenon_H156 zenon_H139 zenon_Hcc zenon_Hbc zenon_Hb6 zenon_Hb2 zenon_Ha9 zenon_Ha0 zenon_H94 zenon_H55 zenon_H82 zenon_H7d zenon_H13a zenon_H13b zenon_H13c zenon_H13d zenon_H140 zenon_H100 zenon_H12e zenon_H117 zenon_H111 zenon_H109 zenon_H11a zenon_H121 zenon_H104 zenon_H13e zenon_H131 zenon_H125 zenon_H129 zenon_H13f zenon_H141 zenon_Hf0 zenon_Hf5 zenon_Hfa zenon_Heb zenon_He4 zenon_He2 zenon_H73 zenon_H6f zenon_H68 zenon_H15d zenon_H5d zenon_H33 zenon_H2c zenon_H24 zenon_H53 zenon_He3 zenon_H4d zenon_H173 zenon_H177 zenon_H179 zenon_H183 zenon_H16a zenon_H8b. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.51/21.69 apply (zenon_L175_); trivial. % 21.51/21.69 apply (zenon_L176_); trivial. % 21.51/21.69 (* end of lemma zenon_L177_ *) % 21.51/21.69 assert (zenon_L178_ : ((op (e3) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_Hbb zenon_Hfe zenon_H177. % 21.51/21.69 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 21.51/21.69 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e0) (e2)) = (op (e3) (e2)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H177. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Hbd. % 21.51/21.69 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.51/21.69 cut (((op (e3) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ad]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e0) (e2)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H1ad. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Hbb. % 21.51/21.69 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 21.51/21.69 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_Hbe. apply refl_equal. % 21.51/21.69 apply zenon_H114. apply sym_equal. exact zenon_Hfe. % 21.51/21.69 apply zenon_Hbe. apply refl_equal. % 21.51/21.69 apply zenon_Hbe. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L178_ *) % 21.51/21.69 assert (zenon_L179_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H13a zenon_Ha0 zenon_H1e zenon_Hb6 zenon_H3d zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.51/21.69 apply (zenon_L41_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.51/21.69 apply (zenon_L55_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.51/21.69 apply (zenon_L178_); trivial. % 21.51/21.69 apply (zenon_L154_); trivial. % 21.51/21.69 (* end of lemma zenon_L179_ *) % 21.51/21.69 assert (zenon_L180_ : ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H65 zenon_H67 zenon_H2c. % 21.51/21.69 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H86 ]. % 21.51/21.69 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e0) (e0)) = (op (e2) (e0)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H2c. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H1ae. % 21.51/21.69 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.51/21.69 cut (((op (e2) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e0) (e0)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H1af. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H65. % 21.51/21.69 cut (((e2) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 21.51/21.69 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H86. apply refl_equal. % 21.51/21.69 apply zenon_H1b0. apply sym_equal. exact zenon_H67. % 21.51/21.69 apply zenon_H86. apply refl_equal. % 21.51/21.69 apply zenon_H86. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L180_ *) % 21.51/21.69 assert (zenon_L181_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H13a zenon_Ha0 zenon_H1e zenon_Ha9 zenon_H6e zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.51/21.69 apply (zenon_L41_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.51/21.69 apply (zenon_L110_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.51/21.69 apply (zenon_L178_); trivial. % 21.51/21.69 apply (zenon_L154_); trivial. % 21.51/21.69 (* end of lemma zenon_L181_ *) % 21.51/21.69 assert (zenon_L182_ : (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (e3)) = (e1)) -> False). % 21.51/21.69 do 0 intro. intros zenon_Hb6 zenon_Hb9 zenon_H128. % 21.51/21.69 cut (((op (e2) (e3)) = (e3)) = ((e1) = (e3))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Hb6. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Hb9. % 21.51/21.69 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.51/21.69 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_H1b1 zenon_H128). % 21.51/21.69 apply zenon_Ha2. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L182_ *) % 21.51/21.69 assert (zenon_L183_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H13f zenon_H65 zenon_H77 zenon_Hf0 zenon_H3f zenon_H153 zenon_H111 zenon_Hb6 zenon_Hb9. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.51/21.69 apply (zenon_L30_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.51/21.69 apply (zenon_L118_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.51/21.69 apply (zenon_L148_); trivial. % 21.51/21.69 apply (zenon_L182_); trivial. % 21.51/21.69 (* end of lemma zenon_L183_ *) % 21.51/21.69 assert (zenon_L184_ : ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H4d zenon_H153 zenon_H73. % 21.51/21.69 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H4f | zenon_intro zenon_H50 ]. % 21.51/21.69 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e0) (e2)) = (op (e1) (e2)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H73. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H4f. % 21.51/21.69 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.51/21.69 cut (((op (e1) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e0) (e2)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H74. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H4d. % 21.51/21.69 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 21.51/21.69 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H50. apply refl_equal. % 21.51/21.69 apply zenon_H1b2. apply sym_equal. exact zenon_H153. % 21.51/21.69 apply zenon_H50. apply refl_equal. % 21.51/21.69 apply zenon_H50. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L184_ *) % 21.51/21.69 assert (zenon_L185_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (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)) = (op (e3) (e0)))) -> (((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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((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)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (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)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e2) (e2)) = (e0))) -> (((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 (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 (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.51/21.69 do 0 intro. intros zenon_Hb2 zenon_H1e zenon_H94 zenon_Hbc zenon_H24 zenon_H164 zenon_H163 zenon_H33 zenon_H13b zenon_H125 zenon_H158 zenon_H156 zenon_H139 zenon_Hcc zenon_Ha9 zenon_H55 zenon_H82 zenon_H7d zenon_H5d zenon_H4e zenon_H13a zenon_H13c zenon_H13d zenon_H140 zenon_H100 zenon_H12e zenon_H117 zenon_H109 zenon_H11a zenon_H121 zenon_H104 zenon_H13e zenon_H131 zenon_H129 zenon_H141 zenon_Hf5 zenon_Hfa zenon_Heb zenon_He4 zenon_He2 zenon_H6f zenon_H15d zenon_H2c zenon_Hb6 zenon_H111 zenon_Hf0 zenon_H77 zenon_H65 zenon_H13f zenon_H73 zenon_H153 zenon_H19a zenon_H68 zenon_Hf6 zenon_H48 zenon_Hb9 zenon_Ha0 zenon_H162. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.51/21.69 apply (zenon_L109_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.51/21.69 apply (zenon_L183_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.51/21.69 apply (zenon_L184_); trivial. % 21.51/21.69 apply (zenon_L166_); trivial. % 21.51/21.69 (* end of lemma zenon_L185_ *) % 21.51/21.69 assert (zenon_L186_ : ((op (e1) (e1)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H3f zenon_Hef zenon_H77. % 21.51/21.69 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.51/21.69 cut (((e2) = (e2)) = ((e1) = (e2))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H77. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H69. % 21.51/21.69 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.51/21.69 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e1) (e1)) = (e1)) = ((e2) = (e1))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H78. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H3f. % 21.51/21.69 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.51/21.69 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1b3]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_H1b3 zenon_Hef). % 21.51/21.69 apply zenon_H4a. apply refl_equal. % 21.51/21.69 apply zenon_H6a. apply refl_equal. % 21.51/21.69 apply zenon_H6a. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L186_ *) % 21.51/21.69 assert (zenon_L187_ : ((op (e3) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H11f zenon_H155 zenon_H1b4. % 21.51/21.69 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.51/21.69 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H1b4. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H12a. % 21.51/21.69 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.51/21.69 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H1b5. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H11f. % 21.51/21.69 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 21.51/21.69 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H12b. apply refl_equal. % 21.51/21.69 apply zenon_H1b6. apply sym_equal. exact zenon_H155. % 21.51/21.69 apply zenon_H12b. apply refl_equal. % 21.51/21.69 apply zenon_H12b. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L187_ *) % 21.51/21.69 assert (zenon_L188_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H17c zenon_H171 zenon_H1b7. % 21.51/21.69 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.51/21.69 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H1b7. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H12a. % 21.51/21.69 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.51/21.69 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H1b8. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H17c. % 21.51/21.69 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 21.51/21.69 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H12b. apply refl_equal. % 21.51/21.69 apply zenon_H172. apply sym_equal. exact zenon_H171. % 21.51/21.69 apply zenon_H12b. apply refl_equal. % 21.51/21.69 apply zenon_H12b. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L188_ *) % 21.51/21.69 assert (zenon_L189_ : ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_Hc3 zenon_Hb9 zenon_H129. % 21.51/21.69 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.51/21.69 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H129. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H12a. % 21.51/21.69 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.51/21.69 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H12c. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Hc3. % 21.51/21.69 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1b9]. % 21.51/21.69 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H12b. apply refl_equal. % 21.51/21.69 apply zenon_H1b9. apply sym_equal. exact zenon_Hb9. % 21.51/21.69 apply zenon_H12b. apply refl_equal. % 21.51/21.69 apply zenon_H12b. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L189_ *) % 21.51/21.69 assert (zenon_L190_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_Hc0 zenon_Hc3 zenon_H129. % 21.51/21.69 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.51/21.69 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.51/21.69 apply (zenon_L189_); trivial. % 21.51/21.69 (* end of lemma zenon_L190_ *) % 21.51/21.69 assert (zenon_L191_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e1)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H1a8 zenon_Ha9 zenon_Hdb zenon_H77 zenon_H3f zenon_H1ba zenon_H1bb zenon_H162 zenon_H1b4 zenon_H155 zenon_H1b7 zenon_Hc0 zenon_H129. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.51/21.69 apply (zenon_L110_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.51/21.69 apply (zenon_L186_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.51/21.69 exact (zenon_H1ba zenon_H6d). % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.51/21.69 exact (zenon_H162 zenon_H167). % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.51/21.69 apply (zenon_L187_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.51/21.69 apply (zenon_L188_); trivial. % 21.51/21.69 apply (zenon_L190_); trivial. % 21.51/21.69 (* end of lemma zenon_L191_ *) % 21.51/21.69 assert (zenon_L192_ : ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H5c zenon_H155 zenon_Hf5. % 21.51/21.69 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H5e | zenon_intro zenon_H5f ]. % 21.51/21.69 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Hf5. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H5e. % 21.51/21.69 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.51/21.69 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_H1be. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H5c. % 21.51/21.69 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 21.51/21.69 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.51/21.69 congruence. % 21.51/21.69 apply zenon_H5f. apply refl_equal. % 21.51/21.69 apply zenon_H1b6. apply sym_equal. exact zenon_H155. % 21.51/21.69 apply zenon_H5f. apply refl_equal. % 21.51/21.69 apply zenon_H5f. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L192_ *) % 21.51/21.69 assert (zenon_L193_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H66 zenon_Hfe zenon_Ha9. % 21.51/21.69 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.51/21.69 cut (((e3) = (e3)) = ((e2) = (e3))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Ha9. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_Ha1. % 21.51/21.69 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.51/21.69 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 21.51/21.69 congruence. % 21.51/21.69 cut (((op (e0) (e2)) = (e2)) = ((e3) = (e2))). % 21.51/21.69 intro zenon_D_pnotp. % 21.51/21.69 apply zenon_Haa. % 21.51/21.69 rewrite <- zenon_D_pnotp. % 21.51/21.69 exact zenon_H66. % 21.51/21.69 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.51/21.69 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 21.51/21.69 congruence. % 21.51/21.69 exact (zenon_Hff zenon_Hfe). % 21.51/21.69 apply zenon_H6a. apply refl_equal. % 21.51/21.69 apply zenon_Ha2. apply refl_equal. % 21.51/21.69 apply zenon_Ha2. apply refl_equal. % 21.51/21.69 (* end of lemma zenon_L193_ *) % 21.51/21.69 assert (zenon_L194_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (((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 (e2) (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) (e1)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (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 (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (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)) = (op (e3) (e0)))) -> (((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))))) -> (~((e0) = (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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H196 zenon_H177 zenon_Hb6 zenon_Ha9 zenon_H48 zenon_H13e zenon_H13d zenon_H131 zenon_H8b zenon_H104 zenon_H1a8 zenon_H1ba zenon_H1bb zenon_H162 zenon_H1b4 zenon_H1b7 zenon_Hc0 zenon_H129 zenon_Heb zenon_Hb2 zenon_Ha0 zenon_H1e zenon_H24 zenon_H164 zenon_H163 zenon_H33 zenon_H13b zenon_H125 zenon_H68 zenon_H158 zenon_H156 zenon_H139 zenon_Hcc zenon_H55 zenon_H82 zenon_H7d zenon_H5d zenon_H4e zenon_H13a zenon_H13c zenon_H140 zenon_H100 zenon_H12e zenon_H117 zenon_H111 zenon_H109 zenon_H11a zenon_H121 zenon_H13f zenon_H141 zenon_Hf0 zenon_Hfa zenon_He4 zenon_He2 zenon_H73 zenon_H6f zenon_H15d zenon_H2c zenon_Hf5 zenon_He3 zenon_H94 zenon_Hb9 zenon_Hbb zenon_Hbc zenon_H155 zenon_H77. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.51/21.69 apply (zenon_L20_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.51/21.69 apply (zenon_L181_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.51/21.69 apply (zenon_L41_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.51/21.69 apply (zenon_L41_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.51/21.69 apply (zenon_L116_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.51/21.69 exact (zenon_He3 zenon_He7). % 21.51/21.69 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.51/21.69 apply (zenon_L109_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.51/21.69 apply (zenon_L191_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.51/21.69 apply (zenon_L117_); trivial. % 21.51/21.69 apply (zenon_L192_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.51/21.69 apply (zenon_L46_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.51/21.69 apply (zenon_L191_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.51/21.69 apply (zenon_L130_); trivial. % 21.51/21.69 apply (zenon_L157_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.51/21.69 apply (zenon_L47_); trivial. % 21.51/21.69 apply (zenon_L48_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.51/21.69 apply (zenon_L193_); trivial. % 21.51/21.69 apply (zenon_L115_); trivial. % 21.51/21.69 apply (zenon_L98_); trivial. % 21.51/21.69 (* end of lemma zenon_L194_ *) % 21.51/21.69 assert (zenon_L195_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (((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 (e2) (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) (e1)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (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 (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (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)) = (op (e3) (e0)))) -> (((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))))) -> (~((e0) = (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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H19a zenon_H65 zenon_H196 zenon_H177 zenon_Hb6 zenon_Ha9 zenon_H48 zenon_H13e zenon_H13d zenon_H131 zenon_H8b zenon_H104 zenon_H1a8 zenon_H1ba zenon_H1bb zenon_H162 zenon_H1b4 zenon_H1b7 zenon_Hc0 zenon_H129 zenon_Heb zenon_Hb2 zenon_Ha0 zenon_H1e zenon_H24 zenon_H164 zenon_H163 zenon_H33 zenon_H13b zenon_H125 zenon_H68 zenon_H158 zenon_H156 zenon_H139 zenon_Hcc zenon_H55 zenon_H82 zenon_H7d zenon_H5d zenon_H4e zenon_H13a zenon_H13c zenon_H140 zenon_H100 zenon_H12e zenon_H117 zenon_H111 zenon_H109 zenon_H11a zenon_H121 zenon_H13f zenon_H141 zenon_Hf0 zenon_Hfa zenon_He4 zenon_He2 zenon_H73 zenon_H6f zenon_H15d zenon_H2c zenon_Hf5 zenon_He3 zenon_H94 zenon_Hb9 zenon_Hbb zenon_Hbc zenon_H77. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.51/21.69 apply (zenon_L13_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.51/21.69 apply (zenon_L179_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.51/21.69 apply (zenon_L180_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.51/21.69 apply (zenon_L181_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.51/21.69 apply (zenon_L94_); trivial. % 21.51/21.69 apply (zenon_L185_); trivial. % 21.51/21.69 apply (zenon_L194_); trivial. % 21.51/21.69 (* end of lemma zenon_L195_ *) % 21.51/21.69 assert (zenon_L196_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H13e zenon_H13d zenon_H1bf zenon_H8b zenon_Hbb zenon_H104. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H14c | zenon_intro zenon_H151 ]. % 21.51/21.69 exact (zenon_H13d zenon_H14c). % 21.51/21.69 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H105 | zenon_intro zenon_H152 ]. % 21.51/21.69 exact (zenon_H1bf zenon_H105). % 21.51/21.69 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H8a | zenon_intro zenon_H110 ]. % 21.51/21.69 exact (zenon_H8b zenon_H8a). % 21.51/21.69 apply (zenon_L129_); trivial. % 21.51/21.69 (* end of lemma zenon_L196_ *) % 21.51/21.69 assert (zenon_L197_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (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))))) -> False). % 21.51/21.69 do 0 intro. intros zenon_H89 zenon_H13d zenon_H1bf zenon_H104 zenon_Hbb zenon_H13e. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.51/21.69 apply (zenon_L196_); trivial. % 21.51/21.69 apply (zenon_L196_); trivial. % 21.51/21.69 (* end of lemma zenon_L197_ *) % 21.51/21.69 assert (zenon_L198_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H5a zenon_H82 zenon_H48 zenon_H1e zenon_H4e zenon_H55 zenon_Hb6 zenon_H9d. % 21.51/21.69 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.51/21.69 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.51/21.69 apply (zenon_L135_); trivial. % 21.51/21.69 (* end of lemma zenon_L198_ *) % 21.51/21.69 assert (zenon_L199_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H125 zenon_H68 zenon_H1e zenon_H4e zenon_H72 zenon_H6d zenon_H55 zenon_Ha9 zenon_H9d. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.51/21.69 apply (zenon_L20_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.51/21.69 apply (zenon_L83_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.51/21.69 apply (zenon_L34_); trivial. % 21.51/21.69 apply (zenon_L91_); trivial. % 21.51/21.69 (* end of lemma zenon_L199_ *) % 21.51/21.69 assert (zenon_L200_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 21.51/21.69 do 0 intro. intros zenon_H87 zenon_H125 zenon_H68 zenon_H1e zenon_H4e zenon_H55 zenon_Ha9 zenon_H9d. % 21.51/21.69 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.51/21.69 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 21.51/21.69 apply (zenon_L199_); trivial. % 21.51/21.69 (* end of lemma zenon_L200_ *) % 21.51/21.69 assert (zenon_L201_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.51/21.69 do 0 intro. intros zenon_Hc0 zenon_H9d zenon_Hbc. % 21.51/21.69 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.51/21.69 apply (zenon_L48_); trivial. % 21.51/21.69 (* end of lemma zenon_L201_ *) % 21.51/21.69 assert (zenon_L202_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 21.51/21.69 do 0 intro. intros zenon_Hcc zenon_H24 zenon_H33 zenon_Hb6 zenon_H77 zenon_H48 zenon_H82 zenon_H55 zenon_H4e zenon_H68 zenon_H125 zenon_H94 zenon_H7d zenon_H65 zenon_Ha9 zenon_H5d zenon_H1e zenon_Ha0 zenon_Hb2 zenon_Hbc zenon_H9d. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.51/21.69 apply (zenon_L2_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.51/21.69 apply (zenon_L4_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.51/21.69 apply (zenon_L28_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.51/21.69 apply (zenon_L8_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.51/21.69 apply (zenon_L9_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.51/21.69 apply (zenon_L11_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.51/21.69 apply (zenon_L198_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.51/21.69 apply (zenon_L33_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.51/21.69 apply (zenon_L19_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.51/21.69 apply (zenon_L200_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.51/21.69 apply (zenon_L37_); trivial. % 21.51/21.69 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.51/21.70 apply (zenon_L39_); trivial. % 21.51/21.70 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.51/21.70 apply (zenon_L40_); trivial. % 21.51/21.70 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.51/21.70 apply (zenon_L45_); trivial. % 21.51/21.70 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.51/21.70 apply (zenon_L201_); trivial. % 21.51/21.70 apply (zenon_L51_); trivial. % 21.51/21.70 (* end of lemma zenon_L202_ *) % 21.51/21.70 assert (zenon_L203_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((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 (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 (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (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 (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((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 (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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (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) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.51/21.70 do 0 intro. intros zenon_H1c0 zenon_H1e zenon_H24 zenon_H2c zenon_H33 zenon_H65 zenon_H16a zenon_H183 zenon_H179 zenon_H177 zenon_H173 zenon_He3 zenon_H5d zenon_H15d zenon_H68 zenon_H6f zenon_H73 zenon_He2 zenon_He4 zenon_Heb zenon_Hfa zenon_Hf5 zenon_Hf0 zenon_H141 zenon_H13f zenon_H129 zenon_H125 zenon_H131 zenon_H13e zenon_H104 zenon_H121 zenon_H11a zenon_H109 zenon_H111 zenon_H117 zenon_H12e zenon_H100 zenon_H140 zenon_H13c zenon_H13b zenon_H13a zenon_H7d zenon_H82 zenon_H55 zenon_H94 zenon_Ha0 zenon_Ha9 zenon_Hb2 zenon_Hb6 zenon_Hbc zenon_Hcc zenon_H139 zenon_H156 zenon_H158 zenon_H163 zenon_H164 zenon_H186 zenon_H189 zenon_H18a zenon_H18d zenon_H77 zenon_H4e zenon_H48 zenon_H190 zenon_H1a8 zenon_H1b4 zenon_H1b7 zenon_H1bb zenon_H19a zenon_H196. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.52/21.70 apply (zenon_L2_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.52/21.70 apply (zenon_L4_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.52/21.70 apply (zenon_L6_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.52/21.70 apply (zenon_L8_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.52/21.70 apply (zenon_L9_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.52/21.70 apply (zenon_L11_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.52/21.70 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.52/21.70 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.52/21.70 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.52/21.70 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.52/21.70 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.52/21.70 exact (zenon_H7b zenon_H65). % 21.52/21.70 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.52/21.70 apply (zenon_L177_); trivial. % 21.52/21.70 apply (zenon_L177_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.52/21.70 apply (zenon_L33_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.52/21.70 apply (zenon_L19_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.52/21.70 apply (zenon_L35_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.52/21.70 apply (zenon_L37_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.52/21.70 apply (zenon_L39_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.52/21.70 apply (zenon_L40_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.52/21.70 apply (zenon_L45_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.52/21.70 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.52/21.70 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.52/21.70 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.52/21.70 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.52/21.70 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.52/21.70 exact (zenon_H7b zenon_H65). % 21.52/21.70 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.52/21.70 apply (zenon_L195_); trivial. % 21.52/21.70 apply (zenon_L195_); trivial. % 21.52/21.70 apply (zenon_L197_); trivial. % 21.52/21.70 apply (zenon_L51_); trivial. % 21.52/21.70 apply (zenon_L202_); trivial. % 21.52/21.70 (* end of lemma zenon_L203_ *) % 21.52/21.70 assert (zenon_L204_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((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)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((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)) = (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 (e2) (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 (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 (e2) (e2)))) -> (((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)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e1) = (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 (e0) (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 (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((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 (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H192 zenon_H7f zenon_H7d zenon_H1bb zenon_H1b7 zenon_H1b4 zenon_H4e zenon_H18d zenon_H18a zenon_H189 zenon_H186 zenon_H164 zenon_H163 zenon_H158 zenon_H156 zenon_H139 zenon_Hcc zenon_Hbc zenon_H94 zenon_H55 zenon_H82 zenon_H13c zenon_H140 zenon_H100 zenon_H12e zenon_H109 zenon_H11a zenon_H121 zenon_H104 zenon_H13e zenon_H131 zenon_H125 zenon_H129 zenon_H141 zenon_Hfa zenon_Heb zenon_He4 zenon_H73 zenon_H6f zenon_H15d zenon_H5d zenon_H173 zenon_H177 zenon_H179 zenon_H183 zenon_H33 zenon_H2c zenon_H24 zenon_H1c0 zenon_Hb2 zenon_H48 zenon_H19d zenon_H77 zenon_H68 zenon_H16a zenon_H195 zenon_H111 zenon_H13f zenon_Hf0 zenon_H162 zenon_Ha0 zenon_H19a zenon_H1a2 zenon_H190 zenon_H1a3 zenon_H117 zenon_H196 zenon_H13a zenon_H1e zenon_He2 zenon_He3 zenon_H1a8 zenon_H13b zenon_Hb6 zenon_Ha9 zenon_H5c zenon_Hf5. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.52/21.70 apply (zenon_L13_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.52/21.70 apply (zenon_L146_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.52/21.70 apply (zenon_L13_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.52/21.70 apply (zenon_L17_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.52/21.70 apply (zenon_L20_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.52/21.70 apply (zenon_L160_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.52/21.70 apply (zenon_L94_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.52/21.70 apply (zenon_L20_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.52/21.70 apply (zenon_L41_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.52/21.70 apply (zenon_L41_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.52/21.70 apply (zenon_L170_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.52/21.70 apply (zenon_L151_); trivial. % 21.52/21.70 apply (zenon_L174_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.52/21.70 apply (zenon_L95_); trivial. % 21.52/21.70 apply (zenon_L92_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.52/21.70 apply (zenon_L203_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.52/21.70 apply (zenon_L41_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.52/21.70 apply (zenon_L170_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.52/21.70 apply (zenon_L151_); trivial. % 21.52/21.70 apply (zenon_L91_); trivial. % 21.52/21.70 apply (zenon_L31_); trivial. % 21.52/21.70 apply (zenon_L192_); trivial. % 21.52/21.70 (* end of lemma zenon_L204_ *) % 21.52/21.70 assert (zenon_L205_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 21.52/21.70 do 0 intro. intros zenon_H6f zenon_Hdb zenon_H10d. % 21.52/21.70 cut (((op (e0) (e1)) = (e3)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 21.52/21.70 intro zenon_D_pnotp. % 21.52/21.70 apply zenon_H6f. % 21.52/21.70 rewrite <- zenon_D_pnotp. % 21.52/21.70 exact zenon_Hdb. % 21.52/21.70 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 21.52/21.70 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 21.52/21.70 congruence. % 21.52/21.70 apply zenon_H193. apply refl_equal. % 21.52/21.70 apply zenon_H10e. apply sym_equal. exact zenon_H10d. % 21.52/21.70 (* end of lemma zenon_L205_ *) % 21.52/21.70 assert (zenon_L206_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H5c zenon_Hf7 zenon_H77. % 21.52/21.70 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.52/21.70 cut (((e2) = (e2)) = ((e1) = (e2))). % 21.52/21.70 intro zenon_D_pnotp. % 21.52/21.70 apply zenon_H77. % 21.52/21.70 rewrite <- zenon_D_pnotp. % 21.52/21.70 exact zenon_H69. % 21.52/21.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.52/21.70 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 21.52/21.70 congruence. % 21.52/21.70 cut (((op (e1) (e3)) = (e1)) = ((e2) = (e1))). % 21.52/21.70 intro zenon_D_pnotp. % 21.52/21.70 apply zenon_H78. % 21.52/21.70 rewrite <- zenon_D_pnotp. % 21.52/21.70 exact zenon_H5c. % 21.52/21.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.52/21.70 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 21.52/21.70 congruence. % 21.52/21.70 exact (zenon_H1c1 zenon_Hf7). % 21.52/21.70 apply zenon_H4a. apply refl_equal. % 21.52/21.70 apply zenon_H6a. apply refl_equal. % 21.52/21.70 apply zenon_H6a. apply refl_equal. % 21.52/21.70 (* end of lemma zenon_L206_ *) % 21.52/21.70 assert (zenon_L207_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 21.52/21.70 do 0 intro. intros zenon_H1c2 zenon_H8a zenon_H93. % 21.52/21.70 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 21.52/21.70 intro zenon_D_pnotp. % 21.52/21.70 apply zenon_H1c2. % 21.52/21.70 rewrite <- zenon_D_pnotp. % 21.52/21.70 exact zenon_H8a. % 21.52/21.70 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17d]. % 21.52/21.70 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.52/21.70 congruence. % 21.52/21.70 apply zenon_H108. apply refl_equal. % 21.52/21.70 apply zenon_H17d. apply sym_equal. exact zenon_H93. % 21.52/21.70 (* end of lemma zenon_L207_ *) % 21.52/21.70 assert (zenon_L208_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H1c3 zenon_H162 zenon_Ha0 zenon_Hb9 zenon_H48 zenon_H68 zenon_H19a zenon_H77 zenon_H5c zenon_H8a zenon_H1c2 zenon_H181. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.52/21.70 apply (zenon_L166_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.52/21.70 apply (zenon_L206_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.52/21.70 apply (zenon_L207_); trivial. % 21.52/21.70 exact (zenon_H181 zenon_H17c). % 21.52/21.70 (* end of lemma zenon_L208_ *) % 21.52/21.70 assert (zenon_L209_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H1c3 zenon_H9e zenon_Ha9 zenon_H77 zenon_H5c zenon_H115 zenon_H68 zenon_H181. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.52/21.70 apply (zenon_L92_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.52/21.70 apply (zenon_L206_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.52/21.70 apply (zenon_L158_); trivial. % 21.52/21.70 exact (zenon_H181 zenon_H17c). % 21.52/21.70 (* end of lemma zenon_L209_ *) % 21.52/21.70 assert (zenon_L210_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H19a zenon_Ha0 zenon_H48 zenon_H181 zenon_H68 zenon_H5c zenon_H77 zenon_Ha9 zenon_H9e zenon_H1c3 zenon_H162. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.52/21.70 apply (zenon_L156_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.52/21.70 apply (zenon_L157_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.52/21.70 apply (zenon_L209_); trivial. % 21.52/21.70 exact (zenon_H162 zenon_H167). % 21.52/21.70 (* end of lemma zenon_L210_ *) % 21.52/21.70 assert (zenon_L211_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H1bb zenon_H162 zenon_H18a zenon_H7e zenon_H181 zenon_Hc4. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.52/21.70 exact (zenon_H162 zenon_H167). % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.52/21.70 apply (zenon_L140_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.52/21.70 exact (zenon_H181 zenon_H17c). % 21.52/21.70 exact (zenon_Hc4 zenon_Hc3). % 21.52/21.70 (* end of lemma zenon_L211_ *) % 21.52/21.70 assert (zenon_L212_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (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) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H15d zenon_H192 zenon_Hc4 zenon_H181 zenon_H18a zenon_H162 zenon_H1bb zenon_H139 zenon_H13a zenon_H1e zenon_H7f zenon_H16a zenon_H195 zenon_H111 zenon_H13f zenon_H1c2 zenon_H6f zenon_H117 zenon_H196 zenon_He3 zenon_He2 zenon_Hb6 zenon_H19a zenon_Ha0 zenon_H48 zenon_H68 zenon_H77 zenon_Ha9 zenon_H1c3 zenon_H61 zenon_H5d zenon_H82 zenon_H5c zenon_Hf5. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.52/21.70 apply (zenon_L13_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.52/21.70 apply (zenon_L146_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.52/21.70 apply (zenon_L13_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.52/21.70 apply (zenon_L18_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.52/21.70 apply (zenon_L20_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.52/21.70 apply (zenon_L160_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.52/21.70 apply (zenon_L94_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.52/21.70 apply (zenon_L41_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.52/21.70 apply (zenon_L53_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.52/21.70 exact (zenon_He3 zenon_He7). % 21.52/21.70 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.52/21.70 apply (zenon_L150_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.52/21.70 apply (zenon_L54_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.52/21.70 apply (zenon_L151_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.52/21.70 apply (zenon_L205_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.52/21.70 apply (zenon_L153_); trivial. % 21.52/21.70 apply (zenon_L208_); trivial. % 21.52/21.70 apply (zenon_L167_); trivial. % 21.52/21.70 apply (zenon_L57_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.52/21.70 apply (zenon_L95_); trivial. % 21.52/21.70 apply (zenon_L210_); trivial. % 21.52/21.70 apply (zenon_L211_); trivial. % 21.52/21.70 apply (zenon_L192_); trivial. % 21.52/21.70 (* end of lemma zenon_L212_ *) % 21.52/21.70 assert (zenon_L213_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((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 (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (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 (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((e1) = (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))))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H15c zenon_H158 zenon_H156 zenon_H3e zenon_H48 zenon_H1e zenon_H68 zenon_H6f zenon_H6d zenon_H73 zenon_H72 zenon_He2 zenon_H40 zenon_He4 zenon_He3 zenon_Heb zenon_Hfa zenon_Hf5 zenon_Hf0 zenon_H141 zenon_H13f zenon_H129 zenon_H87 zenon_H125 zenon_H131 zenon_H13e zenon_H104 zenon_H121 zenon_H11a zenon_H109 zenon_H111 zenon_H117 zenon_H12e zenon_H100 zenon_H140 zenon_H13d zenon_H13c zenon_H13b zenon_H13a zenon_H33 zenon_H4e zenon_H5d zenon_H7d zenon_H82 zenon_H55 zenon_H94 zenon_Ha0 zenon_Ha9 zenon_Hb2 zenon_Hb6 zenon_Hbc zenon_Hcc zenon_H77 zenon_H139 zenon_H15d. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.52/21.70 apply (zenon_L13_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.52/21.70 apply (zenon_L13_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.52/21.70 apply (zenon_L93_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.52/21.70 apply (zenon_L70_); trivial. % 21.52/21.70 apply (zenon_L84_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.52/21.70 apply (zenon_L97_); trivial. % 21.52/21.70 apply (zenon_L99_); trivial. % 21.52/21.70 apply (zenon_L102_); trivial. % 21.52/21.70 (* end of lemma zenon_L213_ *) % 21.52/21.70 assert (zenon_L214_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H3d zenon_H6e zenon_H77. % 21.52/21.70 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.52/21.70 cut (((e2) = (e2)) = ((e1) = (e2))). % 21.52/21.70 intro zenon_D_pnotp. % 21.52/21.70 apply zenon_H77. % 21.52/21.70 rewrite <- zenon_D_pnotp. % 21.52/21.70 exact zenon_H69. % 21.52/21.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.52/21.70 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 21.52/21.70 congruence. % 21.52/21.70 cut (((op (e0) (e1)) = (e1)) = ((e2) = (e1))). % 21.52/21.70 intro zenon_D_pnotp. % 21.52/21.70 apply zenon_H78. % 21.52/21.70 rewrite <- zenon_D_pnotp. % 21.52/21.70 exact zenon_H3d. % 21.52/21.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.52/21.70 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 21.52/21.70 congruence. % 21.52/21.70 exact (zenon_H194 zenon_H6e). % 21.52/21.70 apply zenon_H4a. apply refl_equal. % 21.52/21.70 apply zenon_H6a. apply refl_equal. % 21.52/21.70 apply zenon_H6a. apply refl_equal. % 21.52/21.70 (* end of lemma zenon_L214_ *) % 21.52/21.70 assert (zenon_L215_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H139 zenon_H68 zenon_H1e zenon_H77 zenon_H3d zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.52/21.70 apply (zenon_L20_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.52/21.70 apply (zenon_L214_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.52/21.70 apply (zenon_L122_); trivial. % 21.52/21.70 apply (zenon_L167_); trivial. % 21.52/21.70 (* end of lemma zenon_L215_ *) % 21.52/21.70 assert (zenon_L216_ : ((op (e1) (e1)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H3f zenon_H10c zenon_Hb6. % 21.52/21.70 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.52/21.70 cut (((e3) = (e3)) = ((e1) = (e3))). % 21.52/21.70 intro zenon_D_pnotp. % 21.52/21.70 apply zenon_Hb6. % 21.52/21.70 rewrite <- zenon_D_pnotp. % 21.52/21.70 exact zenon_Ha1. % 21.52/21.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.52/21.70 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 21.52/21.70 congruence. % 21.52/21.70 cut (((op (e1) (e1)) = (e1)) = ((e3) = (e1))). % 21.52/21.70 intro zenon_D_pnotp. % 21.52/21.70 apply zenon_Hb7. % 21.52/21.70 rewrite <- zenon_D_pnotp. % 21.52/21.70 exact zenon_H3f. % 21.52/21.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.52/21.70 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 21.52/21.70 congruence. % 21.52/21.70 exact (zenon_H159 zenon_H10c). % 21.52/21.70 apply zenon_H4a. apply refl_equal. % 21.52/21.70 apply zenon_Ha2. apply refl_equal. % 21.52/21.70 apply zenon_Ha2. apply refl_equal. % 21.52/21.70 (* end of lemma zenon_L216_ *) % 21.52/21.70 assert (zenon_L217_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H2d zenon_H54 zenon_H48. % 21.52/21.70 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H49 | zenon_intro zenon_H4a ]. % 21.52/21.70 cut (((e1) = (e1)) = ((e0) = (e1))). % 21.52/21.70 intro zenon_D_pnotp. % 21.52/21.70 apply zenon_H48. % 21.52/21.70 rewrite <- zenon_D_pnotp. % 21.52/21.70 exact zenon_H49. % 21.52/21.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.52/21.70 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 21.52/21.70 congruence. % 21.52/21.70 cut (((op (e2) (e0)) = (e0)) = ((e1) = (e0))). % 21.52/21.70 intro zenon_D_pnotp. % 21.52/21.70 apply zenon_H4b. % 21.52/21.70 rewrite <- zenon_D_pnotp. % 21.52/21.70 exact zenon_H2d. % 21.52/21.70 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.52/21.70 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 21.52/21.70 congruence. % 21.52/21.70 exact (zenon_H7c zenon_H54). % 21.52/21.70 apply zenon_H46. apply refl_equal. % 21.52/21.70 apply zenon_H4a. apply refl_equal. % 21.52/21.70 apply zenon_H4a. apply refl_equal. % 21.52/21.70 (* end of lemma zenon_L217_ *) % 21.52/21.70 assert (zenon_L218_ : (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> False). % 21.52/21.70 do 0 intro. intros zenon_H77 zenon_H93 zenon_H128. % 21.52/21.70 cut (((op (e2) (e3)) = (e2)) = ((e1) = (e2))). % 21.52/21.70 intro zenon_D_pnotp. % 21.52/21.70 apply zenon_H77. % 21.52/21.70 rewrite <- zenon_D_pnotp. % 21.52/21.70 exact zenon_H93. % 21.52/21.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.52/21.70 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 21.52/21.70 congruence. % 21.52/21.70 exact (zenon_H1b1 zenon_H128). % 21.52/21.70 apply zenon_H6a. apply refl_equal. % 21.52/21.70 (* end of lemma zenon_L218_ *) % 21.52/21.70 assert (zenon_L219_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.52/21.70 do 0 intro. intros zenon_H13f zenon_H48 zenon_H2d zenon_Hf0 zenon_H3f zenon_H153 zenon_H111 zenon_H77 zenon_H93. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.52/21.70 apply (zenon_L217_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.52/21.70 apply (zenon_L118_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.52/21.70 apply (zenon_L148_); trivial. % 21.52/21.70 apply (zenon_L218_); trivial. % 21.52/21.70 (* end of lemma zenon_L219_ *) % 21.52/21.70 assert (zenon_L220_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H1c6 zenon_Ha9 zenon_H6e zenon_Hb6 zenon_H93 zenon_H68 zenon_H13d zenon_Ha0 zenon_H13f zenon_H48 zenon_Hf0 zenon_H3f zenon_H153 zenon_H111 zenon_H77 zenon_H141 zenon_H1c7. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.52/21.70 apply (zenon_L110_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.52/21.70 apply (zenon_L216_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.52/21.70 apply (zenon_L219_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.52/21.70 apply (zenon_L152_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.52/21.70 exact (zenon_H13d zenon_H14c). % 21.52/21.70 apply (zenon_L158_); trivial. % 21.52/21.70 exact (zenon_H1c7 zenon_Hac). % 21.52/21.70 (* end of lemma zenon_L220_ *) % 21.52/21.70 assert (zenon_L221_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.52/21.70 do 0 intro. intros zenon_Hb1 zenon_H9d zenon_H7d. % 21.52/21.70 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.52/21.70 apply (zenon_L44_); trivial. % 21.52/21.70 (* end of lemma zenon_L221_ *) % 21.52/21.70 assert (zenon_L222_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (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) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> False). % 21.52/21.70 do 0 intro. intros zenon_Hcc zenon_H48 zenon_H2c zenon_H33 zenon_H5d zenon_Ha9 zenon_H55 zenon_H4e zenon_H77 zenon_H68 zenon_H125 zenon_H7d zenon_H9d zenon_Hbc zenon_H94 zenon_H3c zenon_Hb6 zenon_H1e zenon_Ha0 zenon_Hb2. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.52/21.70 apply (zenon_L2_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.52/21.70 apply (zenon_L26_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.52/21.70 apply (zenon_L6_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.52/21.70 apply (zenon_L8_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.52/21.70 apply (zenon_L9_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.52/21.70 apply (zenon_L11_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.52/21.70 apply (zenon_L16_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.52/21.70 apply (zenon_L18_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.52/21.70 apply (zenon_L19_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.52/21.70 apply (zenon_L200_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.52/21.70 apply (zenon_L37_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.52/21.70 apply (zenon_L106_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.52/21.70 apply (zenon_L40_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.52/21.70 apply (zenon_L221_); trivial. % 21.52/21.70 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.52/21.70 apply (zenon_L49_); trivial. % 21.52/21.70 apply (zenon_L51_); trivial. % 21.52/21.70 (* end of lemma zenon_L222_ *) % 21.52/21.70 assert (zenon_L223_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (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) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (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 (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 (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (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 (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 (e2) (e2)))) -> (((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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 21.52/21.70 do 0 intro. intros zenon_H1ca zenon_H164 zenon_H163 zenon_H158 zenon_H156 zenon_H48 zenon_H139 zenon_H77 zenon_Hcc zenon_Hbc zenon_Hb6 zenon_Hb2 zenon_Ha9 zenon_Ha0 zenon_H94 zenon_H55 zenon_H82 zenon_H7d zenon_H13a zenon_H13b zenon_H13c zenon_H140 zenon_H100 zenon_H12e zenon_H117 zenon_H111 zenon_H109 zenon_H11a zenon_H121 zenon_H104 zenon_H13e zenon_H131 zenon_H125 zenon_H129 zenon_H13f zenon_H141 zenon_Hf0 zenon_Hf5 zenon_Hfa zenon_Heb zenon_He4 zenon_He2 zenon_H73 zenon_H6f zenon_H68 zenon_H15d zenon_H5d zenon_H4e zenon_H3c zenon_H33 zenon_H2c zenon_H24 zenon_H1e zenon_H1c0. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H13d | zenon_intro zenon_H65 ]. % 21.52/21.70 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 21.52/21.70 apply (zenon_L109_); trivial. % 21.52/21.70 apply (zenon_L222_); trivial. % 21.52/21.70 apply (zenon_L52_); trivial. % 21.52/21.70 (* end of lemma zenon_L223_ *) % 21.52/21.70 assert (zenon_L224_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (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 (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((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 (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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((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)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (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)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 21.54/21.71 do 0 intro. intros zenon_H1c0 zenon_H1e zenon_H24 zenon_H2c zenon_H33 zenon_H4e zenon_H5d zenon_H15d zenon_H6f zenon_He2 zenon_He4 zenon_Heb zenon_Hfa zenon_Hf5 zenon_H129 zenon_H125 zenon_H131 zenon_H13e zenon_H104 zenon_H121 zenon_H11a zenon_H109 zenon_H117 zenon_H12e zenon_H100 zenon_H140 zenon_H13c zenon_H13b zenon_H13a zenon_H7d zenon_H82 zenon_H55 zenon_H94 zenon_Hb2 zenon_Hbc zenon_Hcc zenon_H139 zenon_H156 zenon_H158 zenon_H163 zenon_H164 zenon_H1ca zenon_H1c7 zenon_H141 zenon_H77 zenon_H111 zenon_Hf0 zenon_H13f zenon_Ha0 zenon_H13d zenon_H68 zenon_H93 zenon_Hb6 zenon_H6e zenon_Ha9 zenon_H1c6 zenon_H73 zenon_H153 zenon_H48 zenon_H136. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.71 apply (zenon_L223_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.71 apply (zenon_L220_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.71 apply (zenon_L184_); trivial. % 21.54/21.71 apply (zenon_L157_); trivial. % 21.54/21.71 (* end of lemma zenon_L224_ *) % 21.54/21.71 assert (zenon_L225_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((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 (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 (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (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 (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((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 (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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (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) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.71 do 0 intro. intros zenon_Hbc zenon_H160 zenon_H1c0 zenon_H1e zenon_H24 zenon_H2c zenon_H33 zenon_H16a zenon_H183 zenon_H179 zenon_H177 zenon_H173 zenon_He3 zenon_H5d zenon_H15d zenon_H68 zenon_H6f zenon_H73 zenon_He2 zenon_He4 zenon_Heb zenon_Hfa zenon_Hf5 zenon_Hf0 zenon_H141 zenon_H13f zenon_H129 zenon_H125 zenon_H131 zenon_H13e zenon_H104 zenon_H121 zenon_H11a zenon_H109 zenon_H111 zenon_H117 zenon_H12e zenon_H100 zenon_H140 zenon_H13c zenon_H13b zenon_H13a zenon_H7d zenon_H82 zenon_H55 zenon_H94 zenon_Ha0 zenon_Ha9 zenon_Hb2 zenon_Hb6 zenon_Hcc zenon_H139 zenon_H156 zenon_H158 zenon_H163 zenon_H164 zenon_H186 zenon_H189 zenon_H18a zenon_H18d zenon_H4e zenon_H48 zenon_H190 zenon_H1a8 zenon_H1b4 zenon_H1b7 zenon_H1bb zenon_H19a zenon_H162 zenon_H1ca zenon_H1c7 zenon_H13d zenon_H1c6 zenon_H153 zenon_H77 zenon_H93 zenon_H196. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.71 apply (zenon_L20_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.71 apply (zenon_L20_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.71 apply (zenon_L41_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.71 apply (zenon_L110_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.71 apply (zenon_L95_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.71 apply (zenon_L171_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.71 exact (zenon_He3 zenon_He7). % 21.54/21.71 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.71 apply (zenon_L24_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.71 apply (zenon_L220_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.71 apply (zenon_L117_); trivial. % 21.54/21.71 apply (zenon_L159_); trivial. % 21.54/21.71 apply (zenon_L224_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.71 apply (zenon_L203_); trivial. % 21.54/21.71 apply (zenon_L104_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.71 apply (zenon_L94_); trivial. % 21.54/21.71 apply (zenon_L167_); trivial. % 21.54/21.71 (* end of lemma zenon_L225_ *) % 21.54/21.71 assert (zenon_L226_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> False). % 21.54/21.71 do 0 intro. intros zenon_H173 zenon_H6e zenon_Hef. % 21.54/21.71 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H173. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H6e. % 21.54/21.71 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 21.54/21.71 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 21.54/21.71 congruence. % 21.54/21.71 apply zenon_H193. apply refl_equal. % 21.54/21.71 apply zenon_Hf2. apply sym_equal. exact zenon_Hef. % 21.54/21.71 (* end of lemma zenon_L226_ *) % 21.54/21.71 assert (zenon_L227_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 21.54/21.71 do 0 intro. intros zenon_H163 zenon_H72 zenon_H160. % 21.54/21.71 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H163. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H72. % 21.54/21.71 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 21.54/21.71 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.54/21.71 congruence. % 21.54/21.71 apply zenon_H50. apply refl_equal. % 21.54/21.71 apply zenon_H178. apply sym_equal. exact zenon_H160. % 21.54/21.71 (* end of lemma zenon_L227_ *) % 21.54/21.71 assert (zenon_L228_ : ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H93 zenon_Hf7 zenon_H195. % 21.54/21.71 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 21.54/21.71 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H195. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H95. % 21.54/21.71 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.54/21.71 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 21.54/21.71 congruence. % 21.54/21.71 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H1ab. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H93. % 21.54/21.71 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 21.54/21.71 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.54/21.71 congruence. % 21.54/21.71 apply zenon_H96. apply refl_equal. % 21.54/21.71 apply zenon_Hf8. apply sym_equal. exact zenon_Hf7. % 21.54/21.71 apply zenon_H96. apply refl_equal. % 21.54/21.71 apply zenon_H96. apply refl_equal. % 21.54/21.71 (* end of lemma zenon_L228_ *) % 21.54/21.71 assert (zenon_L229_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.71 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H25 zenon_H6e zenon_H173 zenon_H160 zenon_H163 zenon_H93 zenon_H195. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.71 apply (zenon_L171_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.71 apply (zenon_L226_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.71 apply (zenon_L227_); trivial. % 21.54/21.71 apply (zenon_L228_); trivial. % 21.54/21.71 (* end of lemma zenon_L229_ *) % 21.54/21.71 assert (zenon_L230_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H1c6 zenon_Ha9 zenon_H6e zenon_Hb6 zenon_H3f zenon_H93 zenon_H68 zenon_H13d zenon_Ha0 zenon_H2c zenon_H1e zenon_H141 zenon_H1c7. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.71 apply (zenon_L110_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.71 apply (zenon_L216_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.71 apply (zenon_L5_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.71 apply (zenon_L152_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.71 exact (zenon_H13d zenon_H14c). % 21.54/21.71 apply (zenon_L158_); trivial. % 21.54/21.71 exact (zenon_H1c7 zenon_Hac). % 21.54/21.71 (* end of lemma zenon_L230_ *) % 21.54/21.71 assert (zenon_L231_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 21.54/21.71 do 0 intro. intros zenon_H104 zenon_H8a zenon_H160. % 21.54/21.71 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H104. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H8a. % 21.54/21.71 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 21.54/21.71 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.54/21.71 congruence. % 21.54/21.71 apply zenon_H108. apply refl_equal. % 21.54/21.71 apply zenon_H178. apply sym_equal. exact zenon_H160. % 21.54/21.71 (* end of lemma zenon_L231_ *) % 21.54/21.71 assert (zenon_L232_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 21.54/21.71 do 0 intro. intros zenon_H99 zenon_H104 zenon_H8a. % 21.54/21.71 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.54/21.71 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.54/21.71 apply (zenon_L231_); trivial. % 21.54/21.71 (* end of lemma zenon_L232_ *) % 21.54/21.71 assert (zenon_L233_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H13e zenon_H13d zenon_H4d zenon_H131 zenon_H104 zenon_H99 zenon_Hfe zenon_H111. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H14c | zenon_intro zenon_H151 ]. % 21.54/21.71 exact (zenon_H13d zenon_H14c). % 21.54/21.71 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H105 | zenon_intro zenon_H152 ]. % 21.54/21.71 apply (zenon_L128_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H8a | zenon_intro zenon_H110 ]. % 21.54/21.71 apply (zenon_L232_); trivial. % 21.54/21.71 apply (zenon_L75_); trivial. % 21.54/21.71 (* end of lemma zenon_L233_ *) % 21.54/21.71 assert (zenon_L234_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 21.54/21.71 do 0 intro. intros zenon_Heb zenon_Hbc zenon_H160 zenon_H94 zenon_H77 zenon_H125 zenon_H1c7 zenon_H141 zenon_H1e zenon_H2c zenon_Ha0 zenon_H68 zenon_H93 zenon_Hb6 zenon_H6e zenon_Ha9 zenon_H1c6 zenon_H111 zenon_Hfe zenon_H99 zenon_H104 zenon_H131 zenon_H13d zenon_H13e zenon_H48 zenon_H136. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.71 apply (zenon_L105_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.71 apply (zenon_L230_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.71 apply (zenon_L233_); trivial. % 21.54/21.71 apply (zenon_L157_); trivial. % 21.54/21.71 (* end of lemma zenon_L234_ *) % 21.54/21.71 assert (zenon_L235_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (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)) = (op (e1) (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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H139 zenon_Hb6 zenon_H13b zenon_H195 zenon_H163 zenon_H173 zenon_Hfa zenon_He3 zenon_Hf5 zenon_H100 zenon_H54 zenon_Heb zenon_Hbc zenon_H94 zenon_H125 zenon_H1c7 zenon_H141 zenon_H1e zenon_H2c zenon_Ha0 zenon_H68 zenon_H93 zenon_Ha9 zenon_H1c6 zenon_H111 zenon_H99 zenon_H104 zenon_H131 zenon_H13d zenon_H13e zenon_H48 zenon_H13a zenon_H160 zenon_H177 zenon_H155 zenon_H77. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.71 apply (zenon_L20_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.71 apply (zenon_L41_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.71 apply (zenon_L110_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.71 apply (zenon_L229_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.71 exact (zenon_He3 zenon_He7). % 21.54/21.71 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.71 apply (zenon_L69_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.71 apply (zenon_L230_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.71 apply (zenon_L117_); trivial. % 21.54/21.71 apply (zenon_L192_); trivial. % 21.54/21.71 apply (zenon_L234_); trivial. % 21.54/21.71 apply (zenon_L115_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.71 apply (zenon_L122_); trivial. % 21.54/21.71 apply (zenon_L98_); trivial. % 21.54/21.71 (* end of lemma zenon_L235_ *) % 21.54/21.71 assert (zenon_L236_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H17c zenon_H160 zenon_H1cb. % 21.54/21.71 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.54/21.71 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H1cb. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H12a. % 21.54/21.71 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.71 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1cc]. % 21.54/21.71 congruence. % 21.54/21.71 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H1cc. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H17c. % 21.54/21.71 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 21.54/21.71 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.71 congruence. % 21.54/21.71 apply zenon_H12b. apply refl_equal. % 21.54/21.71 apply zenon_H178. apply sym_equal. exact zenon_H160. % 21.54/21.71 apply zenon_H12b. apply refl_equal. % 21.54/21.71 apply zenon_H12b. apply refl_equal. % 21.54/21.71 (* end of lemma zenon_L236_ *) % 21.54/21.71 assert (zenon_L237_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H1bb zenon_H162 zenon_H120 zenon_H1cb zenon_H160 zenon_Hc4. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.54/21.71 exact (zenon_H162 zenon_H167). % 21.54/21.71 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.54/21.71 exact (zenon_H120 zenon_H11f). % 21.54/21.71 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.54/21.71 apply (zenon_L236_); trivial. % 21.54/21.71 exact (zenon_Hc4 zenon_Hc3). % 21.54/21.71 (* end of lemma zenon_L237_ *) % 21.54/21.71 assert (zenon_L238_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 21.54/21.71 do 0 intro. intros zenon_Hc2 zenon_H162 zenon_H120 zenon_H1cb zenon_H160 zenon_H1bb. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.54/21.71 apply (zenon_L237_); trivial. % 21.54/21.71 apply (zenon_L237_); trivial. % 21.54/21.71 (* end of lemma zenon_L238_ *) % 21.54/21.71 assert (zenon_L239_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H31 zenon_H153 zenon_H48. % 21.54/21.71 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H49 | zenon_intro zenon_H4a ]. % 21.54/21.71 cut (((e1) = (e1)) = ((e0) = (e1))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H48. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H49. % 21.54/21.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.71 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 21.54/21.71 congruence. % 21.54/21.71 cut (((op (e0) (e2)) = (e0)) = ((e1) = (e0))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H4b. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H31. % 21.54/21.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.54/21.71 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 21.54/21.71 congruence. % 21.54/21.71 exact (zenon_H154 zenon_H153). % 21.54/21.71 apply zenon_H46. apply refl_equal. % 21.54/21.71 apply zenon_H4a. apply refl_equal. % 21.54/21.71 apply zenon_H4a. apply refl_equal. % 21.54/21.71 (* end of lemma zenon_L239_ *) % 21.54/21.71 assert (zenon_L240_ : ((op (e3) (e2)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H160 zenon_H171 zenon_H1cd. % 21.54/21.71 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 21.54/21.71 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e1)) = (op (e3) (e2)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H1cd. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_Hbd. % 21.54/21.71 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.54/21.71 cut (((op (e3) (e2)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1ce]. % 21.54/21.71 congruence. % 21.54/21.71 cut (((op (e3) (e2)) = (e2)) = ((op (e3) (e2)) = (op (e3) (e1)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H1ce. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H160. % 21.54/21.71 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 21.54/21.71 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.54/21.71 congruence. % 21.54/21.71 apply zenon_Hbe. apply refl_equal. % 21.54/21.71 apply zenon_H172. apply sym_equal. exact zenon_H171. % 21.54/21.71 apply zenon_Hbe. apply refl_equal. % 21.54/21.71 apply zenon_Hbe. apply refl_equal. % 21.54/21.71 (* end of lemma zenon_L240_ *) % 21.54/21.71 assert (zenon_L241_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H1cf zenon_H153 zenon_H77 zenon_Hf3 zenon_H68 zenon_H8b zenon_H171 zenon_H1cd. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.71 apply (zenon_L94_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.71 apply (zenon_L62_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.71 exact (zenon_H8b zenon_H8a). % 21.54/21.71 apply (zenon_L240_); trivial. % 21.54/21.71 (* end of lemma zenon_L241_ *) % 21.54/21.71 assert (zenon_L242_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 21.54/21.71 do 0 intro. intros zenon_H1a8 zenon_H196 zenon_Hb9 zenon_H177 zenon_Ha9 zenon_H1e zenon_H13a zenon_H3f zenon_H1ba zenon_H140 zenon_H48 zenon_H1cd zenon_H8b zenon_H68 zenon_H77 zenon_H153 zenon_H1cf zenon_H13d zenon_Ha0 zenon_Hbb. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.54/21.71 apply (zenon_L181_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.54/21.71 apply (zenon_L186_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.54/21.71 exact (zenon_H1ba zenon_H6d). % 21.54/21.71 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.71 apply (zenon_L239_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.71 apply (zenon_L241_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.71 exact (zenon_H13d zenon_H14c). % 21.54/21.71 apply (zenon_L80_); trivial. % 21.54/21.71 (* end of lemma zenon_L242_ *) % 21.54/21.71 assert (zenon_L243_ : (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((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 (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (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) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (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))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (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 (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (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 (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((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))))) -> (~((e0) = (e1))) -> False). % 21.54/21.71 do 0 intro. intros zenon_He3 zenon_H162 zenon_Hf6 zenon_H19a zenon_H2c zenon_H15d zenon_H6f zenon_H73 zenon_He2 zenon_He4 zenon_Hfa zenon_Hf5 zenon_Hf0 zenon_H141 zenon_H13f zenon_H129 zenon_H121 zenon_H11a zenon_H109 zenon_H111 zenon_H117 zenon_H12e zenon_H100 zenon_H13c zenon_H4e zenon_H5d zenon_H7d zenon_H82 zenon_H55 zenon_Hcc zenon_H139 zenon_H156 zenon_H158 zenon_H125 zenon_H13b zenon_H33 zenon_H163 zenon_H164 zenon_H24 zenon_Hbc zenon_H94 zenon_Hb2 zenon_Heb zenon_Hb6 zenon_Ha6 zenon_Ha0 zenon_H1cf zenon_H153 zenon_H77 zenon_H68 zenon_H1cd zenon_H140 zenon_H1ba zenon_H13a zenon_H1e zenon_Ha9 zenon_H177 zenon_Hb9 zenon_H196 zenon_H1a8 zenon_H104 zenon_Hbb zenon_H8b zenon_H131 zenon_H13d zenon_H13e zenon_H48. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.71 apply (zenon_L116_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.71 exact (zenon_He3 zenon_He7). % 21.54/21.71 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.71 apply (zenon_L109_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.71 apply (zenon_L242_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.71 apply (zenon_L117_); trivial. % 21.54/21.71 apply (zenon_L166_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.71 apply (zenon_L46_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.71 apply (zenon_L242_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.71 apply (zenon_L130_); trivial. % 21.54/21.71 apply (zenon_L157_); trivial. % 21.54/21.71 (* end of lemma zenon_L243_ *) % 21.54/21.71 assert (zenon_L244_ : (((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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (((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 (e2) (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) (e1)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (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 (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (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)) = (op (e3) (e0)))) -> (((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))))) -> (~((e0) = (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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H19a zenon_H1cf zenon_H1cd zenon_H196 zenon_H177 zenon_Hb6 zenon_Ha9 zenon_H48 zenon_H13e zenon_H13d zenon_H131 zenon_H8b zenon_H104 zenon_H1a8 zenon_H1ba zenon_H1bb zenon_H162 zenon_H1b4 zenon_H1b7 zenon_Hc0 zenon_H129 zenon_Heb zenon_Hb2 zenon_Ha0 zenon_H1e zenon_H24 zenon_H164 zenon_H163 zenon_H33 zenon_H13b zenon_H125 zenon_H68 zenon_H158 zenon_H156 zenon_H139 zenon_Hcc zenon_H55 zenon_H82 zenon_H7d zenon_H5d zenon_H4e zenon_H13a zenon_H13c zenon_H140 zenon_H100 zenon_H12e zenon_H117 zenon_H111 zenon_H109 zenon_H11a zenon_H121 zenon_H13f zenon_H141 zenon_Hf0 zenon_Hfa zenon_He4 zenon_He2 zenon_H73 zenon_H6f zenon_H15d zenon_H2c zenon_Hf5 zenon_He3 zenon_H94 zenon_Hb9 zenon_Hbb zenon_Hbc zenon_H77. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.71 apply (zenon_L13_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.71 apply (zenon_L179_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.71 apply (zenon_L20_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.71 apply (zenon_L181_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.71 apply (zenon_L94_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.71 apply (zenon_L41_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.71 apply (zenon_L243_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.71 apply (zenon_L47_); trivial. % 21.54/21.71 apply (zenon_L48_); trivial. % 21.54/21.71 apply (zenon_L194_); trivial. % 21.54/21.71 (* end of lemma zenon_L244_ *) % 21.54/21.71 assert (zenon_L245_ : ((op (e3) (e0)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H9d zenon_H9f zenon_H33. % 21.54/21.71 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H10a | zenon_intro zenon_H81 ]. % 21.54/21.71 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e0) (e0)) = (op (e3) (e0)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H33. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H10a. % 21.54/21.71 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 21.54/21.71 cut (((op (e3) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d2]. % 21.54/21.71 congruence. % 21.54/21.71 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e0) (e0)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H1d2. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H9d. % 21.54/21.71 cut (((e3) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 21.54/21.71 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 21.54/21.71 congruence. % 21.54/21.71 apply zenon_H81. apply refl_equal. % 21.54/21.71 apply zenon_H1d3. apply sym_equal. exact zenon_H9f. % 21.54/21.71 apply zenon_H81. apply refl_equal. % 21.54/21.71 apply zenon_H81. apply refl_equal. % 21.54/21.71 (* end of lemma zenon_L245_ *) % 21.54/21.71 assert (zenon_L246_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H38 zenon_H155 zenon_H48. % 21.54/21.71 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H49 | zenon_intro zenon_H4a ]. % 21.54/21.71 cut (((e1) = (e1)) = ((e0) = (e1))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H48. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H49. % 21.54/21.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.71 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 21.54/21.71 congruence. % 21.54/21.71 cut (((op (e0) (e3)) = (e0)) = ((e1) = (e0))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H4b. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H38. % 21.54/21.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.54/21.71 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H16f]. % 21.54/21.71 congruence. % 21.54/21.71 exact (zenon_H16f zenon_H155). % 21.54/21.71 apply zenon_H46. apply refl_equal. % 21.54/21.71 apply zenon_H4a. apply refl_equal. % 21.54/21.71 apply zenon_H4a. apply refl_equal. % 21.54/21.71 (* end of lemma zenon_L246_ *) % 21.54/21.71 assert (zenon_L247_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H19a zenon_H48 zenon_H155 zenon_Ha5 zenon_Ha0 zenon_H93 zenon_H68 zenon_H162. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.54/21.71 apply (zenon_L246_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.54/21.71 apply (zenon_L90_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.54/21.71 apply (zenon_L158_); trivial. % 21.54/21.71 exact (zenon_H162 zenon_H167). % 21.54/21.71 (* end of lemma zenon_L247_ *) % 21.54/21.71 assert (zenon_L248_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H13c zenon_H179 zenon_H9d zenon_Hb6 zenon_H3f zenon_Hfe zenon_H73 zenon_H19a zenon_H48 zenon_H155 zenon_Ha0 zenon_H93 zenon_H68 zenon_H162. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.71 apply (zenon_L123_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.71 apply (zenon_L216_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.71 apply (zenon_L89_); trivial. % 21.54/21.71 apply (zenon_L247_); trivial. % 21.54/21.71 (* end of lemma zenon_L248_ *) % 21.54/21.71 assert (zenon_L249_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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))))) -> (~((e0) = (e1))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H13b zenon_He3 zenon_Hf5 zenon_Heb zenon_H77 zenon_H76 zenon_H162 zenon_H68 zenon_H93 zenon_Ha0 zenon_H155 zenon_H19a zenon_H73 zenon_Hb6 zenon_H9d zenon_H179 zenon_H13c zenon_H111 zenon_Hfe zenon_H99 zenon_H104 zenon_H131 zenon_H13d zenon_H13e zenon_H48. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.71 apply (zenon_L171_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.71 exact (zenon_He3 zenon_He7). % 21.54/21.71 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.71 apply (zenon_L24_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.71 apply (zenon_L248_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.71 apply (zenon_L117_); trivial. % 21.54/21.71 apply (zenon_L192_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.71 apply (zenon_L24_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.71 apply (zenon_L248_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.71 apply (zenon_L233_); trivial. % 21.54/21.71 apply (zenon_L157_); trivial. % 21.54/21.71 (* end of lemma zenon_L249_ *) % 21.54/21.71 assert (zenon_L250_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> False). % 21.54/21.71 do 0 intro. intros zenon_Heb zenon_H48 zenon_H25 zenon_H40 zenon_H1d4 zenon_Hec. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.71 apply (zenon_L25_); trivial. % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.71 exact (zenon_H40 zenon_H3f). % 21.54/21.71 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.71 exact (zenon_H1d4 zenon_H4d). % 21.54/21.71 exact (zenon_Hec zenon_H5c). % 21.54/21.71 (* end of lemma zenon_L250_ *) % 21.54/21.71 assert (zenon_L251_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H47 zenon_H67 zenon_H77. % 21.54/21.71 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.54/21.71 cut (((e2) = (e2)) = ((e1) = (e2))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H77. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H69. % 21.54/21.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.54/21.71 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 21.54/21.71 congruence. % 21.54/21.71 cut (((op (e0) (e0)) = (e1)) = ((e2) = (e1))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H78. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H47. % 21.54/21.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.71 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 21.54/21.71 congruence. % 21.54/21.71 exact (zenon_H6c zenon_H67). % 21.54/21.71 apply zenon_H4a. apply refl_equal. % 21.54/21.71 apply zenon_H6a. apply refl_equal. % 21.54/21.71 apply zenon_H6a. apply refl_equal. % 21.54/21.71 (* end of lemma zenon_L251_ *) % 21.54/21.71 assert (zenon_L252_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H66 zenon_H67 zenon_H1d5. % 21.54/21.71 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H135 ]. % 21.54/21.71 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e0)) = (op (e0) (e2)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H1d5. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H1d6. % 21.54/21.71 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 21.54/21.71 cut (((op (e0) (e2)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d7]. % 21.54/21.71 congruence. % 21.54/21.71 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e0) (e0)))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_H1d7. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H66. % 21.54/21.71 cut (((e2) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 21.54/21.71 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 21.54/21.71 congruence. % 21.54/21.71 apply zenon_H135. apply refl_equal. % 21.54/21.71 apply zenon_H1b0. apply sym_equal. exact zenon_H67. % 21.54/21.71 apply zenon_H135. apply refl_equal. % 21.54/21.71 apply zenon_H135. apply refl_equal. % 21.54/21.71 (* end of lemma zenon_L252_ *) % 21.54/21.71 assert (zenon_L253_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 21.54/21.71 do 0 intro. intros zenon_H47 zenon_H9f zenon_Hb6. % 21.54/21.71 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.54/21.71 cut (((e3) = (e3)) = ((e1) = (e3))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_Hb6. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_Ha1. % 21.54/21.71 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.71 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 21.54/21.71 congruence. % 21.54/21.71 cut (((op (e0) (e0)) = (e1)) = ((e3) = (e1))). % 21.54/21.71 intro zenon_D_pnotp. % 21.54/21.71 apply zenon_Hb7. % 21.54/21.71 rewrite <- zenon_D_pnotp. % 21.54/21.71 exact zenon_H47. % 21.54/21.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.72 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 21.54/21.72 congruence. % 21.54/21.72 exact (zenon_Ha4 zenon_H9f). % 21.54/21.72 apply zenon_H4a. apply refl_equal. % 21.54/21.72 apply zenon_Ha2. apply refl_equal. % 21.54/21.72 apply zenon_Ha2. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L253_ *) % 21.54/21.72 assert (zenon_L254_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H31 zenon_H2a zenon_H1d8. % 21.54/21.72 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H135 ]. % 21.54/21.72 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e1)) = (op (e0) (e2)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1d8. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H1d6. % 21.54/21.72 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 21.54/21.72 cut (((op (e0) (e2)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1d9]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e1)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1d9. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H31. % 21.54/21.72 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 21.54/21.72 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H135. apply refl_equal. % 21.54/21.72 apply zenon_H1da. apply sym_equal. exact zenon_H2a. % 21.54/21.72 apply zenon_H135. apply refl_equal. % 21.54/21.72 apply zenon_H135. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L254_ *) % 21.54/21.72 assert (zenon_L255_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H14c zenon_H105 zenon_H48. % 21.54/21.72 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H49 | zenon_intro zenon_H4a ]. % 21.54/21.72 cut (((e1) = (e1)) = ((e0) = (e1))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H48. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H49. % 21.54/21.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.72 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e2) (e2)) = (e0)) = ((e1) = (e0))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H4b. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H14c. % 21.54/21.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.54/21.72 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1bf]. % 21.54/21.72 congruence. % 21.54/21.72 exact (zenon_H1bf zenon_H105). % 21.54/21.72 apply zenon_H46. apply refl_equal. % 21.54/21.72 apply zenon_H4a. apply refl_equal. % 21.54/21.72 apply zenon_H4a. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L255_ *) % 21.54/21.72 assert (zenon_L256_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H13f zenon_H65 zenon_H77 zenon_Hb6 zenon_H10d zenon_H48 zenon_H14c zenon_H195 zenon_H5c. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.54/21.72 apply (zenon_L30_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.54/21.72 apply (zenon_L113_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.54/21.72 apply (zenon_L255_); trivial. % 21.54/21.72 apply (zenon_L149_); trivial. % 21.54/21.72 (* end of lemma zenon_L256_ *) % 21.54/21.72 assert (zenon_L257_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H104 zenon_H14c zenon_H11d. % 21.54/21.72 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H104. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H14c. % 21.54/21.72 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 21.54/21.72 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H108. apply refl_equal. % 21.54/21.72 apply zenon_H168. apply sym_equal. exact zenon_H11d. % 21.54/21.72 (* end of lemma zenon_L257_ *) % 21.54/21.72 assert (zenon_L258_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H111 zenon_H66 zenon_H8a. % 21.54/21.72 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H111. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H66. % 21.54/21.72 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 21.54/21.72 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H135. apply refl_equal. % 21.54/21.72 apply zenon_H132. apply sym_equal. exact zenon_H8a. % 21.54/21.72 (* end of lemma zenon_L258_ *) % 21.54/21.72 assert (zenon_L259_ : ((op (e2) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H110 zenon_H133 zenon_H131. % 21.54/21.72 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H112 | zenon_intro zenon_H108 ]. % 21.54/21.72 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H131. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H112. % 21.54/21.72 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.54/21.72 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1db. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H110. % 21.54/21.72 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 21.54/21.72 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H108. apply refl_equal. % 21.54/21.72 apply zenon_H134. apply sym_equal. exact zenon_H133. % 21.54/21.72 apply zenon_H108. apply refl_equal. % 21.54/21.72 apply zenon_H108. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L259_ *) % 21.54/21.72 assert (zenon_L260_ : (((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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H13e zenon_H11d zenon_H104 zenon_H1bf zenon_H66 zenon_H111 zenon_H133 zenon_H131. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H14c | zenon_intro zenon_H151 ]. % 21.54/21.72 apply (zenon_L257_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H105 | zenon_intro zenon_H152 ]. % 21.54/21.72 exact (zenon_H1bf zenon_H105). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H8a | zenon_intro zenon_H110 ]. % 21.54/21.72 apply (zenon_L258_); trivial. % 21.54/21.72 apply (zenon_L259_); trivial. % 21.54/21.72 (* end of lemma zenon_L260_ *) % 21.54/21.72 assert (zenon_L261_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (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 (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H140 zenon_H1d8 zenon_H2a zenon_Ha0 zenon_H5c zenon_H195 zenon_H48 zenon_H10d zenon_Hb6 zenon_H77 zenon_H65 zenon_H13f zenon_H13e zenon_H104 zenon_H1bf zenon_H66 zenon_H111 zenon_H133 zenon_H131. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.72 apply (zenon_L254_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.72 apply (zenon_L162_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.72 apply (zenon_L256_); trivial. % 21.54/21.72 apply (zenon_L260_); trivial. % 21.54/21.72 (* end of lemma zenon_L261_ *) % 21.54/21.72 assert (zenon_L262_ : ((op (e1) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_Ha5 zenon_H9e zenon_Hf5. % 21.54/21.72 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H5e | zenon_intro zenon_H5f ]. % 21.54/21.72 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_Hf5. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H5e. % 21.54/21.72 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.54/21.72 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1be. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_Ha5. % 21.54/21.72 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 21.54/21.72 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H5f. apply refl_equal. % 21.54/21.72 apply zenon_H198. apply sym_equal. exact zenon_H9e. % 21.54/21.72 apply zenon_H5f. apply refl_equal. % 21.54/21.72 apply zenon_H5f. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L262_ *) % 21.54/21.72 assert (zenon_L263_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha0 zenon_H2a zenon_Ha9 zenon_H66 zenon_Ha5 zenon_Hf5. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.72 apply (zenon_L53_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.72 apply (zenon_L193_); trivial. % 21.54/21.72 apply (zenon_L262_); trivial. % 21.54/21.72 (* end of lemma zenon_L263_ *) % 21.54/21.72 assert (zenon_L264_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H31 zenon_H66 zenon_H68. % 21.54/21.72 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.54/21.72 cut (((e2) = (e2)) = ((e0) = (e2))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H68. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H69. % 21.54/21.72 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.54/21.72 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e0) (e2)) = (e0)) = ((e2) = (e0))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H6b. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H31. % 21.54/21.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.54/21.72 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 21.54/21.72 congruence. % 21.54/21.72 exact (zenon_H1dc zenon_H66). % 21.54/21.72 apply zenon_H46. apply refl_equal. % 21.54/21.72 apply zenon_H6a. apply refl_equal. % 21.54/21.72 apply zenon_H6a. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L264_ *) % 21.54/21.72 assert (zenon_L265_ : ((op (e2) (e2)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H14c zenon_H133 zenon_Hef. % 21.54/21.72 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_H1de | zenon_intro zenon_H1dd ]. % 21.54/21.72 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1df | zenon_intro zenon_H1e0 ]. % 21.54/21.72 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (e1) (e1))))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1de. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H1df. % 21.54/21.72 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 21.54/21.72 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e2) (e2)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1e1. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H14c. % 21.54/21.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.54/21.72 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 21.54/21.72 congruence. % 21.54/21.72 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1df | zenon_intro zenon_H1e0 ]. % 21.54/21.72 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))))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1e2. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H1df. % 21.54/21.72 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 21.54/21.72 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1b3]. % 21.54/21.72 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1b3]. % 21.54/21.72 congruence. % 21.54/21.72 exact (zenon_H1b3 zenon_Hef). % 21.54/21.72 exact (zenon_H1b3 zenon_Hef). % 21.54/21.72 apply zenon_H1e0. apply refl_equal. % 21.54/21.72 apply zenon_H1e0. apply refl_equal. % 21.54/21.72 apply zenon_H46. apply refl_equal. % 21.54/21.72 apply zenon_H1e0. apply refl_equal. % 21.54/21.72 apply zenon_H1e0. apply refl_equal. % 21.54/21.72 apply (zenon_notand_s _ _ zenon_H1dd); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H1e4 ]. % 21.54/21.72 apply zenon_Hf2. apply sym_equal. exact zenon_Hef. % 21.54/21.72 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e6 ]. % 21.54/21.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((e3) = (op (e1) (op (e1) (e1))))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1e4. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H1e5. % 21.54/21.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 21.54/21.72 cut (((op (e1) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e7]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e1) (e2)) = (e3)) = ((op (e1) (op (e1) (e1))) = (e3))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1e7. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H133. % 21.54/21.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.72 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 21.54/21.72 congruence. % 21.54/21.72 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e6 ]. % 21.54/21.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e2)) = (op (e1) (op (e1) (e1))))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1e8. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H1e5. % 21.54/21.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 21.54/21.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1b3]. % 21.54/21.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H4a. apply refl_equal. % 21.54/21.72 exact (zenon_H1b3 zenon_Hef). % 21.54/21.72 apply zenon_H1e6. apply refl_equal. % 21.54/21.72 apply zenon_H1e6. apply refl_equal. % 21.54/21.72 apply zenon_Ha2. apply refl_equal. % 21.54/21.72 apply zenon_H1e6. apply refl_equal. % 21.54/21.72 apply zenon_H1e6. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L265_ *) % 21.54/21.72 assert (zenon_L266_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H167 zenon_H11d zenon_H1cb. % 21.54/21.72 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.54/21.72 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1cb. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H12a. % 21.54/21.72 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.72 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1cc]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1cc. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H167. % 21.54/21.72 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 21.54/21.72 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H12b. apply refl_equal. % 21.54/21.72 apply zenon_H168. apply sym_equal. exact zenon_H11d. % 21.54/21.72 apply zenon_H12b. apply refl_equal. % 21.54/21.72 apply zenon_H12b. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L266_ *) % 21.54/21.72 assert (zenon_L267_ : (((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)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H19a zenon_Ha0 zenon_H9e zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H11d zenon_H1cb. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.54/21.72 apply (zenon_L156_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.54/21.72 apply (zenon_L157_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.54/21.72 apply (zenon_L158_); trivial. % 21.54/21.72 apply (zenon_L266_); trivial. % 21.54/21.72 (* end of lemma zenon_L267_ *) % 21.54/21.72 assert (zenon_L268_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H17c zenon_H102 zenon_H18a. % 21.54/21.72 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.54/21.72 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H18a. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H12a. % 21.54/21.72 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.72 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H18b. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H17c. % 21.54/21.72 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 21.54/21.72 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H12b. apply refl_equal. % 21.54/21.72 apply zenon_H161. apply sym_equal. exact zenon_H102. % 21.54/21.72 apply zenon_H12b. apply refl_equal. % 21.54/21.72 apply zenon_H12b. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L268_ *) % 21.54/21.72 assert (zenon_L269_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H1c3 zenon_Ha9 zenon_H77 zenon_H1cb zenon_H11d zenon_H68 zenon_H48 zenon_H5c zenon_H9e zenon_Ha0 zenon_H19a zenon_H102 zenon_H18a. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.54/21.72 apply (zenon_L92_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.54/21.72 apply (zenon_L206_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.54/21.72 apply (zenon_L267_); trivial. % 21.54/21.72 apply (zenon_L268_); trivial. % 21.54/21.72 (* end of lemma zenon_L269_ *) % 21.54/21.72 assert (zenon_L270_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H140 zenon_H66 zenon_Hef zenon_H133 zenon_H1c3 zenon_Ha9 zenon_H77 zenon_H1cb zenon_H68 zenon_H48 zenon_H5c zenon_H9e zenon_Ha0 zenon_H19a zenon_H102 zenon_H18a. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.72 apply (zenon_L264_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.72 apply (zenon_L162_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.72 apply (zenon_L265_); trivial. % 21.54/21.72 apply (zenon_L269_); trivial. % 21.54/21.72 (* end of lemma zenon_L270_ *) % 21.54/21.72 assert (zenon_L271_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 21.54/21.72 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_H1d4 zenon_Hfa zenon_Hf5 zenon_Ha9 zenon_H2a zenon_Ha0 zenon_H47 zenon_Hb6 zenon_H13a zenon_H140 zenon_H1c3 zenon_H1cb zenon_H68 zenon_H48 zenon_H19a zenon_H102 zenon_H18a zenon_H159 zenon_H25 zenon_H13c zenon_H73 zenon_H66 zenon_H77. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.72 apply (zenon_L53_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.72 apply (zenon_L193_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.72 exact (zenon_H7a zenon_H3c). % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.72 exact (zenon_H40 zenon_H3f). % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.72 exact (zenon_H1d4 zenon_H4d). % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.72 apply (zenon_L171_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.72 apply (zenon_L116_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.72 exact (zenon_H159 zenon_H10c). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.72 apply (zenon_L270_); trivial. % 21.54/21.72 apply (zenon_L263_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.72 apply (zenon_L22_); trivial. % 21.54/21.72 apply (zenon_L206_); trivial. % 21.54/21.72 (* end of lemma zenon_L271_ *) % 21.54/21.72 assert (zenon_L272_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H173 zenon_H2a zenon_He7. % 21.54/21.72 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H173. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H2a. % 21.54/21.72 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1ea]. % 21.54/21.72 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H193. apply refl_equal. % 21.54/21.72 apply zenon_H1ea. apply sym_equal. exact zenon_He7. % 21.54/21.72 (* end of lemma zenon_L272_ *) % 21.54/21.72 assert (zenon_L273_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_H156 zenon_H72 zenon_H159. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 21.54/21.72 apply (zenon_L272_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 21.54/21.72 exact (zenon_H40 zenon_H3f). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 21.54/21.72 apply (zenon_L100_); trivial. % 21.54/21.72 exact (zenon_H159 zenon_H10c). % 21.54/21.72 (* end of lemma zenon_L273_ *) % 21.54/21.72 assert (zenon_L274_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H4e zenon_H25 zenon_Hf3. % 21.54/21.72 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H4e. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H25. % 21.54/21.72 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1eb]. % 21.54/21.72 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H101]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H101. apply refl_equal. % 21.54/21.72 apply zenon_H1eb. apply sym_equal. exact zenon_Hf3. % 21.54/21.72 (* end of lemma zenon_L274_ *) % 21.54/21.72 assert (zenon_L275_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H1ec zenon_H25 zenon_H4e zenon_H1d4 zenon_H8a zenon_H131 zenon_H73 zenon_Hfe. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1ed ]. % 21.54/21.72 apply (zenon_L274_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H4d | zenon_intro zenon_H1ee ]. % 21.54/21.72 exact (zenon_H1d4 zenon_H4d). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H72 | zenon_intro zenon_H133 ]. % 21.54/21.72 apply (zenon_L87_); trivial. % 21.54/21.72 apply (zenon_L89_); trivial. % 21.54/21.72 (* end of lemma zenon_L275_ *) % 21.54/21.72 assert (zenon_L276_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H1cf zenon_Ha9 zenon_H159 zenon_H156 zenon_H40 zenon_H173 zenon_H2a zenon_H158 zenon_H131 zenon_H1ec zenon_H25 zenon_H4e zenon_H1d4 zenon_H163 zenon_H73 zenon_Hfe. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.72 apply (zenon_L193_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.72 apply (zenon_L273_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.72 apply (zenon_L275_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1ed ]. % 21.54/21.72 apply (zenon_L274_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H4d | zenon_intro zenon_H1ee ]. % 21.54/21.72 exact (zenon_H1d4 zenon_H4d). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H72 | zenon_intro zenon_H133 ]. % 21.54/21.72 apply (zenon_L227_); trivial. % 21.54/21.72 apply (zenon_L89_); trivial. % 21.54/21.72 (* end of lemma zenon_L276_ *) % 21.54/21.72 assert (zenon_L277_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((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)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha0 zenon_H73 zenon_H163 zenon_H1d4 zenon_H4e zenon_H25 zenon_H1ec zenon_H131 zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_H156 zenon_H159 zenon_H1cf zenon_Ha9 zenon_Hf6. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.72 apply (zenon_L53_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.72 apply (zenon_L276_); trivial. % 21.54/21.72 apply (zenon_L92_); trivial. % 21.54/21.72 (* end of lemma zenon_L277_ *) % 21.54/21.72 assert (zenon_L278_ : (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_Ha0 zenon_H110 zenon_H14c. % 21.54/21.72 cut (((op (e2) (e2)) = (e3)) = ((e0) = (e3))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_Ha0. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H110. % 21.54/21.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.72 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 21.54/21.72 congruence. % 21.54/21.72 exact (zenon_H13d zenon_H14c). % 21.54/21.72 apply zenon_Ha2. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L278_ *) % 21.54/21.72 assert (zenon_L279_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hb6 zenon_H4d zenon_H14c zenon_Ha0 zenon_H9d zenon_Hbc. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.54/21.72 apply (zenon_L193_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.54/21.72 apply (zenon_L124_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.54/21.72 apply (zenon_L278_); trivial. % 21.54/21.72 apply (zenon_L48_); trivial. % 21.54/21.72 (* end of lemma zenon_L279_ *) % 21.54/21.72 assert (zenon_L280_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H65 zenon_Hb6 zenon_H53 zenon_H14c zenon_Ha0 zenon_H115. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.72 apply (zenon_L43_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.72 apply (zenon_L113_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.72 apply (zenon_L278_); trivial. % 21.54/21.72 apply (zenon_L77_); trivial. % 21.54/21.72 (* end of lemma zenon_L280_ *) % 21.54/21.72 assert (zenon_L281_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H16a zenon_Ha0 zenon_H14c zenon_Hb6 zenon_Ha9 zenon_H117 zenon_H53 zenon_H77 zenon_H66 zenon_H111 zenon_H68 zenon_H115. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.72 apply (zenon_L280_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.72 apply (zenon_L56_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.72 apply (zenon_L258_); trivial. % 21.54/21.72 apply (zenon_L158_); trivial. % 21.54/21.72 (* end of lemma zenon_L281_ *) % 21.54/21.72 assert (zenon_L282_ : ((op (e2) (e2)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H110 zenon_Ha8 zenon_H1ef. % 21.54/21.72 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H112 | zenon_intro zenon_H108 ]. % 21.54/21.72 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1ef. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H112. % 21.54/21.72 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.54/21.72 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f0]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1f0. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H110. % 21.54/21.72 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 21.54/21.72 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H108. apply refl_equal. % 21.54/21.72 apply zenon_Hba. apply sym_equal. exact zenon_Ha8. % 21.54/21.72 apply zenon_H108. apply refl_equal. % 21.54/21.72 apply zenon_H108. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L282_ *) % 21.54/21.72 assert (zenon_L283_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hb6 zenon_H4d zenon_H1ef zenon_Ha8 zenon_Ha0 zenon_H11d. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.54/21.72 apply (zenon_L193_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.54/21.72 apply (zenon_L124_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.54/21.72 apply (zenon_L282_); trivial. % 21.54/21.72 apply (zenon_L80_); trivial. % 21.54/21.72 (* end of lemma zenon_L283_ *) % 21.54/21.72 assert (zenon_L284_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H1f1 zenon_H53 zenon_H7f. % 21.54/21.72 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1f1. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H53. % 21.54/21.72 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 21.54/21.72 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H57. apply refl_equal. % 21.54/21.72 apply zenon_H80. apply sym_equal. exact zenon_H7f. % 21.54/21.72 (* end of lemma zenon_L284_ *) % 21.54/21.72 assert (zenon_L285_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H163 zenon_H4d zenon_H106. % 21.54/21.72 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H163. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H4d. % 21.54/21.72 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 21.54/21.72 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H50. apply refl_equal. % 21.54/21.72 apply zenon_H107. apply sym_equal. exact zenon_H106. % 21.54/21.72 (* end of lemma zenon_L285_ *) % 21.54/21.72 assert (zenon_L286_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H1ec zenon_H25 zenon_H4e zenon_H106 zenon_H163 zenon_H73 zenon_H66 zenon_H110 zenon_H131. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1ed ]. % 21.54/21.72 apply (zenon_L274_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H4d | zenon_intro zenon_H1ee ]. % 21.54/21.72 apply (zenon_L285_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H72 | zenon_intro zenon_H133 ]. % 21.54/21.72 apply (zenon_L22_); trivial. % 21.54/21.72 apply (zenon_L259_); trivial. % 21.54/21.72 (* end of lemma zenon_L286_ *) % 21.54/21.72 assert (zenon_L287_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (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)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H117 zenon_H11d zenon_Ha0 zenon_H1ef zenon_H4d zenon_Ha9 zenon_H1a2 zenon_H10c zenon_Hf0 zenon_H120 zenon_H1ec zenon_H25 zenon_H4e zenon_H163 zenon_H73 zenon_H66 zenon_H131 zenon_H1f1 zenon_H53 zenon_Hb6 zenon_H9d zenon_H12e zenon_H9e zenon_H196. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.72 apply (zenon_L283_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.72 apply (zenon_L74_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.72 apply (zenon_L134_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.72 apply (zenon_L284_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.72 apply (zenon_L286_); trivial. % 21.54/21.72 exact (zenon_H120 zenon_H11f). % 21.54/21.72 apply (zenon_L154_); trivial. % 21.54/21.72 (* end of lemma zenon_L287_ *) % 21.54/21.72 assert (zenon_L288_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H1a8 zenon_H68 zenon_H2a zenon_H1b3 zenon_H65 zenon_H55 zenon_H7f zenon_H77. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.54/21.72 apply (zenon_L147_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.54/21.72 exact (zenon_H1b3 zenon_Hef). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.54/21.72 apply (zenon_L34_); trivial. % 21.54/21.72 apply (zenon_L169_); trivial. % 21.54/21.72 (* end of lemma zenon_L288_ *) % 21.54/21.72 assert (zenon_L289_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H6d zenon_H10d zenon_Ha9. % 21.54/21.72 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.54/21.72 cut (((e3) = (e3)) = ((e2) = (e3))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_Ha9. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_Ha1. % 21.54/21.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.72 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e2) (e1)) = (e2)) = ((e3) = (e2))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_Haa. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H6d. % 21.54/21.72 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.54/21.72 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 21.54/21.72 congruence. % 21.54/21.72 exact (zenon_H16e zenon_H10d). % 21.54/21.72 apply zenon_H6a. apply refl_equal. % 21.54/21.72 apply zenon_Ha2. apply refl_equal. % 21.54/21.72 apply zenon_Ha2. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L289_ *) % 21.54/21.72 assert (zenon_L290_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_H6d zenon_H14c zenon_Ha0 zenon_H9e zenon_H196. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.72 apply (zenon_L151_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.72 apply (zenon_L289_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.72 apply (zenon_L278_); trivial. % 21.54/21.72 apply (zenon_L154_); trivial. % 21.54/21.72 (* end of lemma zenon_L290_ *) % 21.54/21.72 assert (zenon_L291_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H34 zenon_H102 zenon_H68. % 21.54/21.72 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 21.54/21.72 cut (((e2) = (e2)) = ((e0) = (e2))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H68. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H69. % 21.54/21.72 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.54/21.72 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e3) (e0)) = (e0)) = ((e2) = (e0))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H6b. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H34. % 21.54/21.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.54/21.72 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 21.54/21.72 congruence. % 21.54/21.72 exact (zenon_H103 zenon_H102). % 21.54/21.72 apply zenon_H46. apply refl_equal. % 21.54/21.72 apply zenon_H6a. apply refl_equal. % 21.54/21.72 apply zenon_H6a. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L291_ *) % 21.54/21.72 assert (zenon_L292_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H192 zenon_H2a zenon_He0. % 21.54/21.72 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H192. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H2a. % 21.54/21.72 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 21.54/21.72 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H193. apply refl_equal. % 21.54/21.72 apply zenon_H1f2. apply sym_equal. exact zenon_He0. % 21.54/21.72 (* end of lemma zenon_L292_ *) % 21.54/21.72 assert (zenon_L293_ : ((op (e1) (e3)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (op (e1) (op (e1) (e1))))) -> False). % 21.54/21.72 do 0 intro. intros zenon_Hf7 zenon_H10c zenon_H1f3. % 21.54/21.72 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e6 ]. % 21.54/21.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((e2) = (op (e1) (op (e1) (e1))))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1f3. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H1e5. % 21.54/21.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 21.54/21.72 cut (((op (e1) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e1) (e3)) = (e2)) = ((op (e1) (op (e1) (e1))) = (e2))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1f4. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_Hf7. % 21.54/21.72 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.54/21.72 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 21.54/21.72 congruence. % 21.54/21.72 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e6 ]. % 21.54/21.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e3)) = (op (e1) (op (e1) (e1))))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1f5. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H1e5. % 21.54/21.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 21.54/21.72 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 21.54/21.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H4a. apply refl_equal. % 21.54/21.72 exact (zenon_H159 zenon_H10c). % 21.54/21.72 apply zenon_H1e6. apply refl_equal. % 21.54/21.72 apply zenon_H1e6. apply refl_equal. % 21.54/21.72 apply zenon_H6a. apply refl_equal. % 21.54/21.72 apply zenon_H1e6. apply refl_equal. % 21.54/21.72 apply zenon_H1e6. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L293_ *) % 21.54/21.72 assert (zenon_L294_ : ((op (e3) (e3)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H167 zenon_Hf7 zenon_H10c. % 21.54/21.72 apply (zenon_notand_s _ _ ax10); [ zenon_intro zenon_H1de | zenon_intro zenon_H1f7 ]. % 21.54/21.72 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1df | zenon_intro zenon_H1e0 ]. % 21.54/21.72 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (e1) (e1))))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1de. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H1df. % 21.54/21.72 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 21.54/21.72 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e3) (e3)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1e1. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H167. % 21.54/21.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.54/21.72 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 21.54/21.72 congruence. % 21.54/21.72 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1df | zenon_intro zenon_H1e0 ]. % 21.54/21.72 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))))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1f8. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H1df. % 21.54/21.72 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 21.54/21.72 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 21.54/21.72 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 21.54/21.72 congruence. % 21.54/21.72 exact (zenon_H159 zenon_H10c). % 21.54/21.72 exact (zenon_H159 zenon_H10c). % 21.54/21.72 apply zenon_H1e0. apply refl_equal. % 21.54/21.72 apply zenon_H1e0. apply refl_equal. % 21.54/21.72 apply zenon_H46. apply refl_equal. % 21.54/21.72 apply zenon_H1e0. apply refl_equal. % 21.54/21.72 apply zenon_H1e0. apply refl_equal. % 21.54/21.72 apply (zenon_notand_s _ _ zenon_H1f7); [ zenon_intro zenon_H11c | zenon_intro zenon_H1f3 ]. % 21.54/21.72 apply zenon_H11c. apply sym_equal. exact zenon_H10c. % 21.54/21.72 apply (zenon_L293_); trivial. % 21.54/21.72 (* end of lemma zenon_L294_ *) % 21.54/21.72 assert (zenon_L295_ : (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H68 zenon_H17c zenon_H167. % 21.54/21.72 cut (((op (e3) (e3)) = (e2)) = ((e0) = (e2))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H68. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H17c. % 21.54/21.72 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.54/21.72 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 21.54/21.72 congruence. % 21.54/21.72 exact (zenon_H162 zenon_H167). % 21.54/21.72 apply zenon_H6a. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L295_ *) % 21.54/21.72 assert (zenon_L296_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H1c3 zenon_H9e zenon_Ha9 zenon_H10c zenon_H128 zenon_H77 zenon_H68 zenon_H167. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.54/21.72 apply (zenon_L92_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.54/21.72 apply (zenon_L294_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.54/21.72 apply (zenon_L218_); trivial. % 21.54/21.72 apply (zenon_L295_); trivial. % 21.54/21.72 (* end of lemma zenon_L296_ *) % 21.54/21.72 assert (zenon_L297_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H179 zenon_H25 zenon_H34. % 21.54/21.72 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e3) (e0)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H179. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H25. % 21.54/21.72 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 21.54/21.72 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H101]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H101. apply refl_equal. % 21.54/21.72 apply zenon_H35. apply sym_equal. exact zenon_H34. % 21.54/21.72 (* end of lemma zenon_L297_ *) % 21.54/21.72 assert (zenon_L298_ : ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H167 zenon_H115 zenon_H129. % 21.54/21.72 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.54/21.72 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H129. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H12a. % 21.54/21.72 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.72 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H12c. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H167. % 21.54/21.72 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 21.54/21.72 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H12b. apply refl_equal. % 21.54/21.72 apply zenon_H1fa. apply sym_equal. exact zenon_H115. % 21.54/21.72 apply zenon_H12b. apply refl_equal. % 21.54/21.72 apply zenon_H12b. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L298_ *) % 21.54/21.72 assert (zenon_L299_ : (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> False). % 21.54/21.72 do 0 intro. intros zenon_Ha9 zenon_Ha5 zenon_Hf7. % 21.54/21.72 cut (((op (e1) (e3)) = (e3)) = ((e2) = (e3))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_Ha9. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_Ha5. % 21.54/21.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.72 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 21.54/21.72 congruence. % 21.54/21.72 exact (zenon_H1c1 zenon_Hf7). % 21.54/21.72 apply zenon_Ha2. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L299_ *) % 21.54/21.72 assert (zenon_L300_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> (~((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))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (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 (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H13c zenon_H129 zenon_Ha0 zenon_H48 zenon_H7f zenon_H179 zenon_H25 zenon_H164 zenon_Ha8 zenon_H1ef zenon_H66 zenon_H1a2 zenon_H13f zenon_H196 zenon_H6d zenon_H117 zenon_H1f1 zenon_H102 zenon_H2a zenon_H192 zenon_H1c3 zenon_H9e zenon_H77 zenon_H68 zenon_H141 zenon_Hb6 zenon_H4d zenon_Ha9 zenon_Hf7. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.72 apply (zenon_L116_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.72 apply (zenon_L67_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.72 apply (zenon_L54_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.54/21.72 apply (zenon_L290_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.54/21.72 apply (zenon_L284_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.54/21.72 apply (zenon_L255_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.54/21.72 apply (zenon_L193_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.54/21.72 apply (zenon_L124_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.54/21.72 apply (zenon_L278_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.72 apply (zenon_L291_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.72 apply (zenon_L292_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.72 apply (zenon_L80_); trivial. % 21.54/21.72 apply (zenon_L296_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.54/21.72 apply (zenon_L193_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.54/21.72 apply (zenon_L124_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.54/21.72 apply (zenon_L282_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.72 apply (zenon_L297_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.72 apply (zenon_L57_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.72 apply (zenon_L80_); trivial. % 21.54/21.72 apply (zenon_L298_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.72 apply (zenon_L124_); trivial. % 21.54/21.72 apply (zenon_L299_); trivial. % 21.54/21.72 (* end of lemma zenon_L300_ *) % 21.54/21.72 assert (zenon_L301_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((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))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (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 (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 21.54/21.72 do 0 intro. intros zenon_He4 zenon_H40 zenon_Hfa zenon_H1b3 zenon_H13c zenon_H129 zenon_Ha0 zenon_H48 zenon_H179 zenon_H25 zenon_H164 zenon_Ha8 zenon_H1ef zenon_H66 zenon_H1a2 zenon_H13f zenon_H196 zenon_H6d zenon_H117 zenon_H1f1 zenon_H102 zenon_H2a zenon_H192 zenon_H1c3 zenon_H9e zenon_H77 zenon_H68 zenon_H141 zenon_Hb6 zenon_H4d zenon_Ha9. % 21.54/21.72 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.72 apply (zenon_L65_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.72 exact (zenon_H40 zenon_H3f). % 21.54/21.72 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.72 apply (zenon_L56_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.72 apply (zenon_L171_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.72 exact (zenon_H1b3 zenon_Hef). % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.72 apply (zenon_L59_); trivial. % 21.54/21.72 apply (zenon_L300_); trivial. % 21.54/21.72 (* end of lemma zenon_L301_ *) % 21.54/21.72 assert (zenon_L302_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H18d zenon_H9e zenon_Hb6 zenon_H186 zenon_H4d zenon_H93 zenon_H77 zenon_H120. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.54/21.72 apply (zenon_L115_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.54/21.72 apply (zenon_L138_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.54/21.72 apply (zenon_L218_); trivial. % 21.54/21.72 exact (zenon_H120 zenon_H11f). % 21.54/21.72 (* end of lemma zenon_L302_ *) % 21.54/21.72 assert (zenon_L303_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.54/21.72 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H1b3 zenon_Hec zenon_H77 zenon_H40 zenon_H25 zenon_H48 zenon_Heb zenon_Hf5 zenon_Hf6. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.72 apply (zenon_L171_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.72 exact (zenon_H1b3 zenon_Hef). % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.72 apply (zenon_L60_); trivial. % 21.54/21.72 apply (zenon_L63_); trivial. % 21.54/21.72 (* end of lemma zenon_L303_ *) % 21.54/21.72 assert (zenon_L304_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_H1b3 zenon_H159. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 21.54/21.72 apply (zenon_L272_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 21.54/21.72 exact (zenon_H40 zenon_H3f). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 21.54/21.72 exact (zenon_H1b3 zenon_Hef). % 21.54/21.72 exact (zenon_H159 zenon_H10c). % 21.54/21.72 (* end of lemma zenon_L304_ *) % 21.54/21.72 assert (zenon_L305_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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 (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (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 (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (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 (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H15c zenon_H173 zenon_H158 zenon_H77 zenon_H47 zenon_H68 zenon_H2a zenon_H125 zenon_H186 zenon_H18d zenon_Hfa zenon_H129 zenon_H192 zenon_H1c3 zenon_H164 zenon_H13f zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_Hb2 zenon_H28 zenon_H48 zenon_H40 zenon_He4 zenon_H1b3 zenon_H55 zenon_H1a8 zenon_H179 zenon_H141 zenon_H16a zenon_H111 zenon_H117 zenon_H196 zenon_H1f1 zenon_H1ec zenon_H131 zenon_H73 zenon_H163 zenon_H4e zenon_H120 zenon_H12e zenon_Hf0 zenon_H1ef zenon_H140 zenon_Hbc zenon_H1a2 zenon_H13a zenon_Hf5 zenon_H13c zenon_Heb zenon_H25 zenon_H1d5 zenon_H139. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.72 apply (zenon_L251_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.72 apply (zenon_L147_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.72 apply (zenon_L252_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.72 apply (zenon_L171_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.72 apply (zenon_L53_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.72 apply (zenon_L193_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.72 apply (zenon_L116_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.72 apply (zenon_L43_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.72 apply (zenon_L26_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.72 exact (zenon_H40 zenon_H3f). % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.72 apply (zenon_L65_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.72 exact (zenon_H40 zenon_H3f). % 21.54/21.72 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.72 apply (zenon_L123_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.72 apply (zenon_L27_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.72 apply (zenon_L111_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.72 apply (zenon_L279_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.72 apply (zenon_L264_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.72 apply (zenon_L117_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.72 apply (zenon_L281_); trivial. % 21.54/21.72 apply (zenon_L287_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.72 apply (zenon_L124_); trivial. % 21.54/21.72 apply (zenon_L263_); trivial. % 21.54/21.72 apply (zenon_L288_); trivial. % 21.54/21.72 exact (zenon_Hec zenon_H5c). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.72 apply (zenon_L53_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.72 apply (zenon_L193_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.72 apply (zenon_L116_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.72 apply (zenon_L25_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.72 exact (zenon_H40 zenon_H3f). % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.72 apply (zenon_L43_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.72 apply (zenon_L301_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.72 apply (zenon_L258_); trivial. % 21.54/21.72 apply (zenon_L302_); trivial. % 21.54/21.72 exact (zenon_Hec zenon_H5c). % 21.54/21.72 apply (zenon_L91_); trivial. % 21.54/21.72 apply (zenon_L303_); trivial. % 21.54/21.72 apply (zenon_L304_); trivial. % 21.54/21.72 (* end of lemma zenon_L305_ *) % 21.54/21.72 assert (zenon_L306_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H158 zenon_He3 zenon_H40 zenon_H6e zenon_H173 zenon_H159. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 21.54/21.72 exact (zenon_He3 zenon_He7). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 21.54/21.72 exact (zenon_H40 zenon_H3f). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 21.54/21.72 apply (zenon_L226_); trivial. % 21.54/21.72 exact (zenon_H159 zenon_H10c). % 21.54/21.72 (* end of lemma zenon_L306_ *) % 21.54/21.72 assert (zenon_L307_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_Hb2 zenon_Hb6 zenon_H47 zenon_Ha0 zenon_H25 zenon_Ha9 zenon_H65 zenon_Hac zenon_H7d. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.72 apply (zenon_L116_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.72 apply (zenon_L43_); trivial. % 21.54/21.72 apply (zenon_L44_); trivial. % 21.54/21.72 (* end of lemma zenon_L307_ *) % 21.54/21.72 assert (zenon_L308_ : ((op (e1) (e3)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_Ha5 zenon_H133 zenon_H186. % 21.54/21.72 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H5e | zenon_intro zenon_H5f ]. % 21.54/21.72 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e2)) = (op (e1) (e3)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H186. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H5e. % 21.54/21.72 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.54/21.72 cut (((op (e1) (e3)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e1) (e2)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H187. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_Ha5. % 21.54/21.72 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 21.54/21.72 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H5f. apply refl_equal. % 21.54/21.72 apply zenon_H134. apply sym_equal. exact zenon_H133. % 21.54/21.72 apply zenon_H5f. apply refl_equal. % 21.54/21.72 apply zenon_H5f. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L308_ *) % 21.54/21.72 assert (zenon_L309_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H1ec zenon_H25 zenon_H4e zenon_H1d4 zenon_H159 zenon_H156 zenon_H40 zenon_He3 zenon_H158 zenon_Ha5 zenon_H186. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1ed ]. % 21.54/21.72 apply (zenon_L274_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H4d | zenon_intro zenon_H1ee ]. % 21.54/21.72 exact (zenon_H1d4 zenon_H4d). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H72 | zenon_intro zenon_H133 ]. % 21.54/21.72 apply (zenon_L101_); trivial. % 21.54/21.72 apply (zenon_L308_); trivial. % 21.54/21.72 (* end of lemma zenon_L309_ *) % 21.54/21.72 assert (zenon_L310_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H15c zenon_He3 zenon_H40 zenon_H156 zenon_H72 zenon_H158 zenon_H5c. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.54/21.72 exact (zenon_Hec zenon_H5c). % 21.54/21.72 apply (zenon_L101_); trivial. % 21.54/21.72 (* end of lemma zenon_L310_ *) % 21.54/21.72 assert (zenon_L311_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H3e zenon_H5c zenon_H158 zenon_H72 zenon_H156 zenon_He3 zenon_H15c. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 21.54/21.72 apply (zenon_L310_); trivial. % 21.54/21.72 apply (zenon_L310_); trivial. % 21.54/21.72 (* end of lemma zenon_L311_ *) % 21.54/21.72 assert (zenon_L312_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (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) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e1) (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)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((e1) = (e2))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_H73 zenon_H163 zenon_H131 zenon_H2a zenon_H173 zenon_H1cf zenon_Heb zenon_H28 zenon_Hfa zenon_H186 zenon_H40 zenon_H159 zenon_H1d4 zenon_H4e zenon_H25 zenon_H1ec zenon_H140 zenon_H66 zenon_H1c3 zenon_Ha9 zenon_H1cb zenon_H68 zenon_H48 zenon_Ha0 zenon_H19a zenon_H102 zenon_H18a zenon_H13c zenon_H15c zenon_He3 zenon_H156 zenon_H158 zenon_H3e zenon_H77. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.72 apply (zenon_L53_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.72 apply (zenon_L276_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.72 apply (zenon_L26_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.72 exact (zenon_H40 zenon_H3f). % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.72 exact (zenon_H1d4 zenon_H4d). % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.72 apply (zenon_L171_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.72 apply (zenon_L116_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.72 exact (zenon_H159 zenon_H10c). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.72 apply (zenon_L270_); trivial. % 21.54/21.72 apply (zenon_L309_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.72 apply (zenon_L311_); trivial. % 21.54/21.72 apply (zenon_L206_); trivial. % 21.54/21.72 (* end of lemma zenon_L312_ *) % 21.54/21.72 assert (zenon_L313_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((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 (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((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)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H139 zenon_H77 zenon_H3e zenon_He3 zenon_H15c zenon_H13c zenon_H18a zenon_H19a zenon_H48 zenon_H68 zenon_H1cb zenon_H1c3 zenon_H140 zenon_H186 zenon_Hfa zenon_H28 zenon_Heb zenon_Hb2 zenon_Hac zenon_H7d zenon_H1d5 zenon_H125 zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha0 zenon_H73 zenon_H163 zenon_H1d4 zenon_H4e zenon_H25 zenon_H1ec zenon_H131 zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_H156 zenon_H159 zenon_H1cf zenon_Ha9. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.72 apply (zenon_L251_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.72 apply (zenon_L306_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.72 apply (zenon_L252_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.72 apply (zenon_L171_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.72 apply (zenon_L307_); trivial. % 21.54/21.72 apply (zenon_L312_); trivial. % 21.54/21.72 apply (zenon_L277_); trivial. % 21.54/21.72 (* end of lemma zenon_L313_ *) % 21.54/21.72 assert (zenon_L314_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((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)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H139 zenon_H77 zenon_H68 zenon_Hf5 zenon_Ha5 zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha0 zenon_H73 zenon_H163 zenon_H1d4 zenon_H4e zenon_H25 zenon_H1ec zenon_H131 zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_H156 zenon_H159 zenon_H1cf zenon_Ha9. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.72 apply (zenon_L251_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.72 apply (zenon_L147_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.72 apply (zenon_L263_); trivial. % 21.54/21.72 apply (zenon_L277_); trivial. % 21.54/21.72 (* end of lemma zenon_L314_ *) % 21.54/21.72 assert (zenon_L315_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H2f zenon_H2a zenon_H1d8. % 21.54/21.72 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.54/21.72 apply (zenon_L254_); trivial. % 21.54/21.72 (* end of lemma zenon_L315_ *) % 21.54/21.72 assert (zenon_L316_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H38 zenon_H2a zenon_H1fb. % 21.54/21.72 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H1fc | zenon_intro zenon_Hf9 ]. % 21.54/21.72 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e1)) = (op (e0) (e3)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1fb. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H1fc. % 21.54/21.72 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 21.54/21.72 cut (((op (e0) (e3)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 21.54/21.72 congruence. % 21.54/21.72 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e1)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1fd. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H38. % 21.54/21.72 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 21.54/21.72 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_Hf9. apply refl_equal. % 21.54/21.72 apply zenon_H1da. apply sym_equal. exact zenon_H2a. % 21.54/21.72 apply zenon_Hf9. apply refl_equal. % 21.54/21.72 apply zenon_Hf9. apply refl_equal. % 21.54/21.72 (* end of lemma zenon_L316_ *) % 21.54/21.72 assert (zenon_L317_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H36 zenon_H2a zenon_H1fb. % 21.54/21.72 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 21.54/21.72 apply (zenon_L316_); trivial. % 21.54/21.72 (* end of lemma zenon_L317_ *) % 21.54/21.72 assert (zenon_L318_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H3a zenon_H2a zenon_H48. % 21.54/21.72 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 21.54/21.72 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 21.54/21.72 apply (zenon_L65_); trivial. % 21.54/21.72 (* end of lemma zenon_L318_ *) % 21.54/21.72 assert (zenon_L319_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H5a zenon_H77 zenon_H6d. % 21.54/21.72 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.54/21.72 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.54/21.72 apply (zenon_L56_); trivial. % 21.54/21.72 (* end of lemma zenon_L319_ *) % 21.54/21.72 assert (zenon_L320_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H13a zenon_H47 zenon_Ha0 zenon_H2a zenon_Ha9 zenon_H66 zenon_H16a zenon_H7b zenon_H5a zenon_H8b zenon_H18d zenon_Hb6 zenon_H186 zenon_H4d zenon_H77 zenon_H120. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.72 apply (zenon_L53_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.72 apply (zenon_L193_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.72 exact (zenon_H7b zenon_H65). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.72 apply (zenon_L319_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.72 exact (zenon_H8b zenon_H8a). % 21.54/21.72 apply (zenon_L302_); trivial. % 21.54/21.72 (* end of lemma zenon_L320_ *) % 21.54/21.72 assert (zenon_L321_ : (((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))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H16a zenon_H7b zenon_H53 zenon_H77 zenon_H8b zenon_Hf6 zenon_H196. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.72 exact (zenon_H7b zenon_H65). % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.72 apply (zenon_L56_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.72 exact (zenon_H8b zenon_H8a). % 21.54/21.72 apply (zenon_L167_); trivial. % 21.54/21.72 (* end of lemma zenon_L321_ *) % 21.54/21.72 assert (zenon_L322_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((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 (e2) (e0)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H139 zenon_H68 zenon_H120 zenon_H4d zenon_H186 zenon_Hb6 zenon_H18d zenon_H5a zenon_Ha9 zenon_H2a zenon_Ha0 zenon_H47 zenon_H13a zenon_H16a zenon_H7b zenon_H53 zenon_H77 zenon_H8b zenon_H196. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.72 apply (zenon_L251_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.72 apply (zenon_L147_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.72 apply (zenon_L320_); trivial. % 21.54/21.72 apply (zenon_L321_); trivial. % 21.54/21.72 (* end of lemma zenon_L322_ *) % 21.54/21.72 assert (zenon_L323_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (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 (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_Hb2 zenon_Hb6 zenon_H47 zenon_Ha0 zenon_H25 zenon_H16b zenon_H8b zenon_H77 zenon_H53 zenon_Ha9 zenon_H16a zenon_Hac zenon_H7d. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.72 apply (zenon_L116_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.72 apply (zenon_L112_); trivial. % 21.54/21.72 apply (zenon_L44_); trivial. % 21.54/21.72 (* end of lemma zenon_L323_ *) % 21.54/21.72 assert (zenon_L324_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (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 (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((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))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (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 (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H1c6 zenon_H2a zenon_Hfe zenon_H111 zenon_Hf0 zenon_H109 zenon_H117 zenon_H13d zenon_H48 zenon_H65 zenon_H68 zenon_H141 zenon_Hb2 zenon_Hb6 zenon_H47 zenon_Ha0 zenon_H25 zenon_H16b zenon_H8b zenon_H77 zenon_H53 zenon_Ha9 zenon_H16a zenon_H7d. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.72 apply (zenon_L116_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.72 apply (zenon_L43_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.72 apply (zenon_L53_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.72 apply (zenon_L27_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.72 apply (zenon_L111_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.72 exact (zenon_H13d zenon_H14c). % 21.54/21.72 apply (zenon_L78_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.72 apply (zenon_L113_); trivial. % 21.54/21.72 apply (zenon_L323_); trivial. % 21.54/21.72 (* end of lemma zenon_L324_ *) % 21.54/21.72 assert (zenon_L325_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 21.54/21.72 do 0 intro. intros zenon_Hb2 zenon_Hb6 zenon_H47 zenon_Ha0 zenon_H25 zenon_H16b zenon_H8b zenon_H77 zenon_H53 zenon_H16a zenon_Ha9 zenon_H102. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.72 apply (zenon_L116_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.72 apply (zenon_L112_); trivial. % 21.54/21.72 apply (zenon_L91_); trivial. % 21.54/21.72 (* end of lemma zenon_L325_ *) % 21.54/21.72 assert (zenon_L326_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((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))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H13a zenon_H7d zenon_H16a zenon_H53 zenon_H77 zenon_H8b zenon_H16b zenon_H25 zenon_Ha0 zenon_H47 zenon_Hb6 zenon_Hb2 zenon_H141 zenon_H68 zenon_H65 zenon_H48 zenon_H13d zenon_H117 zenon_H109 zenon_Hf0 zenon_H111 zenon_H2a zenon_H1c6 zenon_Ha9 zenon_Hf6. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.72 apply (zenon_L53_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.72 apply (zenon_L324_); trivial. % 21.54/21.72 apply (zenon_L92_); trivial. % 21.54/21.72 (* end of lemma zenon_L326_ *) % 21.54/21.72 assert (zenon_L327_ : (((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)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H16a zenon_H68 zenon_H2d zenon_H53 zenon_H77 zenon_H8b zenon_H16b. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.72 apply (zenon_L27_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.72 apply (zenon_L56_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.72 exact (zenon_H8b zenon_H8a). % 21.54/21.72 exact (zenon_H16b zenon_H93). % 21.54/21.72 (* end of lemma zenon_L327_ *) % 21.54/21.72 assert (zenon_L328_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_Hbc zenon_H34 zenon_H11d. % 21.54/21.72 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_Hbc. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H34. % 21.54/21.72 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 21.54/21.72 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_H81. apply refl_equal. % 21.54/21.72 apply zenon_H168. apply sym_equal. exact zenon_H11d. % 21.54/21.72 (* end of lemma zenon_L328_ *) % 21.54/21.72 assert (zenon_L329_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H140 zenon_H1d8 zenon_H2a zenon_H4d zenon_H48 zenon_H13d zenon_Hbc zenon_H34. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.72 apply (zenon_L254_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.72 apply (zenon_L117_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.72 exact (zenon_H13d zenon_H14c). % 21.54/21.72 apply (zenon_L328_); trivial. % 21.54/21.72 (* end of lemma zenon_L329_ *) % 21.54/21.72 assert (zenon_L330_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (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) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (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) (e2)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 21.54/21.72 do 0 intro. intros zenon_H92 zenon_H190 zenon_H13e zenon_H48 zenon_H47 zenon_H139 zenon_H13a zenon_H13c zenon_Hf5 zenon_H4e zenon_H196 zenon_H1f1 zenon_H1ec zenon_H131 zenon_H73 zenon_H163 zenon_H120 zenon_H12e zenon_H4d zenon_H1ef zenon_H1a2 zenon_H140 zenon_H179 zenon_Ha9 zenon_H1c6 zenon_H16a zenon_H8b zenon_H7d zenon_Hb2 zenon_H53 zenon_H13d zenon_H117 zenon_H111 zenon_Hf0 zenon_H109 zenon_H141 zenon_Ha0 zenon_Hb6 zenon_H125 zenon_H2a zenon_H68 zenon_H77 zenon_Hbc zenon_H1d8 zenon_H1fe. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.72 apply (zenon_L13_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.72 apply (zenon_L251_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.72 apply (zenon_L147_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.72 apply (zenon_L251_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.72 apply (zenon_L171_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.72 apply (zenon_L53_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.72 apply (zenon_L324_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.72 apply (zenon_L253_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.72 apply (zenon_L116_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.72 apply (zenon_L112_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.72 apply (zenon_L123_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.72 apply (zenon_L264_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.72 apply (zenon_L274_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.72 exact (zenon_H13d zenon_H14c). % 21.54/21.72 apply (zenon_L287_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.72 apply (zenon_L124_); trivial. % 21.54/21.72 apply (zenon_L262_); trivial. % 21.54/21.72 apply (zenon_L325_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.72 apply (zenon_L251_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.72 apply (zenon_L171_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.72 apply (zenon_L326_); trivial. % 21.54/21.72 apply (zenon_L325_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.72 apply (zenon_L327_); trivial. % 21.54/21.72 apply (zenon_L329_); trivial. % 21.54/21.72 apply (zenon_L144_); trivial. % 21.54/21.72 (* end of lemma zenon_L330_ *) % 21.54/21.72 assert (zenon_L331_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H1cd zenon_H7f zenon_H106. % 21.54/21.72 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 21.54/21.72 intro zenon_D_pnotp. % 21.54/21.72 apply zenon_H1cd. % 21.54/21.72 rewrite <- zenon_D_pnotp. % 21.54/21.72 exact zenon_H7f. % 21.54/21.72 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 21.54/21.72 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 21.54/21.72 congruence. % 21.54/21.72 apply zenon_Hae. apply refl_equal. % 21.54/21.72 apply zenon_H107. apply sym_equal. exact zenon_H106. % 21.54/21.72 (* end of lemma zenon_L331_ *) % 21.54/21.72 assert (zenon_L332_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 21.54/21.72 do 0 intro. intros zenon_H201 zenon_H66 zenon_H77 zenon_Hf3 zenon_H48 zenon_H1bf zenon_H1cd zenon_H7f. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.72 apply (zenon_L94_); trivial. % 21.54/21.72 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.73 apply (zenon_L117_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.73 exact (zenon_H1bf zenon_H105). % 21.54/21.73 apply (zenon_L331_); trivial. % 21.54/21.73 (* end of lemma zenon_L332_ *) % 21.54/21.73 assert (zenon_L333_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.54/21.73 do 0 intro. intros zenon_H13b zenon_Ha0 zenon_Ha6 zenon_H2a zenon_H173 zenon_H7f zenon_H1cd zenon_H1bf zenon_H77 zenon_H66 zenon_H201 zenon_H48 zenon_H5c. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.73 apply (zenon_L116_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.73 apply (zenon_L272_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.73 apply (zenon_L332_); trivial. % 21.54/21.73 apply (zenon_L157_); trivial. % 21.54/21.73 (* end of lemma zenon_L333_ *) % 21.54/21.73 assert (zenon_L334_ : (((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) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.54/21.73 do 0 intro. intros zenon_H13f zenon_Hb6 zenon_Ha8 zenon_H7f zenon_H1f1 zenon_H1bf zenon_H195 zenon_H5c. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.54/21.73 apply (zenon_L151_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.54/21.73 apply (zenon_L284_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.54/21.73 exact (zenon_H1bf zenon_H105). % 21.54/21.73 apply (zenon_L149_); trivial. % 21.54/21.73 (* end of lemma zenon_L334_ *) % 21.54/21.73 assert (zenon_L335_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H61 zenon_H4d zenon_H186. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.54/21.73 apply (zenon_L138_); trivial. % 21.54/21.73 (* end of lemma zenon_L335_ *) % 21.54/21.73 assert (zenon_L336_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.54/21.73 do 0 intro. intros zenon_H13a zenon_H47 zenon_Ha0 zenon_H2a zenon_H7f zenon_H1cd zenon_H1bf zenon_H61 zenon_H186 zenon_Hb6 zenon_H201 zenon_Ha9 zenon_Hf6. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.73 apply (zenon_L253_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.73 apply (zenon_L53_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.73 apply (zenon_L95_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.73 apply (zenon_L335_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.73 exact (zenon_H1bf zenon_H105). % 21.54/21.73 apply (zenon_L331_); trivial. % 21.54/21.73 apply (zenon_L92_); trivial. % 21.54/21.73 (* end of lemma zenon_L336_ *) % 21.54/21.73 assert (zenon_L337_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.54/21.73 do 0 intro. intros zenon_H13b zenon_H68 zenon_H76 zenon_H2a zenon_H173 zenon_H7f zenon_H1cd zenon_H1bf zenon_H77 zenon_H66 zenon_H201 zenon_H48 zenon_H5c. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.73 apply (zenon_L171_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.73 apply (zenon_L272_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.73 apply (zenon_L332_); trivial. % 21.54/21.73 apply (zenon_L157_); trivial. % 21.54/21.73 (* end of lemma zenon_L337_ *) % 21.54/21.73 assert (zenon_L338_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.54/21.73 do 0 intro. intros zenon_H13f zenon_H65 zenon_H77 zenon_H7f zenon_H1f1 zenon_H1bf zenon_H195 zenon_H5c. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.54/21.73 apply (zenon_L30_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.54/21.73 apply (zenon_L284_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.54/21.73 exact (zenon_H1bf zenon_H105). % 21.54/21.73 apply (zenon_L149_); trivial. % 21.54/21.73 (* end of lemma zenon_L338_ *) % 21.54/21.73 assert (zenon_L339_ : (((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) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (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)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H164 zenon_H2a zenon_H192 zenon_H18a zenon_H102 zenon_H19a zenon_Ha0 zenon_H9e zenon_H5c zenon_H48 zenon_H68 zenon_H1cb zenon_H77 zenon_Ha9 zenon_H1c3 zenon_H162. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.73 apply (zenon_L291_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.73 apply (zenon_L292_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.73 apply (zenon_L269_); trivial. % 21.54/21.73 exact (zenon_H162 zenon_H167). % 21.54/21.73 (* end of lemma zenon_L339_ *) % 21.54/21.73 assert (zenon_L340_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (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)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_H66 zenon_H164 zenon_H2a zenon_H192 zenon_H18a zenon_H102 zenon_H19a zenon_Ha0 zenon_H5c zenon_H48 zenon_H68 zenon_H1cb zenon_H77 zenon_Ha9 zenon_H1c3 zenon_H162. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.73 apply (zenon_L253_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.73 apply (zenon_L53_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.73 apply (zenon_L193_); trivial. % 21.54/21.73 apply (zenon_L339_); trivial. % 21.54/21.73 (* end of lemma zenon_L340_ *) % 21.54/21.73 assert (zenon_L341_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> False). % 21.54/21.73 do 0 intro. intros zenon_H204 zenon_H47 zenon_H2a. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 21.54/21.73 exact (zenon_H205 zenon_H2a). % 21.54/21.73 exact (zenon_H4c zenon_H47). % 21.54/21.73 (* end of lemma zenon_L341_ *) % 21.54/21.73 assert (zenon_L342_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> False). % 21.54/21.73 do 0 intro. intros zenon_H63 zenon_H47 zenon_H2a. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.54/21.73 apply (zenon_L341_); trivial. % 21.54/21.73 (* end of lemma zenon_L342_ *) % 21.54/21.73 assert (zenon_L343_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H87 zenon_H4d zenon_H77. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 21.54/21.73 apply (zenon_L59_); trivial. % 21.54/21.73 (* end of lemma zenon_L343_ *) % 21.54/21.73 assert (zenon_L344_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 21.54/21.73 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_H77 zenon_H87 zenon_Hec. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.73 exact (zenon_H7a zenon_H3c). % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.73 apply (zenon_L343_); trivial. % 21.54/21.73 exact (zenon_Hec zenon_H5c). % 21.54/21.73 (* end of lemma zenon_L344_ *) % 21.54/21.73 assert (zenon_L345_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H15c zenon_H173 zenon_H2a zenon_H156 zenon_H72 zenon_H158 zenon_H7a zenon_H40 zenon_H87 zenon_H77 zenon_Heb. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.54/21.73 apply (zenon_L344_); trivial. % 21.54/21.73 apply (zenon_L273_); trivial. % 21.54/21.73 (* end of lemma zenon_L345_ *) % 21.54/21.73 assert (zenon_L346_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e3)) = (e1))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H125 zenon_H4e zenon_H68 zenon_Hb2 zenon_H47 zenon_Hec zenon_H72 zenon_H77 zenon_H40 zenon_Hb6 zenon_Heb zenon_Ha0 zenon_H2d zenon_Ha9. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.73 apply (zenon_L251_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.73 apply (zenon_L83_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.73 apply (zenon_L27_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.73 apply (zenon_L253_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.73 apply (zenon_L66_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.73 apply (zenon_L67_); trivial. % 21.54/21.73 apply (zenon_L91_); trivial. % 21.54/21.73 (* end of lemma zenon_L346_ *) % 21.54/21.73 assert (zenon_L347_ : ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H17c zenon_Hf6 zenon_H1b4. % 21.54/21.73 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.54/21.73 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 21.54/21.73 intro zenon_D_pnotp. % 21.54/21.73 apply zenon_H1b4. % 21.54/21.73 rewrite <- zenon_D_pnotp. % 21.54/21.73 exact zenon_H12a. % 21.54/21.73 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.73 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 21.54/21.73 congruence. % 21.54/21.73 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 21.54/21.73 intro zenon_D_pnotp. % 21.54/21.73 apply zenon_H1b5. % 21.54/21.73 rewrite <- zenon_D_pnotp. % 21.54/21.73 exact zenon_H17c. % 21.54/21.73 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1a6]. % 21.54/21.73 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.73 congruence. % 21.54/21.73 apply zenon_H12b. apply refl_equal. % 21.54/21.73 apply zenon_H1a6. apply sym_equal. exact zenon_Hf6. % 21.54/21.73 apply zenon_H12b. apply refl_equal. % 21.54/21.73 apply zenon_H12b. apply refl_equal. % 21.54/21.73 (* end of lemma zenon_L347_ *) % 21.54/21.73 assert (zenon_L348_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H7f zenon_H72 zenon_H163 zenon_Hf6 zenon_H1b4. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.54/21.73 apply (zenon_L291_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.54/21.73 apply (zenon_L169_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.54/21.73 apply (zenon_L227_); trivial. % 21.54/21.73 apply (zenon_L347_); trivial. % 21.54/21.73 (* end of lemma zenon_L348_ *) % 21.54/21.73 assert (zenon_L349_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_He4 zenon_H48 zenon_H2a zenon_H40 zenon_H6d zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H72 zenon_H163 zenon_Hf6 zenon_H1b4. % 21.54/21.73 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.73 apply (zenon_L65_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.73 apply (zenon_L56_); trivial. % 21.54/21.73 apply (zenon_L348_); trivial. % 21.54/21.73 (* end of lemma zenon_L349_ *) % 21.54/21.73 assert (zenon_L350_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H139 zenon_H47 zenon_H73 zenon_He4 zenon_H48 zenon_H2a zenon_H40 zenon_H6d zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H72 zenon_H163 zenon_H1b4. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.73 apply (zenon_L251_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.73 apply (zenon_L147_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.73 apply (zenon_L22_); trivial. % 21.54/21.73 apply (zenon_L349_); trivial. % 21.54/21.73 (* end of lemma zenon_L350_ *) % 21.54/21.73 assert (zenon_L351_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((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 (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e1) (e1)) = (e1))) -> (((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)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H1fe zenon_H73 zenon_He4 zenon_H163 zenon_H1b4 zenon_H183 zenon_H139 zenon_H47 zenon_H4e zenon_H68 zenon_Hb2 zenon_Ha9 zenon_Ha0 zenon_Hb6 zenon_H125 zenon_H48 zenon_H19d zenon_Heb zenon_H77 zenon_H87 zenon_H40 zenon_H158 zenon_H156 zenon_H2a zenon_H173. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 21.54/21.73 apply (zenon_L345_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.73 apply (zenon_L161_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.73 apply (zenon_L60_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.73 apply (zenon_L346_); trivial. % 21.54/21.73 apply (zenon_L350_); trivial. % 21.54/21.73 apply (zenon_L102_); trivial. % 21.54/21.73 (* end of lemma zenon_L351_ *) % 21.54/21.73 assert (zenon_L352_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H139 zenon_H77 zenon_H47 zenon_H68 zenon_H2a zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.73 apply (zenon_L251_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.73 apply (zenon_L147_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.73 apply (zenon_L122_); trivial. % 21.54/21.73 apply (zenon_L167_); trivial. % 21.54/21.73 (* end of lemma zenon_L352_ *) % 21.54/21.73 assert (zenon_L353_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H99 zenon_H139 zenon_H77 zenon_H47 zenon_H68 zenon_H2a zenon_H177 zenon_H196. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.54/21.73 apply (zenon_L352_); trivial. % 21.54/21.73 (* end of lemma zenon_L353_ *) % 21.54/21.73 assert (zenon_L354_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> False). % 21.54/21.73 do 0 intro. intros zenon_H9b zenon_H47 zenon_H2a. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.54/21.73 apply (zenon_L341_); trivial. % 21.54/21.73 (* end of lemma zenon_L354_ *) % 21.54/21.73 assert (zenon_L355_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_Hb2 zenon_Hb6 zenon_H47 zenon_H5d zenon_Ha5 zenon_Ha0 zenon_H2d zenon_Hac zenon_H7d. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.73 apply (zenon_L253_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.73 apply (zenon_L42_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.73 apply (zenon_L67_); trivial. % 21.54/21.73 apply (zenon_L44_); trivial. % 21.54/21.73 (* end of lemma zenon_L355_ *) % 21.54/21.73 assert (zenon_L356_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_Hb2 zenon_Hb6 zenon_H47 zenon_H5d zenon_Ha5 zenon_Ha9 zenon_H65 zenon_Hac zenon_H7d. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.73 apply (zenon_L253_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.73 apply (zenon_L42_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.73 apply (zenon_L43_); trivial. % 21.54/21.73 apply (zenon_L44_); trivial. % 21.54/21.73 (* end of lemma zenon_L356_ *) % 21.54/21.73 assert (zenon_L357_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H1fe zenon_H19d zenon_H2a zenon_H48 zenon_Ha0 zenon_H125 zenon_Hec zenon_H1d4 zenon_H40 zenon_H77 zenon_Heb zenon_H7d zenon_Hac zenon_Ha9 zenon_Ha5 zenon_H5d zenon_H47 zenon_Hb6 zenon_Hb2 zenon_H68. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.73 apply (zenon_L161_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.73 apply (zenon_L250_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.73 apply (zenon_L355_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.73 apply (zenon_L251_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.73 apply (zenon_L24_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.73 exact (zenon_H1d4 zenon_H4d). % 21.54/21.73 exact (zenon_Hec zenon_H5c). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.73 apply (zenon_L356_); trivial. % 21.54/21.73 apply (zenon_L291_); trivial. % 21.54/21.73 (* end of lemma zenon_L357_ *) % 21.54/21.73 assert (zenon_L358_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H158 zenon_H2a zenon_H40 zenon_H6e zenon_H173 zenon_Hac zenon_H11a. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 21.54/21.73 apply (zenon_L272_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 21.54/21.73 apply (zenon_L226_); trivial. % 21.54/21.73 apply (zenon_L79_); trivial. % 21.54/21.73 (* end of lemma zenon_L358_ *) % 21.54/21.73 assert (zenon_L359_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> False). % 21.54/21.73 do 0 intro. intros zenon_H109 zenon_H2d zenon_H34. % 21.54/21.73 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e3) (e0)))). % 21.54/21.73 intro zenon_D_pnotp. % 21.54/21.73 apply zenon_H109. % 21.54/21.73 rewrite <- zenon_D_pnotp. % 21.54/21.73 exact zenon_H2d. % 21.54/21.73 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 21.54/21.73 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.54/21.73 congruence. % 21.54/21.73 apply zenon_H86. apply refl_equal. % 21.54/21.73 apply zenon_H35. apply sym_equal. exact zenon_H34. % 21.54/21.73 (* end of lemma zenon_L359_ *) % 21.54/21.73 assert (zenon_L360_ : ((op (e3) (e2)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_Hbb zenon_Hac zenon_H1cd. % 21.54/21.73 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 21.54/21.73 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e1)) = (op (e3) (e2)))). % 21.54/21.73 intro zenon_D_pnotp. % 21.54/21.73 apply zenon_H1cd. % 21.54/21.73 rewrite <- zenon_D_pnotp. % 21.54/21.73 exact zenon_Hbd. % 21.54/21.73 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.54/21.73 cut (((op (e3) (e2)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1ce]. % 21.54/21.73 congruence. % 21.54/21.73 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e1)))). % 21.54/21.73 intro zenon_D_pnotp. % 21.54/21.73 apply zenon_H1ce. % 21.54/21.73 rewrite <- zenon_D_pnotp. % 21.54/21.73 exact zenon_Hbb. % 21.54/21.73 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 21.54/21.73 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.54/21.73 congruence. % 21.54/21.73 apply zenon_Hbe. apply refl_equal. % 21.54/21.73 apply zenon_H207. apply sym_equal. exact zenon_Hac. % 21.54/21.73 apply zenon_Hbe. apply refl_equal. % 21.54/21.73 apply zenon_Hbe. apply refl_equal. % 21.54/21.73 (* end of lemma zenon_L360_ *) % 21.54/21.73 assert (zenon_L361_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_Hb1 zenon_Hbb zenon_H1cd. % 21.54/21.73 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.54/21.73 apply (zenon_L360_); trivial. % 21.54/21.73 (* end of lemma zenon_L361_ *) % 21.54/21.73 assert (zenon_L362_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Hf3 zenon_H14c zenon_Ha0 zenon_Hb1 zenon_H1cd. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.54/21.73 apply (zenon_L95_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.54/21.73 apply (zenon_L162_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.54/21.73 apply (zenon_L278_); trivial. % 21.54/21.73 apply (zenon_L361_); trivial. % 21.54/21.73 (* end of lemma zenon_L362_ *) % 21.54/21.73 assert (zenon_L363_ : (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> False). % 21.54/21.73 do 0 intro. intros zenon_Hb6 zenon_Hbb zenon_H106. % 21.54/21.73 cut (((op (e3) (e2)) = (e3)) = ((e1) = (e3))). % 21.54/21.73 intro zenon_D_pnotp. % 21.54/21.73 apply zenon_Hb6. % 21.54/21.73 rewrite <- zenon_D_pnotp. % 21.54/21.73 exact zenon_Hbb. % 21.54/21.73 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.73 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H208]. % 21.54/21.73 congruence. % 21.54/21.73 exact (zenon_H208 zenon_H106). % 21.54/21.73 apply zenon_Ha2. apply refl_equal. % 21.54/21.73 (* end of lemma zenon_L363_ *) % 21.54/21.73 assert (zenon_L364_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> False). % 21.54/21.73 do 0 intro. intros zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hf3 zenon_H14c zenon_Ha0 zenon_Hb6 zenon_H106. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.54/21.73 apply (zenon_L193_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.54/21.73 apply (zenon_L162_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.54/21.73 apply (zenon_L278_); trivial. % 21.54/21.73 apply (zenon_L363_); trivial. % 21.54/21.73 (* end of lemma zenon_L364_ *) % 21.54/21.73 assert (zenon_L365_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H201 zenon_H77 zenon_H48 zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hf3 zenon_H14c zenon_Ha0 zenon_Hb6. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.73 apply (zenon_L94_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.73 apply (zenon_L117_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.73 apply (zenon_L255_); trivial. % 21.54/21.73 apply (zenon_L364_); trivial. % 21.54/21.73 (* end of lemma zenon_L365_ *) % 21.54/21.73 assert (zenon_L366_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H8a zenon_H6d zenon_H190. % 21.54/21.73 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H112 | zenon_intro zenon_H108 ]. % 21.54/21.73 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 21.54/21.73 intro zenon_D_pnotp. % 21.54/21.73 apply zenon_H190. % 21.54/21.73 rewrite <- zenon_D_pnotp. % 21.54/21.73 exact zenon_H112. % 21.54/21.73 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.54/21.73 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 21.54/21.73 congruence. % 21.54/21.73 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 21.54/21.73 intro zenon_D_pnotp. % 21.54/21.73 apply zenon_H1a1. % 21.54/21.73 rewrite <- zenon_D_pnotp. % 21.54/21.73 exact zenon_H8a. % 21.54/21.73 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 21.54/21.73 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.54/21.73 congruence. % 21.54/21.73 apply zenon_H108. apply refl_equal. % 21.54/21.73 apply zenon_H85. apply sym_equal. exact zenon_H6d. % 21.54/21.73 apply zenon_H108. apply refl_equal. % 21.54/21.73 apply zenon_H108. apply refl_equal. % 21.54/21.73 (* end of lemma zenon_L366_ *) % 21.54/21.73 assert (zenon_L367_ : (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e1)) -> False). % 21.54/21.73 do 0 intro. intros zenon_H77 zenon_H160 zenon_H106. % 21.54/21.73 cut (((op (e3) (e2)) = (e2)) = ((e1) = (e2))). % 21.54/21.73 intro zenon_D_pnotp. % 21.54/21.73 apply zenon_H77. % 21.54/21.73 rewrite <- zenon_D_pnotp. % 21.54/21.73 exact zenon_H160. % 21.54/21.73 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.54/21.73 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H208]. % 21.54/21.73 congruence. % 21.54/21.73 exact (zenon_H208 zenon_H106). % 21.54/21.73 apply zenon_H6a. apply refl_equal. % 21.54/21.73 (* end of lemma zenon_L367_ *) % 21.54/21.73 assert (zenon_L368_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> False). % 21.54/21.73 do 0 intro. intros zenon_H1cf zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Hf3 zenon_Ha9 zenon_H1a2 zenon_H48 zenon_H201 zenon_H4e zenon_H76 zenon_H190 zenon_H6d zenon_H77 zenon_H106. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.73 apply (zenon_L365_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.73 apply (zenon_L83_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.73 apply (zenon_L366_); trivial. % 21.54/21.73 apply (zenon_L367_); trivial. % 21.54/21.73 (* end of lemma zenon_L368_ *) % 21.54/21.73 assert (zenon_L369_ : (((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 (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H183 zenon_H68 zenon_H34 zenon_Hef zenon_H11a zenon_H8a zenon_H104 zenon_Hf6 zenon_H1b4. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.54/21.73 apply (zenon_L291_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.54/21.73 apply (zenon_L119_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.54/21.73 apply (zenon_L231_); trivial. % 21.54/21.73 apply (zenon_L347_); trivial. % 21.54/21.73 (* end of lemma zenon_L369_ *) % 21.54/21.73 assert (zenon_L370_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H141 zenon_H109 zenon_H53 zenon_H196 zenon_H1cf zenon_Hb6 zenon_Ha0 zenon_Hf3 zenon_H1a2 zenon_H48 zenon_H201 zenon_H4e zenon_H76 zenon_H190 zenon_H77 zenon_Hb2 zenon_H47 zenon_H5d zenon_Ha5 zenon_Hac zenon_H7d zenon_H1bf zenon_H1d4 zenon_Hb1 zenon_H1cd zenon_H16a zenon_Ha9 zenon_Ha8 zenon_Hf0 zenon_H1b4 zenon_Hf6 zenon_H104 zenon_H11a zenon_Hef zenon_H34 zenon_H183 zenon_H68. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.73 apply (zenon_L359_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.73 apply (zenon_L111_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.73 apply (zenon_L362_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.73 exact (zenon_H1d4 zenon_H4d). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.73 exact (zenon_H1bf zenon_H105). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.73 apply (zenon_L356_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.73 apply (zenon_L368_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.73 apply (zenon_L369_); trivial. % 21.54/21.73 apply (zenon_L167_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.73 apply (zenon_L43_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.73 apply (zenon_L61_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.73 apply (zenon_L369_); trivial. % 21.54/21.73 apply (zenon_L158_); trivial. % 21.54/21.73 (* end of lemma zenon_L370_ *) % 21.54/21.73 assert (zenon_L371_ : (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> False). % 21.54/21.73 do 0 intro. intros zenon_Ha9 zenon_Hac zenon_H171. % 21.54/21.73 cut (((op (e3) (e1)) = (e3)) = ((e2) = (e3))). % 21.54/21.73 intro zenon_D_pnotp. % 21.54/21.73 apply zenon_Ha9. % 21.54/21.73 rewrite <- zenon_D_pnotp. % 21.54/21.73 exact zenon_Hac. % 21.54/21.73 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.73 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 21.54/21.73 congruence. % 21.54/21.73 exact (zenon_H1a7 zenon_H171). % 21.54/21.73 apply zenon_Ha2. apply refl_equal. % 21.54/21.73 (* end of lemma zenon_L371_ *) % 21.54/21.73 assert (zenon_L372_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_H1b3 zenon_Hac zenon_H11a. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 21.54/21.73 apply (zenon_L272_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 21.54/21.73 exact (zenon_H1b3 zenon_Hef). % 21.54/21.73 apply (zenon_L79_); trivial. % 21.54/21.73 (* end of lemma zenon_L372_ *) % 21.54/21.73 assert (zenon_L373_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H158 zenon_He3 zenon_H40 zenon_H1b3 zenon_Hac zenon_H11a. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 21.54/21.73 exact (zenon_He3 zenon_He7). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 21.54/21.73 exact (zenon_H1b3 zenon_Hef). % 21.54/21.73 apply (zenon_L79_); trivial. % 21.54/21.73 (* end of lemma zenon_L373_ *) % 21.54/21.73 assert (zenon_L374_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H3e zenon_He3 zenon_H1b3 zenon_H11a zenon_Hac zenon_H158. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 21.54/21.73 apply (zenon_L373_); trivial. % 21.54/21.73 apply (zenon_L373_); trivial. % 21.54/21.73 (* end of lemma zenon_L374_ *) % 21.54/21.73 assert (zenon_L375_ : (~((op (e1) (e2)) = (op (e1) (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)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((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 (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (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) (e0)) = (op (e3) (e0)))) -> (((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)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H186 zenon_H139 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Hf5 zenon_H13a zenon_H13b zenon_He4 zenon_H1f1 zenon_H195 zenon_H13f zenon_H141 zenon_Hf0 zenon_H1a2 zenon_H1cd zenon_Hb1 zenon_H1bf zenon_H16a zenon_H196 zenon_H104 zenon_H1b4 zenon_H183 zenon_H201 zenon_H190 zenon_H109 zenon_H1a8 zenon_H11a zenon_H19d zenon_H2a zenon_Heb zenon_H40 zenon_H48 zenon_Hb2 zenon_H7d zenon_Ha0 zenon_H5d zenon_H47 zenon_Hb6 zenon_H125 zenon_H68 zenon_Ha9 zenon_H77 zenon_H1fe. % 21.54/21.73 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.54/21.73 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.54/21.73 apply (zenon_L357_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.73 apply (zenon_L13_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.73 apply (zenon_L314_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.73 apply (zenon_L355_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.73 apply (zenon_L251_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.73 apply (zenon_L358_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.73 apply (zenon_L263_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.73 apply (zenon_L251_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.73 apply (zenon_L253_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.73 apply (zenon_L53_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.73 apply (zenon_L253_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.73 apply (zenon_L42_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.73 apply (zenon_L276_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.73 apply (zenon_L272_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.73 exact (zenon_H7a zenon_H3c). % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.73 exact (zenon_H1d4 zenon_H4d). % 21.54/21.73 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.73 apply (zenon_L65_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.54/21.73 apply (zenon_L358_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.54/21.73 apply (zenon_L370_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.54/21.73 apply (zenon_L56_); trivial. % 21.54/21.73 apply (zenon_L371_); trivial. % 21.54/21.73 apply (zenon_L334_); trivial. % 21.54/21.73 apply (zenon_L90_); trivial. % 21.54/21.73 apply (zenon_L221_); trivial. % 21.54/21.73 apply (zenon_L262_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.73 apply (zenon_L356_); trivial. % 21.54/21.73 apply (zenon_L291_); trivial. % 21.54/21.73 apply (zenon_L372_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.54/21.73 apply (zenon_L357_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.73 apply (zenon_L13_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.73 apply (zenon_L309_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.73 apply (zenon_L355_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.73 apply (zenon_L251_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.73 apply (zenon_L147_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.73 apply (zenon_L263_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.73 apply (zenon_L251_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.73 apply (zenon_L253_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.73 apply (zenon_L53_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.73 apply (zenon_L253_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.73 apply (zenon_L42_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.73 apply (zenon_L276_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.73 exact (zenon_He3 zenon_He7). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.73 apply (zenon_L24_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.73 exact (zenon_H1d4 zenon_H4d). % 21.54/21.73 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.73 apply (zenon_L65_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.54/21.73 apply (zenon_L306_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.54/21.73 apply (zenon_L370_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.54/21.73 apply (zenon_L56_); trivial. % 21.54/21.73 apply (zenon_L371_); trivial. % 21.54/21.73 apply (zenon_L334_); trivial. % 21.54/21.73 apply (zenon_L90_); trivial. % 21.54/21.73 apply (zenon_L221_); trivial. % 21.54/21.73 apply (zenon_L92_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.73 apply (zenon_L356_); trivial. % 21.54/21.73 apply (zenon_L291_); trivial. % 21.54/21.73 apply (zenon_L374_); trivial. % 21.54/21.73 (* end of lemma zenon_L375_ *) % 21.54/21.73 assert (zenon_L376_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha0 zenon_H2a zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.73 apply (zenon_L253_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.73 apply (zenon_L53_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.73 apply (zenon_L178_); trivial. % 21.54/21.73 apply (zenon_L154_); trivial. % 21.54/21.73 (* end of lemma zenon_L376_ *) % 21.54/21.73 assert (zenon_L377_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_Hc0 zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha0 zenon_H2a zenon_H177 zenon_H196. % 21.54/21.73 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.54/21.73 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.54/21.73 apply (zenon_L376_); trivial. % 21.54/21.73 (* end of lemma zenon_L377_ *) % 21.54/21.73 assert (zenon_L378_ : (((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))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H16a zenon_H7b zenon_H53 zenon_H77 zenon_H8b zenon_H16b. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.73 exact (zenon_H7b zenon_H65). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.73 apply (zenon_L56_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.73 exact (zenon_H8b zenon_H8a). % 21.54/21.73 exact (zenon_H16b zenon_H93). % 21.54/21.73 (* end of lemma zenon_L378_ *) % 21.54/21.73 assert (zenon_L379_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hb6 zenon_H4d zenon_H191 zenon_Hac zenon_H1cd. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.54/21.73 apply (zenon_L193_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.54/21.73 apply (zenon_L124_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.54/21.73 exact (zenon_H191 zenon_H110). % 21.54/21.73 apply (zenon_L360_); trivial. % 21.54/21.73 (* end of lemma zenon_L379_ *) % 21.54/21.73 assert (zenon_L380_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (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 (e2) (e0)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H139 zenon_H47 zenon_H11a zenon_H173 zenon_H40 zenon_H2a zenon_H158 zenon_H1cd zenon_Hac zenon_H191 zenon_H4d zenon_Hb6 zenon_Ha9 zenon_H1a2 zenon_H16a zenon_H7b zenon_H53 zenon_H77 zenon_H8b zenon_H196. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.73 apply (zenon_L251_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.73 apply (zenon_L358_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.73 apply (zenon_L379_); trivial. % 21.54/21.73 apply (zenon_L321_); trivial. % 21.54/21.73 (* end of lemma zenon_L380_ *) % 21.54/21.73 assert (zenon_L381_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H92 zenon_H47 zenon_H158 zenon_Hac zenon_H11a zenon_H40 zenon_H2a zenon_H173 zenon_H1a2 zenon_H1cd zenon_H4d zenon_Hb6 zenon_Ha9 zenon_H196 zenon_H139 zenon_H7b zenon_H77 zenon_H53 zenon_H8b zenon_H16a. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.54/21.73 apply (zenon_L378_); trivial. % 21.54/21.73 apply (zenon_L380_); trivial. % 21.54/21.73 (* end of lemma zenon_L381_ *) % 21.54/21.73 assert (zenon_L382_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H13e zenon_H13d zenon_H1bf zenon_H8b zenon_H191. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H14c | zenon_intro zenon_H151 ]. % 21.54/21.73 exact (zenon_H13d zenon_H14c). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H105 | zenon_intro zenon_H152 ]. % 21.54/21.73 exact (zenon_H1bf zenon_H105). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H8a | zenon_intro zenon_H110 ]. % 21.54/21.73 exact (zenon_H8b zenon_H8a). % 21.54/21.73 exact (zenon_H191 zenon_H110). % 21.54/21.73 (* end of lemma zenon_L382_ *) % 21.54/21.73 assert (zenon_L383_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H92 zenon_H1bf zenon_H13e zenon_H19d zenon_H2a zenon_Hb2 zenon_Hac zenon_H7d zenon_Ha9 zenon_H77 zenon_H53 zenon_H8b zenon_H16a zenon_Ha0 zenon_H47 zenon_Hb6 zenon_H68 zenon_H140 zenon_Hbc zenon_H13d zenon_H4d zenon_H48 zenon_H1d8 zenon_H1fe. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.73 apply (zenon_L161_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.73 apply (zenon_L323_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.73 apply (zenon_L327_); trivial. % 21.54/21.73 apply (zenon_L329_); trivial. % 21.54/21.73 apply (zenon_L382_); trivial. % 21.54/21.73 (* end of lemma zenon_L383_ *) % 21.54/21.73 assert (zenon_L384_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_Hb2 zenon_H47 zenon_H48 zenon_H201 zenon_H66 zenon_H77 zenon_H1cd zenon_H173 zenon_H2a zenon_Ha0 zenon_H13b zenon_H5c zenon_H195 zenon_H1bf zenon_H1f1 zenon_H7f zenon_Hb6 zenon_H13f zenon_Hac zenon_H7d. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.73 apply (zenon_L253_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.73 apply (zenon_L333_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.73 apply (zenon_L334_); trivial. % 21.54/21.73 apply (zenon_L44_); trivial. % 21.54/21.73 (* end of lemma zenon_L384_ *) % 21.54/21.73 assert (zenon_L385_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H158 zenon_He3 zenon_H40 zenon_Hf0 zenon_H6d zenon_Hac zenon_H11a. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 21.54/21.73 exact (zenon_He3 zenon_He7). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 21.54/21.73 apply (zenon_L61_); trivial. % 21.54/21.73 apply (zenon_L79_); trivial. % 21.54/21.73 (* end of lemma zenon_L385_ *) % 21.54/21.73 assert (zenon_L386_ : ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H44 zenon_Hf0 zenon_H6d zenon_H11a zenon_Hac zenon_Heb zenon_H77 zenon_H87 zenon_H40 zenon_H158 zenon_H72 zenon_H156 zenon_H2a zenon_H173 zenon_H15c. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 21.54/21.73 apply (zenon_L345_); trivial. % 21.54/21.73 apply (zenon_L385_); trivial. % 21.54/21.73 (* end of lemma zenon_L386_ *) % 21.54/21.73 assert (zenon_L387_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H9b zenon_Hac zenon_H7d. % 21.54/21.73 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.54/21.73 apply (zenon_L44_); trivial. % 21.54/21.73 (* end of lemma zenon_L387_ *) % 21.54/21.73 assert (zenon_L388_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_Hc0 zenon_Hac zenon_H1cd. % 21.54/21.73 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.54/21.73 apply (zenon_L360_); trivial. % 21.54/21.73 (* end of lemma zenon_L388_ *) % 21.54/21.73 assert (zenon_L389_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_Hf0 zenon_H6d zenon_H159. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 21.54/21.73 apply (zenon_L272_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 21.54/21.73 apply (zenon_L61_); trivial. % 21.54/21.73 exact (zenon_H159 zenon_H10c). % 21.54/21.73 (* end of lemma zenon_L389_ *) % 21.54/21.73 assert (zenon_L390_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((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))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (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) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 21.54/21.73 do 0 intro. intros zenon_Hb2 zenon_H47 zenon_Hec zenon_He4 zenon_H40 zenon_Hfa zenon_H1b3 zenon_H13c zenon_H129 zenon_Ha0 zenon_H48 zenon_H179 zenon_H25 zenon_H164 zenon_H1ef zenon_H66 zenon_H1a2 zenon_H13f zenon_H196 zenon_H6d zenon_H117 zenon_H1f1 zenon_H2a zenon_H192 zenon_H1c3 zenon_H9e zenon_H77 zenon_H68 zenon_H141 zenon_Hb6 zenon_Heb zenon_Ha9 zenon_H102. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.73 apply (zenon_L253_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.73 apply (zenon_L116_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.73 apply (zenon_L25_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.73 apply (zenon_L301_); trivial. % 21.54/21.73 exact (zenon_Hec zenon_H5c). % 21.54/21.73 apply (zenon_L91_); trivial. % 21.54/21.73 (* end of lemma zenon_L390_ *) % 21.54/21.73 assert (zenon_L391_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> False). % 21.54/21.73 do 0 intro. intros zenon_Heb zenon_H48 zenon_H28 zenon_H40 zenon_H105 zenon_H131 zenon_Hec. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.73 apply (zenon_L26_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.73 apply (zenon_L128_); trivial. % 21.54/21.73 exact (zenon_Hec zenon_H5c). % 21.54/21.73 (* end of lemma zenon_L391_ *) % 21.54/21.73 assert (zenon_L392_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H15c zenon_H173 zenon_H2a zenon_Hf0 zenon_H6d zenon_H158 zenon_H28 zenon_H48 zenon_H40 zenon_H131 zenon_H105 zenon_Heb. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.54/21.73 apply (zenon_L391_); trivial. % 21.54/21.73 apply (zenon_L389_); trivial. % 21.54/21.73 (* end of lemma zenon_L392_ *) % 21.54/21.73 assert (zenon_L393_ : (((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)) = (e3))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H121 zenon_H209 zenon_H11a zenon_H10c zenon_H177 zenon_Hfe zenon_Hc4. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.54/21.73 exact (zenon_H209 zenon_H9d). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.54/21.73 apply (zenon_L79_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.54/21.73 apply (zenon_L178_); trivial. % 21.54/21.73 exact (zenon_Hc4 zenon_Hc3). % 21.54/21.73 (* end of lemma zenon_L393_ *) % 21.54/21.73 assert (zenon_L394_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_Hf0 zenon_H6d zenon_Hac zenon_H11a. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 21.54/21.73 apply (zenon_L272_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 21.54/21.73 exact (zenon_H40 zenon_H3f). % 21.54/21.73 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 21.54/21.73 apply (zenon_L61_); trivial. % 21.54/21.73 apply (zenon_L79_); trivial. % 21.54/21.73 (* end of lemma zenon_L394_ *) % 21.54/21.73 assert (zenon_L395_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((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))))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H1c6 zenon_Ha0 zenon_Hc4 zenon_Hfe zenon_H177 zenon_H209 zenon_H121 zenon_Ha9 zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_Hf0 zenon_H6d zenon_H11a. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.73 apply (zenon_L53_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.73 apply (zenon_L393_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.73 apply (zenon_L289_); trivial. % 21.54/21.73 apply (zenon_L394_); trivial. % 21.54/21.73 (* end of lemma zenon_L395_ *) % 21.54/21.73 assert (zenon_L396_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.54/21.73 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H25 zenon_Hf0 zenon_H6d zenon_H73 zenon_H66 zenon_H5c zenon_H77. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.73 apply (zenon_L171_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.73 apply (zenon_L61_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.73 apply (zenon_L22_); trivial. % 21.54/21.73 apply (zenon_L206_); trivial. % 21.54/21.73 (* end of lemma zenon_L396_ *) % 21.54/21.73 assert (zenon_L397_ : (((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) (e1)) = (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))))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> False). % 21.54/21.73 do 0 intro. intros zenon_H1a2 zenon_Hc4 zenon_H177 zenon_H10c zenon_H11a zenon_H209 zenon_H121 zenon_Ha0 zenon_Hf3 zenon_H1ef zenon_Ha8 zenon_H1a3. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.54/21.73 apply (zenon_L393_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.54/21.73 apply (zenon_L162_); trivial. % 21.54/21.73 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.54/21.73 apply (zenon_L282_); trivial. % 21.54/21.73 exact (zenon_H1a3 zenon_Hbb). % 21.54/21.73 (* end of lemma zenon_L397_ *) % 21.54/21.73 assert (zenon_L398_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (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))))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H1c6 zenon_H1a3 zenon_Ha8 zenon_H1ef zenon_Hf3 zenon_Ha0 zenon_H121 zenon_H209 zenon_H177 zenon_Hc4 zenon_H1a2 zenon_Ha9 zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_Hf0 zenon_H6d zenon_H11a. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.74 apply (zenon_L53_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.74 apply (zenon_L397_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.74 apply (zenon_L289_); trivial. % 21.54/21.74 apply (zenon_L394_); trivial. % 21.54/21.74 (* end of lemma zenon_L398_ *) % 21.54/21.74 assert (zenon_L399_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (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 (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (((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)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (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)) = (e1)) -> False). % 21.54/21.74 do 0 intro. intros zenon_H13b zenon_H77 zenon_H66 zenon_H73 zenon_H68 zenon_Hfa zenon_H11a zenon_H6d zenon_Hf0 zenon_H40 zenon_H173 zenon_H2a zenon_H158 zenon_Ha9 zenon_H1a2 zenon_Hc4 zenon_H177 zenon_H209 zenon_H121 zenon_Ha0 zenon_H1ef zenon_Ha8 zenon_H1a3 zenon_H1c6 zenon_H48 zenon_H5c. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.74 apply (zenon_L396_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.74 apply (zenon_L272_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.74 apply (zenon_L398_); trivial. % 21.54/21.74 apply (zenon_L157_); trivial. % 21.54/21.74 (* end of lemma zenon_L399_ *) % 21.54/21.74 assert (zenon_L400_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H105 zenon_H110 zenon_Hb6. % 21.54/21.74 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.54/21.74 cut (((e3) = (e3)) = ((e1) = (e3))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_Hb6. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_Ha1. % 21.54/21.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.74 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 21.54/21.74 congruence. % 21.54/21.74 cut (((op (e2) (e2)) = (e1)) = ((e3) = (e1))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_Hb7. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H105. % 21.54/21.74 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.74 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 21.54/21.74 congruence. % 21.54/21.74 exact (zenon_H191 zenon_H110). % 21.54/21.74 apply zenon_H4a. apply refl_equal. % 21.54/21.74 apply zenon_Ha2. apply refl_equal. % 21.54/21.74 apply zenon_Ha2. apply refl_equal. % 21.54/21.74 (* end of lemma zenon_L400_ *) % 21.54/21.74 assert (zenon_L401_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.54/21.74 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_H11a zenon_H6d zenon_Hf0 zenon_H40 zenon_H173 zenon_H2a zenon_H158 zenon_H121 zenon_H209 zenon_H177 zenon_Hc4 zenon_Ha0 zenon_H1c6 zenon_Ha9 zenon_Hf6. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.74 apply (zenon_L253_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.74 apply (zenon_L53_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.74 apply (zenon_L395_); trivial. % 21.54/21.74 apply (zenon_L92_); trivial. % 21.54/21.74 (* end of lemma zenon_L401_ *) % 21.54/21.74 assert (zenon_L402_ : (((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 (e3) (e3)) = (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)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (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))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (e3))) -> (~((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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H15d zenon_Ha9 zenon_H1c6 zenon_Ha0 zenon_Hc4 zenon_H177 zenon_H209 zenon_H121 zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_Hf0 zenon_H6d zenon_H11a zenon_Hb6 zenon_H13a zenon_H117 zenon_H48 zenon_H1a3 zenon_H1ef zenon_H1a2 zenon_Hfa zenon_H68 zenon_H73 zenon_H77 zenon_H13b zenon_H196 zenon_H6f zenon_H139 zenon_H7f zenon_H192 zenon_H105 zenon_H111 zenon_H5c zenon_Hf5. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.74 apply (zenon_L251_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.74 apply (zenon_L21_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.74 apply (zenon_L253_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.74 apply (zenon_L53_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.74 apply (zenon_L395_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.74 apply (zenon_L399_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.74 apply (zenon_L289_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.74 apply (zenon_L400_); trivial. % 21.54/21.74 apply (zenon_L154_); trivial. % 21.54/21.74 apply (zenon_L401_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.74 apply (zenon_L146_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.74 apply (zenon_L148_); trivial. % 21.54/21.74 apply (zenon_L192_); trivial. % 21.54/21.74 (* end of lemma zenon_L402_ *) % 21.54/21.74 assert (zenon_L403_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H139 zenon_H77 zenon_H5c zenon_H73 zenon_H25 zenon_H68 zenon_Hfa zenon_H13a zenon_Hb6 zenon_H47 zenon_H11a zenon_H6d zenon_Hf0 zenon_H40 zenon_H173 zenon_H2a zenon_H158 zenon_H121 zenon_H209 zenon_H177 zenon_Hc4 zenon_Ha0 zenon_H1c6 zenon_Ha9. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.74 apply (zenon_L251_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.74 apply (zenon_L147_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.74 apply (zenon_L396_); trivial. % 21.54/21.74 apply (zenon_L401_); trivial. % 21.54/21.74 (* end of lemma zenon_L403_ *) % 21.54/21.74 assert (zenon_L404_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H117 zenon_Ha0 zenon_H2d zenon_Ha9 zenon_H6d zenon_Hb6 zenon_H105 zenon_H9e zenon_H196. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.74 apply (zenon_L67_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.74 apply (zenon_L289_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.74 apply (zenon_L400_); trivial. % 21.54/21.74 apply (zenon_L154_); trivial. % 21.54/21.74 (* end of lemma zenon_L404_ *) % 21.54/21.74 assert (zenon_L405_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 21.54/21.74 do 0 intro. intros zenon_H1ef zenon_H2d zenon_H14c. % 21.54/21.74 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H1ef. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H2d. % 21.54/21.74 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20a]. % 21.54/21.74 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.54/21.74 congruence. % 21.54/21.74 apply zenon_H86. apply refl_equal. % 21.54/21.74 apply zenon_H20a. apply sym_equal. exact zenon_H14c. % 21.54/21.74 (* end of lemma zenon_L405_ *) % 21.54/21.74 assert (zenon_L406_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 21.54/21.74 do 0 intro. intros zenon_H177 zenon_H31 zenon_H11d. % 21.54/21.74 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H177. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H31. % 21.54/21.74 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 21.54/21.74 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 21.54/21.74 congruence. % 21.54/21.74 apply zenon_H135. apply refl_equal. % 21.54/21.74 apply zenon_H168. apply sym_equal. exact zenon_H11d. % 21.54/21.74 (* end of lemma zenon_L406_ *) % 21.54/21.74 assert (zenon_L407_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H183 zenon_H9d zenon_Ha9 zenon_H77 zenon_H7f zenon_H72 zenon_H163 zenon_Hf6 zenon_H1b4. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.54/21.74 apply (zenon_L91_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.54/21.74 apply (zenon_L169_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.54/21.74 apply (zenon_L227_); trivial. % 21.54/21.74 apply (zenon_L347_); trivial. % 21.54/21.74 (* end of lemma zenon_L407_ *) % 21.54/21.74 assert (zenon_L408_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H121 zenon_H1b4 zenon_Hf6 zenon_H163 zenon_H72 zenon_H7f zenon_H77 zenon_Ha9 zenon_H183 zenon_H11a zenon_H10c zenon_H11d zenon_Ha0 zenon_Hb9 zenon_H129. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.54/21.74 apply (zenon_L407_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.54/21.74 apply (zenon_L79_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.54/21.74 apply (zenon_L80_); trivial. % 21.54/21.74 apply (zenon_L189_); trivial. % 21.54/21.74 (* end of lemma zenon_L408_ *) % 21.54/21.74 assert (zenon_L409_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H117 zenon_H2d zenon_H6d zenon_H111 zenon_Hfe zenon_H121 zenon_H1b4 zenon_Hf6 zenon_H163 zenon_H72 zenon_H7f zenon_H77 zenon_Ha9 zenon_H183 zenon_H11a zenon_H10c zenon_H11d zenon_Ha0 zenon_H129. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.74 apply (zenon_L67_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.74 apply (zenon_L289_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.74 apply (zenon_L75_); trivial. % 21.54/21.74 apply (zenon_L408_); trivial. % 21.54/21.74 (* end of lemma zenon_L409_ *) % 21.54/21.74 assert (zenon_L410_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H140 zenon_H1d8 zenon_H2a zenon_H68 zenon_H1ef zenon_H20b zenon_H177 zenon_H105 zenon_H73 zenon_H117 zenon_H2d zenon_H6d zenon_H111 zenon_H121 zenon_H1b4 zenon_Hf6 zenon_H163 zenon_H72 zenon_H7f zenon_H77 zenon_Ha9 zenon_H183 zenon_H11a zenon_H10c zenon_Ha0 zenon_H129. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.74 apply (zenon_L254_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.74 apply (zenon_L62_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.74 apply (zenon_L405_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H31 | zenon_intro zenon_H20c ]. % 21.54/21.74 apply (zenon_L406_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H153 | zenon_intro zenon_H20d ]. % 21.54/21.74 apply (zenon_L148_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H66 | zenon_intro zenon_Hfe ]. % 21.54/21.74 apply (zenon_L22_); trivial. % 21.54/21.74 apply (zenon_L409_); trivial. % 21.54/21.74 (* end of lemma zenon_L410_ *) % 21.54/21.74 assert (zenon_L411_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 21.54/21.74 do 0 intro. intros zenon_H1b4 zenon_H38 zenon_H167. % 21.54/21.74 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H1b4. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H38. % 21.54/21.74 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 21.54/21.74 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 21.54/21.74 congruence. % 21.54/21.74 apply zenon_Hf9. apply refl_equal. % 21.54/21.74 apply zenon_H20e. apply sym_equal. exact zenon_H167. % 21.54/21.74 (* end of lemma zenon_L411_ *) % 21.54/21.74 assert (zenon_L412_ : ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H11f zenon_H5c zenon_H20f. % 21.54/21.74 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.54/21.74 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H20f. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H12a. % 21.54/21.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.74 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 21.54/21.74 congruence. % 21.54/21.74 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H210. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H11f. % 21.54/21.74 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H211]. % 21.54/21.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.74 congruence. % 21.54/21.74 apply zenon_H12b. apply refl_equal. % 21.54/21.74 apply zenon_H211. apply sym_equal. exact zenon_H5c. % 21.54/21.74 apply zenon_H12b. apply refl_equal. % 21.54/21.74 apply zenon_H12b. apply refl_equal. % 21.54/21.74 (* end of lemma zenon_L412_ *) % 21.54/21.74 assert (zenon_L413_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H5c zenon_H129 zenon_H93 zenon_Hc4. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.54/21.74 apply (zenon_L411_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.54/21.74 apply (zenon_L412_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.54/21.74 apply (zenon_L126_); trivial. % 21.54/21.74 exact (zenon_Hc4 zenon_Hc3). % 21.54/21.74 (* end of lemma zenon_L413_ *) % 21.54/21.74 assert (zenon_L414_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H181. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.54/21.74 apply (zenon_L165_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.54/21.74 apply (zenon_L206_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.54/21.74 apply (zenon_L413_); trivial. % 21.54/21.74 exact (zenon_H181 zenon_H17c). % 21.54/21.74 (* end of lemma zenon_L414_ *) % 21.54/21.74 assert (zenon_L415_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H1bb zenon_H129 zenon_H115 zenon_H120 zenon_H181 zenon_Hc4. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.54/21.74 apply (zenon_L298_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.54/21.74 exact (zenon_H120 zenon_H11f). % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.54/21.74 exact (zenon_H181 zenon_H17c). % 21.54/21.74 exact (zenon_Hc4 zenon_Hc3). % 21.54/21.74 (* end of lemma zenon_L415_ *) % 21.54/21.74 assert (zenon_L416_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H167 zenon_H34 zenon_H18a. % 21.54/21.74 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.54/21.74 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H18a. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H12a. % 21.54/21.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.74 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 21.54/21.74 congruence. % 21.54/21.74 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H18b. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H167. % 21.54/21.74 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 21.54/21.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.74 congruence. % 21.54/21.74 apply zenon_H12b. apply refl_equal. % 21.54/21.74 apply zenon_H35. apply sym_equal. exact zenon_H34. % 21.54/21.74 apply zenon_H12b. apply refl_equal. % 21.54/21.74 apply zenon_H12b. apply refl_equal. % 21.54/21.74 (* end of lemma zenon_L416_ *) % 21.54/21.74 assert (zenon_L417_ : (((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 (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H212 zenon_H18a zenon_H167 zenon_H7f zenon_H7d zenon_Hbc zenon_H160 zenon_H209. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H34 | zenon_intro zenon_H213 ]. % 21.54/21.74 apply (zenon_L416_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H7e | zenon_intro zenon_H214 ]. % 21.54/21.74 apply (zenon_L31_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H102 | zenon_intro zenon_H9d ]. % 21.54/21.74 apply (zenon_L104_); trivial. % 21.54/21.74 exact (zenon_H209 zenon_H9d). % 21.54/21.74 (* end of lemma zenon_L417_ *) % 21.54/21.74 assert (zenon_L418_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H19a zenon_H1b4 zenon_H20f zenon_H77 zenon_H68 zenon_H1c3 zenon_H5c zenon_H48 zenon_Hc4 zenon_H181 zenon_H120 zenon_H129 zenon_H1bb zenon_H212 zenon_H18a zenon_H7f zenon_H7d zenon_Hbc zenon_H160 zenon_H209. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.54/21.74 apply (zenon_L414_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.54/21.74 apply (zenon_L157_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.54/21.74 apply (zenon_L415_); trivial. % 21.54/21.74 apply (zenon_L417_); trivial. % 21.54/21.74 (* end of lemma zenon_L418_ *) % 21.54/21.74 assert (zenon_L419_ : (((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)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H19a zenon_Ha0 zenon_H9e zenon_H5c zenon_H48 zenon_Hc4 zenon_H181 zenon_H120 zenon_H129 zenon_H1bb zenon_H34 zenon_H18a. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.54/21.74 apply (zenon_L156_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.54/21.74 apply (zenon_L157_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.54/21.74 apply (zenon_L415_); trivial. % 21.54/21.74 apply (zenon_L416_); trivial. % 21.54/21.74 (* end of lemma zenon_L419_ *) % 21.54/21.74 assert (zenon_L420_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H7f zenon_H8a zenon_H104 zenon_H181. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.54/21.74 apply (zenon_L291_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.54/21.74 apply (zenon_L169_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.54/21.74 apply (zenon_L231_); trivial. % 21.54/21.74 exact (zenon_H181 zenon_H17c). % 21.54/21.74 (* end of lemma zenon_L420_ *) % 21.54/21.74 assert (zenon_L421_ : ((op (e3) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H167 zenon_H136 zenon_H20f. % 21.54/21.74 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.54/21.74 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H20f. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H12a. % 21.54/21.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.74 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 21.54/21.74 congruence. % 21.54/21.74 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H210. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H167. % 21.54/21.74 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 21.54/21.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.74 congruence. % 21.54/21.74 apply zenon_H12b. apply refl_equal. % 21.54/21.74 apply zenon_H215. apply sym_equal. exact zenon_H136. % 21.54/21.74 apply zenon_H12b. apply refl_equal. % 21.54/21.74 apply zenon_H12b. apply refl_equal. % 21.54/21.74 (* end of lemma zenon_L421_ *) % 21.54/21.74 assert (zenon_L422_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H1bb zenon_H20f zenon_H136 zenon_H120 zenon_H181 zenon_Hc4. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.54/21.74 apply (zenon_L421_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.54/21.74 exact (zenon_H120 zenon_H11f). % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.54/21.74 exact (zenon_H181 zenon_H17c). % 21.54/21.74 exact (zenon_Hc4 zenon_Hc3). % 21.54/21.74 (* end of lemma zenon_L422_ *) % 21.54/21.74 assert (zenon_L423_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((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))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H139 zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha0 zenon_Hc4 zenon_H181 zenon_H120 zenon_H20f zenon_H1bb zenon_H1cf zenon_H104 zenon_H34 zenon_H183 zenon_H19a zenon_H1b4 zenon_H77 zenon_H68 zenon_H1c3 zenon_H5c zenon_H48 zenon_H129 zenon_H212 zenon_H18a zenon_H7f zenon_H7d zenon_Hbc zenon_H209 zenon_H173 zenon_H2a zenon_H179 zenon_H13b zenon_Ha9. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.74 apply (zenon_L251_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.74 apply (zenon_L147_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.74 apply (zenon_L253_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.74 apply (zenon_L53_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.74 apply (zenon_L193_); trivial. % 21.54/21.74 apply (zenon_L419_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.74 apply (zenon_L253_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.74 apply (zenon_L53_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.74 apply (zenon_L297_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.74 apply (zenon_L272_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.74 apply (zenon_L193_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.74 apply (zenon_L62_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.74 apply (zenon_L420_); trivial. % 21.54/21.74 apply (zenon_L418_); trivial. % 21.54/21.74 apply (zenon_L422_); trivial. % 21.54/21.74 apply (zenon_L92_); trivial. % 21.54/21.74 (* end of lemma zenon_L423_ *) % 21.54/21.74 assert (zenon_L424_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((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 (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H1fe zenon_H19d zenon_Hfa zenon_H192 zenon_H6f zenon_H196 zenon_H11a zenon_H6d zenon_Hf0 zenon_H40 zenon_H158 zenon_H163 zenon_H121 zenon_H117 zenon_H73 zenon_H177 zenon_H20b zenon_H1ef zenon_H1d8 zenon_H140 zenon_H190 zenon_H1c6 zenon_H15d zenon_Ha9 zenon_H13b zenon_H179 zenon_H173 zenon_H209 zenon_Hbc zenon_H7d zenon_H7f zenon_H18a zenon_H212 zenon_H129 zenon_H1c3 zenon_H68 zenon_H77 zenon_H1b4 zenon_H19a zenon_H183 zenon_H104 zenon_H1cf zenon_H1bb zenon_H20f zenon_H120 zenon_H181 zenon_Hc4 zenon_Ha0 zenon_Hb6 zenon_H13a zenon_H139 zenon_H48 zenon_H2a zenon_H105 zenon_H111 zenon_H5c zenon_Hf5. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.74 apply (zenon_L161_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.74 apply (zenon_L403_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.74 apply (zenon_L65_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.74 apply (zenon_L148_); trivial. % 21.54/21.74 apply (zenon_L192_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.74 apply (zenon_L251_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.74 apply (zenon_L21_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.74 apply (zenon_L253_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.74 apply (zenon_L53_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.74 apply (zenon_L193_); trivial. % 21.54/21.74 apply (zenon_L404_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.74 apply (zenon_L253_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.74 apply (zenon_L53_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.74 apply (zenon_L53_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.74 apply (zenon_L193_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.74 apply (zenon_L410_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.74 apply (zenon_L366_); trivial. % 21.54/21.74 apply (zenon_L418_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.74 apply (zenon_L289_); trivial. % 21.54/21.74 apply (zenon_L394_); trivial. % 21.54/21.74 apply (zenon_L92_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.74 apply (zenon_L146_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.74 apply (zenon_L148_); trivial. % 21.54/21.74 apply (zenon_L192_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.74 apply (zenon_L423_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.74 apply (zenon_L65_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.74 apply (zenon_L148_); trivial. % 21.54/21.74 apply (zenon_L192_); trivial. % 21.54/21.74 (* end of lemma zenon_L424_ *) % 21.54/21.74 assert (zenon_L425_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H1cf zenon_Ha9 zenon_Hfe zenon_Hf3 zenon_H68 zenon_H190 zenon_H6d zenon_H1bb zenon_H162 zenon_H120 zenon_H1cb zenon_Hc4. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.74 apply (zenon_L193_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.74 apply (zenon_L62_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.74 apply (zenon_L366_); trivial. % 21.54/21.74 apply (zenon_L237_); trivial. % 21.54/21.74 (* end of lemma zenon_L425_ *) % 21.54/21.74 assert (zenon_L426_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.54/21.74 do 0 intro. intros zenon_H13b zenon_H76 zenon_H2a zenon_H173 zenon_Hc4 zenon_H1cb zenon_H120 zenon_H162 zenon_H1bb zenon_H6d zenon_H190 zenon_H68 zenon_Hfe zenon_Ha9 zenon_H1cf zenon_H48 zenon_H5c. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.74 apply (zenon_L171_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.74 apply (zenon_L272_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.74 apply (zenon_L425_); trivial. % 21.54/21.74 apply (zenon_L157_); trivial. % 21.54/21.74 (* end of lemma zenon_L426_ *) % 21.54/21.74 assert (zenon_L427_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.54/21.74 do 0 intro. intros zenon_H13b zenon_H76 zenon_H2a zenon_H173 zenon_H1a3 zenon_Ha8 zenon_H1ef zenon_Ha0 zenon_H1cf zenon_Ha9 zenon_H68 zenon_H190 zenon_H6d zenon_H1bb zenon_H162 zenon_H120 zenon_H1cb zenon_Hc4 zenon_H1a2 zenon_H48 zenon_H5c. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.74 apply (zenon_L171_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.74 apply (zenon_L272_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.54/21.74 apply (zenon_L425_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.54/21.74 apply (zenon_L162_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.54/21.74 apply (zenon_L282_); trivial. % 21.54/21.74 exact (zenon_H1a3 zenon_Hbb). % 21.54/21.74 apply (zenon_L157_); trivial. % 21.54/21.74 (* end of lemma zenon_L427_ *) % 21.54/21.74 assert (zenon_L428_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((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 (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (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)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H125 zenon_H196 zenon_H105 zenon_H13b zenon_H173 zenon_H1a3 zenon_H1ef zenon_H1cf zenon_H190 zenon_H1bb zenon_H120 zenon_Hc4 zenon_H1a2 zenon_H117 zenon_H6d zenon_H55 zenon_H13a zenon_Hb6 zenon_H47 zenon_H66 zenon_H164 zenon_H2a zenon_H192 zenon_H18a zenon_H19a zenon_Ha0 zenon_H5c zenon_H48 zenon_H68 zenon_H1cb zenon_H77 zenon_Ha9 zenon_H1c3 zenon_H162. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.74 apply (zenon_L251_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.74 apply (zenon_L253_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.74 apply (zenon_L53_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.74 apply (zenon_L426_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.74 apply (zenon_L427_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.74 apply (zenon_L289_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.74 apply (zenon_L400_); trivial. % 21.54/21.74 apply (zenon_L154_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.74 apply (zenon_L34_); trivial. % 21.54/21.74 apply (zenon_L340_); trivial. % 21.54/21.74 (* end of lemma zenon_L428_ *) % 21.54/21.74 assert (zenon_L429_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (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) (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.54/21.74 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha0 zenon_H5c zenon_H48 zenon_H1cf zenon_H68 zenon_H190 zenon_H6d zenon_H1bb zenon_H162 zenon_H120 zenon_H1cb zenon_Hc4 zenon_H173 zenon_H2a zenon_H76 zenon_H13b zenon_Ha9 zenon_Hf6. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.74 apply (zenon_L253_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.74 apply (zenon_L53_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.74 apply (zenon_L426_); trivial. % 21.54/21.74 apply (zenon_L92_); trivial. % 21.54/21.74 (* end of lemma zenon_L429_ *) % 21.54/21.74 assert (zenon_L430_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_He4 zenon_H48 zenon_H2a zenon_H40 zenon_H105 zenon_H190 zenon_H183 zenon_H9d zenon_Ha9 zenon_H77 zenon_H72 zenon_H163 zenon_Hf6 zenon_H1b4. % 21.54/21.74 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.74 apply (zenon_L65_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.74 exact (zenon_H40 zenon_H3f). % 21.54/21.74 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.74 apply (zenon_L143_); trivial. % 21.54/21.74 apply (zenon_L407_); trivial. % 21.54/21.74 (* end of lemma zenon_L430_ *) % 21.54/21.74 assert (zenon_L431_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((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)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H121 zenon_H1b4 zenon_Hf6 zenon_H163 zenon_H72 zenon_H77 zenon_Ha9 zenon_H183 zenon_H190 zenon_H105 zenon_H40 zenon_H2a zenon_H48 zenon_He4 zenon_H11a zenon_H10c zenon_H1a3 zenon_Hc4. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.54/21.74 apply (zenon_L430_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.54/21.74 apply (zenon_L79_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.54/21.74 exact (zenon_H1a3 zenon_Hbb). % 21.54/21.74 exact (zenon_Hc4 zenon_Hc3). % 21.54/21.74 (* end of lemma zenon_L431_ *) % 21.54/21.74 assert (zenon_L432_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((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 (e3) (e2)) = (op (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((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) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (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 (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H15d zenon_H77 zenon_H1c6 zenon_Ha0 zenon_Hc4 zenon_H1a3 zenon_He4 zenon_H48 zenon_H190 zenon_H183 zenon_H163 zenon_H1b4 zenon_H121 zenon_Ha9 zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_Hf0 zenon_H6d zenon_H11a zenon_H13a zenon_Hb6 zenon_H1cf zenon_H68 zenon_H1bb zenon_H162 zenon_H120 zenon_H1cb zenon_H13b zenon_Hfa zenon_H125 zenon_H196 zenon_H1ef zenon_H1a2 zenon_H117 zenon_H55 zenon_H164 zenon_H18a zenon_H19a zenon_H1c3 zenon_H6f zenon_H139 zenon_H7f zenon_H192 zenon_H105 zenon_H111 zenon_H5c zenon_Hf5. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.74 apply (zenon_L251_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.74 apply (zenon_L21_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.74 apply (zenon_L428_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.74 apply (zenon_L429_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.74 apply (zenon_L61_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.74 apply (zenon_L53_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.74 apply (zenon_L431_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.74 apply (zenon_L289_); trivial. % 21.54/21.74 apply (zenon_L394_); trivial. % 21.54/21.74 apply (zenon_L206_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.74 apply (zenon_L146_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.74 apply (zenon_L148_); trivial. % 21.54/21.74 apply (zenon_L192_); trivial. % 21.54/21.74 (* end of lemma zenon_L432_ *) % 21.54/21.74 assert (zenon_L433_ : (((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) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H1bb zenon_H162 zenon_H120 zenon_H181 zenon_Hc4. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.54/21.74 exact (zenon_H162 zenon_H167). % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.54/21.74 exact (zenon_H120 zenon_H11f). % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.54/21.74 exact (zenon_H181 zenon_H17c). % 21.54/21.74 exact (zenon_Hc4 zenon_Hc3). % 21.54/21.74 (* end of lemma zenon_L433_ *) % 21.54/21.74 assert (zenon_L434_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 21.54/21.74 do 0 intro. intros zenon_Hc2 zenon_H162 zenon_H120 zenon_H181 zenon_H1bb. % 21.54/21.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.54/21.74 apply (zenon_L433_); trivial. % 21.54/21.74 apply (zenon_L433_); trivial. % 21.54/21.74 (* end of lemma zenon_L434_ *) % 21.54/21.74 assert (zenon_L435_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> False). % 21.54/21.74 do 0 intro. intros zenon_H63 zenon_H55 zenon_H6d. % 21.54/21.74 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 21.54/21.74 apply (zenon_L34_); trivial. % 21.54/21.74 (* end of lemma zenon_L435_ *) % 21.54/21.74 assert (zenon_L436_ : ((op (e1) (e2)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H72 zenon_H133 zenon_Ha9. % 21.54/21.74 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.54/21.74 cut (((e3) = (e3)) = ((e2) = (e3))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_Ha9. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_Ha1. % 21.54/21.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.74 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 21.54/21.74 congruence. % 21.54/21.74 cut (((op (e1) (e2)) = (e2)) = ((e3) = (e2))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_Haa. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H72. % 21.54/21.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.54/21.74 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 21.54/21.74 congruence. % 21.54/21.74 exact (zenon_H17b zenon_H133). % 21.54/21.74 apply zenon_H6a. apply refl_equal. % 21.54/21.74 apply zenon_Ha2. apply refl_equal. % 21.54/21.74 apply zenon_Ha2. apply refl_equal. % 21.54/21.74 (* end of lemma zenon_L436_ *) % 21.54/21.74 assert (zenon_L437_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e3))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H13b zenon_He3 zenon_He4 zenon_H48 zenon_H40 zenon_H13c zenon_Hb6 zenon_H3c zenon_H129 zenon_H11a zenon_H183 zenon_H77 zenon_H163 zenon_Hf6 zenon_H1b4 zenon_H121 zenon_H111 zenon_H6d zenon_H2d zenon_H117 zenon_H73 zenon_H105 zenon_H177 zenon_H20b zenon_H1ef zenon_H68 zenon_H2a zenon_H1d8 zenon_H140 zenon_Ha9 zenon_H72 zenon_Ha0. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.74 apply (zenon_L25_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.74 exact (zenon_He3 zenon_He7). % 21.54/21.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.74 apply (zenon_L62_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.74 apply (zenon_L65_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.74 exact (zenon_H40 zenon_H3f). % 21.54/21.74 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.74 apply (zenon_L56_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.74 apply (zenon_L46_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.74 apply (zenon_L410_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.74 apply (zenon_L436_); trivial. % 21.54/21.74 apply (zenon_L90_); trivial. % 21.54/21.74 (* end of lemma zenon_L437_ *) % 21.54/21.74 assert (zenon_L438_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 21.54/21.74 do 0 intro. intros zenon_H186 zenon_H72 zenon_Hf7. % 21.54/21.74 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e1) (e3)))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H186. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H72. % 21.54/21.74 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 21.54/21.74 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.54/21.74 congruence. % 21.54/21.74 apply zenon_H50. apply refl_equal. % 21.54/21.74 apply zenon_Hf8. apply sym_equal. exact zenon_Hf7. % 21.54/21.74 (* end of lemma zenon_L438_ *) % 21.54/21.74 assert (zenon_L439_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H93 zenon_H6d zenon_H189. % 21.54/21.74 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 21.54/21.74 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e1)) = (op (e2) (e3)))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H189. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H95. % 21.54/21.74 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.54/21.74 cut (((op (e2) (e3)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H216]. % 21.54/21.74 congruence. % 21.54/21.74 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e1)))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H216. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H93. % 21.54/21.74 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 21.54/21.74 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 21.54/21.74 congruence. % 21.54/21.74 apply zenon_H96. apply refl_equal. % 21.54/21.74 apply zenon_H85. apply sym_equal. exact zenon_H6d. % 21.54/21.74 apply zenon_H96. apply refl_equal. % 21.54/21.74 apply zenon_H96. apply refl_equal. % 21.54/21.74 (* end of lemma zenon_L439_ *) % 21.54/21.74 assert (zenon_L440_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H1a8 zenon_H68 zenon_H2a zenon_H156 zenon_H72 zenon_H189 zenon_H93 zenon_H7f zenon_H77. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.54/21.74 apply (zenon_L147_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.54/21.74 apply (zenon_L100_); trivial. % 21.54/21.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.54/21.74 apply (zenon_L439_); trivial. % 21.54/21.74 apply (zenon_L169_); trivial. % 21.54/21.74 (* end of lemma zenon_L440_ *) % 21.54/21.74 assert (zenon_L441_ : (~((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> False). % 21.54/21.74 do 0 intro. intros zenon_H217 zenon_H9f. % 21.54/21.74 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 21.54/21.74 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 21.54/21.74 congruence. % 21.54/21.74 exact (zenon_Ha4 zenon_H9f). % 21.54/21.74 exact (zenon_Ha4 zenon_H9f). % 21.54/21.74 (* end of lemma zenon_L441_ *) % 21.54/21.74 assert (zenon_L442_ : (~((op (e0) (op (e0) (e0))) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e3)) -> False). % 21.54/21.74 do 0 intro. intros zenon_H218 zenon_H9f. % 21.54/21.74 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 21.54/21.74 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.54/21.74 congruence. % 21.54/21.74 apply zenon_H46. apply refl_equal. % 21.54/21.74 exact (zenon_Ha4 zenon_H9f). % 21.54/21.74 (* end of lemma zenon_L442_ *) % 21.54/21.74 assert (zenon_L443_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (op (e0) (op (e0) (e0))))) -> False). % 21.54/21.74 do 0 intro. intros zenon_H155 zenon_H9f zenon_H219. % 21.54/21.74 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H21a | zenon_intro zenon_H21b ]. % 21.54/21.74 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((e1) = (op (e0) (op (e0) (e0))))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H219. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H21a. % 21.54/21.74 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 21.54/21.74 cut (((op (e0) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 21.54/21.74 congruence. % 21.54/21.74 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (op (e0) (e0))) = (e1))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H21c. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H155. % 21.54/21.74 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.74 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 21.54/21.74 congruence. % 21.54/21.74 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H21a | zenon_intro zenon_H21b ]. % 21.54/21.74 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e3)) = (op (e0) (op (e0) (e0))))). % 21.54/21.74 intro zenon_D_pnotp. % 21.54/21.74 apply zenon_H21d. % 21.54/21.74 rewrite <- zenon_D_pnotp. % 21.54/21.74 exact zenon_H21a. % 21.54/21.74 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 21.54/21.74 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 21.54/21.75 congruence. % 21.54/21.75 apply (zenon_L442_); trivial. % 21.54/21.75 apply zenon_H21b. apply refl_equal. % 21.54/21.75 apply zenon_H21b. apply refl_equal. % 21.54/21.75 apply zenon_H4a. apply refl_equal. % 21.54/21.75 apply zenon_H21b. apply refl_equal. % 21.54/21.75 apply zenon_H21b. apply refl_equal. % 21.54/21.75 (* end of lemma zenon_L443_ *) % 21.54/21.75 assert (zenon_L444_ : ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 21.54/21.75 do 0 intro. intros zenon_H17c zenon_H155 zenon_H9f. % 21.54/21.75 apply (zenon_notand_s _ _ ax22); [ zenon_intro zenon_H21f | zenon_intro zenon_H21e ]. % 21.54/21.75 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H220 | zenon_intro zenon_H221 ]. % 21.54/21.75 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e2) = (op (op (e0) (e0)) (op (e0) (e0))))). % 21.54/21.75 intro zenon_D_pnotp. % 21.54/21.75 apply zenon_H21f. % 21.54/21.75 rewrite <- zenon_D_pnotp. % 21.54/21.75 exact zenon_H220. % 21.54/21.75 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 21.54/21.75 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H222]. % 21.54/21.75 congruence. % 21.54/21.75 cut (((op (e3) (e3)) = (e2)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e2))). % 21.54/21.75 intro zenon_D_pnotp. % 21.54/21.75 apply zenon_H222. % 21.54/21.75 rewrite <- zenon_D_pnotp. % 21.54/21.75 exact zenon_H17c. % 21.54/21.75 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.54/21.75 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 21.54/21.75 congruence. % 21.54/21.75 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H220 | zenon_intro zenon_H221 ]. % 21.54/21.75 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))))). % 21.54/21.75 intro zenon_D_pnotp. % 21.54/21.75 apply zenon_H223. % 21.54/21.75 rewrite <- zenon_D_pnotp. % 21.54/21.75 exact zenon_H220. % 21.54/21.75 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 21.54/21.75 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H217]. % 21.54/21.75 congruence. % 21.54/21.75 apply (zenon_L441_); trivial. % 21.54/21.75 apply zenon_H221. apply refl_equal. % 21.54/21.75 apply zenon_H221. apply refl_equal. % 21.54/21.75 apply zenon_H6a. apply refl_equal. % 21.54/21.75 apply zenon_H221. apply refl_equal. % 21.54/21.75 apply zenon_H221. apply refl_equal. % 21.54/21.75 apply (zenon_notand_s _ _ zenon_H21e); [ zenon_intro zenon_H1d3 | zenon_intro zenon_H219 ]. % 21.54/21.75 apply zenon_H1d3. apply sym_equal. exact zenon_H9f. % 21.54/21.75 apply (zenon_L443_); trivial. % 21.54/21.75 (* end of lemma zenon_L444_ *) % 21.54/21.75 assert (zenon_L445_ : ((op (e0) (e2)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (~((e3) = (op (e0) (op (e0) (e0))))) -> False). % 21.54/21.75 do 0 intro. intros zenon_Hfe zenon_H67 zenon_H224. % 21.54/21.75 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H21a | zenon_intro zenon_H21b ]. % 21.54/21.75 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((e3) = (op (e0) (op (e0) (e0))))). % 21.54/21.75 intro zenon_D_pnotp. % 21.54/21.75 apply zenon_H224. % 21.54/21.75 rewrite <- zenon_D_pnotp. % 21.54/21.75 exact zenon_H21a. % 21.54/21.75 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 21.54/21.75 cut (((op (e0) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H225]. % 21.54/21.75 congruence. % 21.54/21.75 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (op (e0) (e0))) = (e3))). % 21.54/21.75 intro zenon_D_pnotp. % 21.54/21.75 apply zenon_H225. % 21.54/21.75 rewrite <- zenon_D_pnotp. % 21.54/21.75 exact zenon_Hfe. % 21.54/21.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.75 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H226]. % 21.54/21.75 congruence. % 21.54/21.75 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H21a | zenon_intro zenon_H21b ]. % 21.54/21.75 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e0) (e0))))). % 21.54/21.75 intro zenon_D_pnotp. % 21.54/21.75 apply zenon_H226. % 21.54/21.75 rewrite <- zenon_D_pnotp. % 21.54/21.75 exact zenon_H21a. % 21.54/21.75 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 21.54/21.75 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 21.54/21.75 congruence. % 21.54/21.75 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 21.54/21.75 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.54/21.75 congruence. % 21.54/21.75 apply zenon_H46. apply refl_equal. % 21.54/21.75 exact (zenon_H6c zenon_H67). % 21.54/21.75 apply zenon_H21b. apply refl_equal. % 21.54/21.75 apply zenon_H21b. apply refl_equal. % 21.54/21.75 apply zenon_Ha2. apply refl_equal. % 21.54/21.75 apply zenon_H21b. apply refl_equal. % 21.54/21.75 apply zenon_H21b. apply refl_equal. % 21.54/21.75 (* end of lemma zenon_L445_ *) % 21.54/21.75 assert (zenon_L446_ : ((op (e2) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 21.54/21.75 do 0 intro. intros zenon_H105 zenon_Hfe zenon_H67. % 21.54/21.75 apply (zenon_notand_s _ _ ax14); [ zenon_intro zenon_H229 | zenon_intro zenon_H228 ]. % 21.54/21.75 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H220 | zenon_intro zenon_H221 ]. % 21.54/21.75 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (e0) (e0))))). % 21.54/21.75 intro zenon_D_pnotp. % 21.54/21.75 apply zenon_H229. % 21.54/21.75 rewrite <- zenon_D_pnotp. % 21.54/21.75 exact zenon_H220. % 21.54/21.75 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 21.54/21.75 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22a]. % 21.54/21.75 congruence. % 21.54/21.75 cut (((op (e2) (e2)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 21.54/21.75 intro zenon_D_pnotp. % 21.54/21.75 apply zenon_H22a. % 21.54/21.75 rewrite <- zenon_D_pnotp. % 21.54/21.75 exact zenon_H105. % 21.54/21.75 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.75 cut (((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H22b]. % 21.54/21.75 congruence. % 21.54/21.75 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H220 | zenon_intro zenon_H221 ]. % 21.54/21.75 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))))). % 21.54/21.75 intro zenon_D_pnotp. % 21.54/21.75 apply zenon_H22b. % 21.54/21.75 rewrite <- zenon_D_pnotp. % 21.54/21.75 exact zenon_H220. % 21.54/21.75 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 21.54/21.75 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H22c]. % 21.54/21.75 congruence. % 21.54/21.75 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 21.54/21.75 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 21.54/21.75 congruence. % 21.54/21.75 exact (zenon_H6c zenon_H67). % 21.54/21.75 exact (zenon_H6c zenon_H67). % 21.54/21.75 apply zenon_H221. apply refl_equal. % 21.54/21.75 apply zenon_H221. apply refl_equal. % 21.54/21.75 apply zenon_H4a. apply refl_equal. % 21.54/21.75 apply zenon_H221. apply refl_equal. % 21.54/21.75 apply zenon_H221. apply refl_equal. % 21.54/21.75 apply (zenon_notand_s _ _ zenon_H228); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H224 ]. % 21.54/21.75 apply zenon_H1b0. apply sym_equal. exact zenon_H67. % 21.54/21.75 apply (zenon_L445_); trivial. % 21.54/21.75 (* end of lemma zenon_L446_ *) % 21.54/21.75 assert (zenon_L447_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((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) (e1)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e3))) -> False). % 21.54/21.75 do 0 intro. intros zenon_H139 zenon_H155 zenon_H190 zenon_H1c3 zenon_H186 zenon_H189 zenon_H156 zenon_H1a8 zenon_H13a zenon_H6f zenon_H13b zenon_He3 zenon_He4 zenon_H48 zenon_H40 zenon_H13c zenon_Hb6 zenon_H3c zenon_H129 zenon_H11a zenon_H183 zenon_H77 zenon_H163 zenon_H1b4 zenon_H121 zenon_H111 zenon_H6d zenon_H2d zenon_H117 zenon_H73 zenon_H105 zenon_H177 zenon_H20b zenon_H1ef zenon_H68 zenon_H2a zenon_H1d8 zenon_H140 zenon_Ha9 zenon_H72 zenon_Ha0. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.75 apply (zenon_L65_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.75 exact (zenon_H40 zenon_H3f). % 21.54/21.75 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.75 apply (zenon_L143_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.54/21.75 apply (zenon_L437_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.54/21.75 apply (zenon_L438_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.54/21.75 apply (zenon_L440_); trivial. % 21.54/21.75 apply (zenon_L444_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.75 apply (zenon_L53_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.75 apply (zenon_L446_); trivial. % 21.54/21.75 apply (zenon_L115_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.75 apply (zenon_L21_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.75 apply (zenon_L22_); trivial. % 21.54/21.75 apply (zenon_L437_); trivial. % 21.54/21.75 (* end of lemma zenon_L447_ *) % 21.54/21.75 assert (zenon_L448_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 21.54/21.75 do 0 intro. intros zenon_He4 zenon_H48 zenon_H2a zenon_H40 zenon_H6d zenon_H77 zenon_H7d zenon_H7e. % 21.54/21.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.75 apply (zenon_L65_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.75 exact (zenon_H40 zenon_H3f). % 21.54/21.75 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.75 apply (zenon_L56_); trivial. % 21.54/21.75 apply (zenon_L31_); trivial. % 21.54/21.75 (* end of lemma zenon_L448_ *) % 21.54/21.75 assert (zenon_L449_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 21.54/21.75 do 0 intro. intros zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H7f zenon_H72 zenon_H163 zenon_H155 zenon_H9f. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.54/21.75 apply (zenon_L291_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.54/21.75 apply (zenon_L169_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.54/21.75 apply (zenon_L227_); trivial. % 21.54/21.75 apply (zenon_L444_); trivial. % 21.54/21.75 (* end of lemma zenon_L449_ *) % 21.54/21.75 assert (zenon_L450_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 21.54/21.75 do 0 intro. intros zenon_He4 zenon_H48 zenon_H2a zenon_H40 zenon_H105 zenon_H190 zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H72 zenon_H163 zenon_H155 zenon_H9f. % 21.54/21.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.75 apply (zenon_L65_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.75 exact (zenon_H40 zenon_H3f). % 21.54/21.75 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.75 apply (zenon_L143_); trivial. % 21.54/21.75 apply (zenon_L449_); trivial. % 21.54/21.75 (* end of lemma zenon_L450_ *) % 21.54/21.75 assert (zenon_L451_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (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) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.75 do 0 intro. intros zenon_H1fe zenon_H19d zenon_H1d4 zenon_H7d zenon_H1c3 zenon_H186 zenon_H189 zenon_H156 zenon_H1a8 zenon_H13b zenon_He3 zenon_H13c zenon_H129 zenon_H11a zenon_H121 zenon_H117 zenon_H177 zenon_H20b zenon_H1ef zenon_H1d8 zenon_H140 zenon_Ha9 zenon_H125 zenon_H4e zenon_Hb2 zenon_Hec zenon_Heb zenon_H82 zenon_H15d zenon_H111 zenon_H139 zenon_Hb6 zenon_H105 zenon_Ha0 zenon_H190 zenon_H13a zenon_H6f zenon_H73 zenon_He4 zenon_H48 zenon_H2a zenon_H40 zenon_H6d zenon_H183 zenon_H68 zenon_H77 zenon_H72 zenon_H163 zenon_H1b4. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.75 apply (zenon_L161_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.75 apply (zenon_L250_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.75 apply (zenon_L346_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.75 apply (zenon_L65_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.75 apply (zenon_L148_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.75 apply (zenon_L346_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.75 apply (zenon_L447_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.75 apply (zenon_L217_); trivial. % 21.54/21.75 apply (zenon_L448_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.75 apply (zenon_L350_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.75 apply (zenon_L65_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.75 apply (zenon_L148_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.75 apply (zenon_L450_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.75 apply (zenon_L53_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.75 apply (zenon_L446_); trivial. % 21.54/21.75 apply (zenon_L115_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.75 apply (zenon_L21_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.75 apply (zenon_L22_); trivial. % 21.54/21.75 apply (zenon_L349_); trivial. % 21.54/21.75 (* end of lemma zenon_L451_ *) % 21.54/21.75 assert (zenon_L452_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (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) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.75 do 0 intro. intros zenon_H140 zenon_H1d8 zenon_H2a zenon_H68 zenon_H1ef zenon_H117 zenon_H2d zenon_H6d zenon_H111 zenon_Hfe zenon_H121 zenon_H1b4 zenon_Hf6 zenon_H163 zenon_H72 zenon_H7f zenon_H77 zenon_Ha9 zenon_H183 zenon_H11a zenon_H10c zenon_Ha0 zenon_H129. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.75 apply (zenon_L254_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.75 apply (zenon_L62_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.75 apply (zenon_L405_); trivial. % 21.54/21.75 apply (zenon_L409_); trivial. % 21.54/21.75 (* end of lemma zenon_L452_ *) % 21.54/21.75 assert (zenon_L453_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((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) (e2)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> False). % 21.54/21.75 do 0 intro. intros zenon_H13b zenon_Hf5 zenon_H1b3 zenon_Hfa zenon_He3 zenon_He4 zenon_H48 zenon_H105 zenon_H190 zenon_H13c zenon_Hec zenon_H40 zenon_Hb6 zenon_Heb zenon_H129 zenon_H11a zenon_H183 zenon_Ha9 zenon_H77 zenon_H72 zenon_H163 zenon_Hf6 zenon_H1b4 zenon_H121 zenon_H111 zenon_H6d zenon_H2d zenon_H117 zenon_H1ef zenon_H68 zenon_H2a zenon_H1d8 zenon_H140 zenon_Hfe zenon_H73 zenon_Ha0. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.75 apply (zenon_L303_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.75 exact (zenon_He3 zenon_He7). % 21.54/21.75 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.75 apply (zenon_L62_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.75 apply (zenon_L65_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.75 exact (zenon_H40 zenon_H3f). % 21.54/21.75 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.75 apply (zenon_L143_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.75 apply (zenon_L66_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.75 apply (zenon_L452_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.75 apply (zenon_L89_); trivial. % 21.54/21.75 apply (zenon_L90_); trivial. % 21.54/21.75 (* end of lemma zenon_L453_ *) % 21.54/21.75 assert (zenon_L454_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (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) (e0)) = (e0)) -> ((op (e2) (e1)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((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)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 21.54/21.75 do 0 intro. intros zenon_H139 zenon_H13a zenon_H47 zenon_Ha0 zenon_H73 zenon_H140 zenon_H1d8 zenon_H2a zenon_H68 zenon_H1ef zenon_H117 zenon_H2d zenon_H6d zenon_H111 zenon_H121 zenon_H1b4 zenon_H163 zenon_H72 zenon_H77 zenon_H183 zenon_H11a zenon_H129 zenon_Heb zenon_Hb6 zenon_H40 zenon_Hec zenon_H13c zenon_H190 zenon_H105 zenon_H48 zenon_He4 zenon_He3 zenon_Hfa zenon_H1b3 zenon_Hf5 zenon_H13b zenon_Ha9. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.75 apply (zenon_L251_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.75 apply (zenon_L147_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.75 apply (zenon_L22_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.75 apply (zenon_L253_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.75 apply (zenon_L53_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.75 apply (zenon_L453_); trivial. % 21.54/21.75 apply (zenon_L92_); trivial. % 21.54/21.75 (* end of lemma zenon_L454_ *) % 21.54/21.75 assert (zenon_L455_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 21.54/21.75 do 0 intro. intros zenon_H117 zenon_H109 zenon_H9d zenon_Ha9 zenon_H6d zenon_H111 zenon_Hfe zenon_H22d zenon_H14c zenon_H1ef zenon_H3c zenon_H100 zenon_H77 zenon_H7f zenon_H55 zenon_H1b3 zenon_H2a zenon_H68 zenon_H1a8 zenon_H94. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.75 apply (zenon_L73_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.75 apply (zenon_L289_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.75 apply (zenon_L75_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H2d | zenon_intro zenon_H22e ]. % 21.54/21.75 apply (zenon_L405_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H54 | zenon_intro zenon_H22f ]. % 21.54/21.75 apply (zenon_L69_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H65 | zenon_intro zenon_Ha8 ]. % 21.54/21.75 apply (zenon_L288_); trivial. % 21.54/21.75 apply (zenon_L47_); trivial. % 21.54/21.75 (* end of lemma zenon_L455_ *) % 21.54/21.75 assert (zenon_L456_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.54/21.75 do 0 intro. intros zenon_H34 zenon_H7e zenon_H48. % 21.54/21.75 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H49 | zenon_intro zenon_H4a ]. % 21.54/21.75 cut (((e1) = (e1)) = ((e0) = (e1))). % 21.54/21.75 intro zenon_D_pnotp. % 21.54/21.75 apply zenon_H48. % 21.54/21.75 rewrite <- zenon_D_pnotp. % 21.54/21.75 exact zenon_H49. % 21.54/21.75 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.75 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 21.54/21.75 congruence. % 21.54/21.75 cut (((op (e3) (e0)) = (e0)) = ((e1) = (e0))). % 21.54/21.75 intro zenon_D_pnotp. % 21.54/21.75 apply zenon_H4b. % 21.54/21.75 rewrite <- zenon_D_pnotp. % 21.54/21.75 exact zenon_H34. % 21.54/21.75 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.54/21.75 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 21.54/21.75 congruence. % 21.54/21.75 exact (zenon_H182 zenon_H7e). % 21.54/21.75 apply zenon_H46. apply refl_equal. % 21.54/21.75 apply zenon_H4a. apply refl_equal. % 21.54/21.75 apply zenon_H4a. apply refl_equal. % 21.54/21.75 (* end of lemma zenon_L456_ *) % 21.54/21.75 assert (zenon_L457_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((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 (e3) (e0)) = (op (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (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 (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> False). % 21.54/21.75 do 0 intro. intros zenon_H1fe zenon_H19d zenon_H7d zenon_H1c3 zenon_H186 zenon_H189 zenon_H156 zenon_H6f zenon_H129 zenon_H20b zenon_H1d8 zenon_Hfa zenon_Hf5 zenon_H15d zenon_H82 zenon_H1b4 zenon_H139 zenon_Hb6 zenon_H13b zenon_He3 zenon_He4 zenon_H13c zenon_Hbc zenon_H183 zenon_H163 zenon_H121 zenon_H94 zenon_H1a8 zenon_H68 zenon_H2a zenon_H1b3 zenon_H55 zenon_H1ef zenon_H22d zenon_H111 zenon_H6d zenon_H109 zenon_H117 zenon_H11a zenon_H177 zenon_Ha9 zenon_H140 zenon_H73 zenon_Ha0 zenon_H105 zenon_H190 zenon_H13a zenon_Hec zenon_H72 zenon_H77 zenon_H40 zenon_H100 zenon_Heb zenon_H48. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.75 apply (zenon_L161_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.75 apply (zenon_L60_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.75 apply (zenon_L454_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.75 apply (zenon_L65_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.75 apply (zenon_L148_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.75 apply (zenon_L454_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.75 apply (zenon_L447_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.75 apply (zenon_L70_); trivial. % 21.54/21.75 apply (zenon_L448_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.75 apply (zenon_L350_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.75 apply (zenon_L65_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.75 apply (zenon_L148_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.75 apply (zenon_L350_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.75 apply (zenon_L450_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.75 apply (zenon_L53_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.75 apply (zenon_L25_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.75 exact (zenon_He3 zenon_He7). % 21.54/21.75 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.75 apply (zenon_L62_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.75 apply (zenon_L65_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.75 exact (zenon_H40 zenon_H3f). % 21.54/21.75 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.75 apply (zenon_L56_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.75 apply (zenon_L46_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.75 apply (zenon_L68_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.75 apply (zenon_L62_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.54/21.75 apply (zenon_L291_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.54/21.75 apply (zenon_L169_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.54/21.75 apply (zenon_L227_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.54/21.75 apply (zenon_L455_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.54/21.75 apply (zenon_L79_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.54/21.75 apply (zenon_L178_); trivial. % 21.54/21.75 apply (zenon_L133_); trivial. % 21.54/21.75 apply (zenon_L328_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.75 apply (zenon_L89_); trivial. % 21.54/21.75 apply (zenon_L90_); trivial. % 21.54/21.75 apply (zenon_L115_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.75 apply (zenon_L70_); trivial. % 21.54/21.75 apply (zenon_L456_); trivial. % 21.54/21.75 (* end of lemma zenon_L457_ *) % 21.54/21.75 assert (zenon_L458_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 21.54/21.75 do 0 intro. intros zenon_H99 zenon_H6d zenon_H189. % 21.54/21.75 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.54/21.75 apply (zenon_L439_); trivial. % 21.54/21.75 (* end of lemma zenon_L458_ *) % 21.54/21.75 assert (zenon_L459_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 21.54/21.75 do 0 intro. intros zenon_H15d zenon_H4c zenon_H48 zenon_H2a zenon_H105 zenon_H111 zenon_Hb6 zenon_H9e. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.75 exact (zenon_H4c zenon_H47). % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.75 apply (zenon_L65_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.75 apply (zenon_L148_); trivial. % 21.54/21.75 apply (zenon_L115_); trivial. % 21.54/21.75 (* end of lemma zenon_L459_ *) % 21.54/21.75 assert (zenon_L460_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> False). % 21.54/21.75 do 0 intro. intros zenon_H9b zenon_H48 zenon_H111 zenon_H105 zenon_Hb6 zenon_H15d zenon_H2a. % 21.54/21.75 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.54/21.75 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 21.54/21.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.54/21.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 21.54/21.75 exact (zenon_H205 zenon_H2a). % 21.54/21.75 apply (zenon_L459_); trivial. % 21.54/21.75 (* end of lemma zenon_L460_ *) % 21.54/21.75 assert (zenon_L461_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.54/21.75 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_H1d4 zenon_H155 zenon_Hf5. % 21.54/21.75 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.75 exact (zenon_H7a zenon_H3c). % 21.54/21.75 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.75 exact (zenon_H40 zenon_H3f). % 21.54/21.75 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.75 exact (zenon_H1d4 zenon_H4d). % 21.54/21.75 apply (zenon_L192_); trivial. % 21.54/21.75 (* end of lemma zenon_L461_ *) % 21.54/21.75 assert (zenon_L462_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> False). % 21.54/21.75 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_Hf3 zenon_H48 zenon_Hec. % 21.54/21.75 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.54/21.75 exact (zenon_H7a zenon_H3c). % 21.54/21.75 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.54/21.75 exact (zenon_H40 zenon_H3f). % 21.54/21.75 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.54/21.75 apply (zenon_L117_); trivial. % 21.54/21.75 exact (zenon_Hec zenon_H5c). % 21.54/21.75 (* end of lemma zenon_L462_ *) % 21.54/21.75 assert (zenon_L463_ : (((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 (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 21.54/21.75 do 0 intro. intros zenon_H13b zenon_H34 zenon_H179 zenon_H2a zenon_H173 zenon_Hec zenon_H48 zenon_H40 zenon_H7a zenon_Heb zenon_Ha0 zenon_Ha5. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.75 apply (zenon_L297_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.75 apply (zenon_L272_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.75 apply (zenon_L462_); trivial. % 21.54/21.75 apply (zenon_L90_); trivial. % 21.54/21.75 (* end of lemma zenon_L463_ *) % 21.54/21.75 assert (zenon_L464_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 21.54/21.75 do 0 intro. intros zenon_H15c zenon_Hf0 zenon_H6d zenon_H158 zenon_H15d zenon_H7a zenon_H40 zenon_H1d4 zenon_Hf5 zenon_Heb zenon_H105 zenon_H111 zenon_H2a zenon_H48 zenon_Hb6 zenon_H5d zenon_Ha5 zenon_Ha0 zenon_H7d zenon_Hac zenon_Hb2 zenon_H13b zenon_H173 zenon_H179 zenon_H1fe. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.75 apply (zenon_L13_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.75 apply (zenon_L65_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.75 apply (zenon_L148_); trivial. % 21.54/21.75 apply (zenon_L461_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.75 apply (zenon_L250_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.75 apply (zenon_L355_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.75 apply (zenon_L65_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.75 apply (zenon_L148_); trivial. % 21.54/21.75 apply (zenon_L461_); trivial. % 21.54/21.75 apply (zenon_L463_); trivial. % 21.54/21.75 apply (zenon_L389_); trivial. % 21.54/21.75 (* end of lemma zenon_L464_ *) % 21.54/21.75 assert (zenon_L465_ : ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (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 (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> False). % 21.54/21.75 do 0 intro. intros zenon_H44 zenon_H15c zenon_Hf0 zenon_H6d zenon_H158 zenon_H15d zenon_H40 zenon_Hf5 zenon_Heb zenon_H105 zenon_H111 zenon_H2a zenon_H48 zenon_Hb6 zenon_H5d zenon_Ha5 zenon_Ha0 zenon_H7d zenon_Hac zenon_Hb2 zenon_H13b zenon_H173 zenon_H179 zenon_H1fe zenon_H11a zenon_H169. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 21.54/21.75 apply (zenon_L464_); trivial. % 21.54/21.75 apply (zenon_L372_); trivial. % 21.54/21.75 apply (zenon_L385_); trivial. % 21.54/21.75 (* end of lemma zenon_L465_ *) % 21.54/21.75 assert (zenon_L466_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> False). % 21.54/21.75 do 0 intro. intros zenon_H91 zenon_H105 zenon_H6d. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.54/21.75 exact (zenon_H1ba zenon_H6d). % 21.54/21.75 exact (zenon_H1bf zenon_H105). % 21.54/21.75 (* end of lemma zenon_L466_ *) % 21.54/21.75 assert (zenon_L467_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> False). % 21.54/21.75 do 0 intro. intros zenon_Hc0 zenon_H105 zenon_H6d. % 21.54/21.75 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.54/21.75 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.54/21.75 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.54/21.75 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.54/21.75 apply (zenon_L466_); trivial. % 21.54/21.75 (* end of lemma zenon_L467_ *) % 21.54/21.75 assert (zenon_L468_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (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)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (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)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)))) -> (((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)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (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 (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> False). % 21.54/21.75 do 0 intro. intros zenon_H230 zenon_Heb zenon_H105 zenon_H131 zenon_H40 zenon_H48 zenon_H158 zenon_H6d zenon_Hf0 zenon_H2a zenon_H173 zenon_H1d8 zenon_H1fb zenon_H77 zenon_H1fe zenon_H104 zenon_H179 zenon_H140 zenon_H183 zenon_H1b4 zenon_H163 zenon_H129 zenon_H20b zenon_H190 zenon_H19a zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1bb zenon_H20f zenon_H1c3 zenon_H1cf zenon_H19d zenon_H15d zenon_Hf5 zenon_H111 zenon_H192 zenon_H6f zenon_H13a zenon_H13b zenon_H1a2 zenon_H1ef zenon_H68 zenon_H73 zenon_Hfa zenon_H196 zenon_H117 zenon_H121 zenon_H177 zenon_H11a zenon_Ha9 zenon_H1c6 zenon_Ha0 zenon_Hb6 zenon_H139 zenon_H125 zenon_H164 zenon_H55 zenon_H1cb zenon_He4 zenon_H156 zenon_H94 zenon_H22d zenon_H109 zenon_H100 zenon_Hb2 zenon_H4e zenon_H82 zenon_H189 zenon_H1a8 zenon_H186 zenon_H13c zenon_H5d zenon_Hcc. % 21.54/21.75 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 21.54/21.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.54/21.75 apply (zenon_L2_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.54/21.75 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 21.54/21.75 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 21.54/21.75 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.54/21.75 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.54/21.75 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.54/21.75 apply (zenon_L392_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.54/21.75 apply (zenon_L315_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.54/21.75 apply (zenon_L317_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.54/21.75 apply (zenon_L318_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.54/21.75 apply (zenon_L11_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.54/21.75 apply (zenon_L319_); trivial. % 21.54/21.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.54/21.76 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.54/21.76 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.54/21.76 apply (zenon_L402_); trivial. % 21.54/21.76 apply (zenon_L402_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.54/21.76 apply (zenon_L424_); trivial. % 21.54/21.76 apply (zenon_L424_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.54/21.76 apply (zenon_L432_); trivial. % 21.54/21.76 apply (zenon_L432_); trivial. % 21.54/21.76 apply (zenon_L434_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.54/21.76 apply (zenon_L435_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 21.54/21.76 apply (zenon_L345_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.54/21.76 apply (zenon_L451_); trivial. % 21.54/21.76 apply (zenon_L389_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.54/21.76 apply (zenon_L457_); trivial. % 21.54/21.76 apply (zenon_L304_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.54/21.76 apply (zenon_L37_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.54/21.76 apply (zenon_L458_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.54/21.76 apply (zenon_L460_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.54/21.76 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.54/21.76 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.54/21.76 apply (zenon_L465_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.54/21.76 apply (zenon_L467_); trivial. % 21.54/21.76 apply (zenon_L51_); trivial. % 21.54/21.76 apply (zenon_L394_); trivial. % 21.54/21.76 (* end of lemma zenon_L468_ *) % 21.54/21.76 assert (zenon_L469_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((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) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((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)) = (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) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((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 (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H201 zenon_H66 zenon_Hf3 zenon_Hcc zenon_H5d zenon_H13c zenon_H186 zenon_H1a8 zenon_H189 zenon_H82 zenon_H4e zenon_Hb2 zenon_H100 zenon_H109 zenon_H22d zenon_H94 zenon_H156 zenon_He4 zenon_H1cb zenon_H55 zenon_H164 zenon_H125 zenon_H139 zenon_Hb6 zenon_Ha0 zenon_H1c6 zenon_Ha9 zenon_H11a zenon_H177 zenon_H121 zenon_H117 zenon_H196 zenon_Hfa zenon_H73 zenon_H68 zenon_H1ef zenon_H1a2 zenon_H13b zenon_H13a zenon_H6f zenon_H192 zenon_H111 zenon_Hf5 zenon_H15d zenon_H19d zenon_H1cf zenon_H1c3 zenon_H20f zenon_H1bb zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H19a zenon_H190 zenon_H20b zenon_H129 zenon_H163 zenon_H1b4 zenon_H183 zenon_H140 zenon_H179 zenon_H104 zenon_H1fe zenon_H77 zenon_H1fb zenon_H1d8 zenon_H173 zenon_H2a zenon_Hf0 zenon_H6d zenon_H158 zenon_H48 zenon_H40 zenon_H131 zenon_Heb zenon_H230 zenon_H1cd zenon_H7f. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.76 apply (zenon_L94_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.76 apply (zenon_L117_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.76 apply (zenon_L468_); trivial. % 21.54/21.76 apply (zenon_L331_); trivial. % 21.54/21.76 (* end of lemma zenon_L469_ *) % 21.54/21.76 assert (zenon_L470_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (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) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (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)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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)) = (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))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)))) -> (((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)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (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 (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H13b zenon_H77 zenon_H73 zenon_H68 zenon_Hfa zenon_H1a2 zenon_H1ef zenon_H1a3 zenon_H48 zenon_H5c zenon_H7f zenon_H1cd zenon_H230 zenon_Heb zenon_H131 zenon_H1d8 zenon_H1fb zenon_H1fe zenon_H104 zenon_H179 zenon_H140 zenon_H183 zenon_H1b4 zenon_H163 zenon_H129 zenon_H20b zenon_H190 zenon_H19a zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1bb zenon_H20f zenon_H1c3 zenon_H1cf zenon_H19d zenon_H15d zenon_Hf5 zenon_H111 zenon_H192 zenon_H6f zenon_H196 zenon_H117 zenon_H139 zenon_H125 zenon_H164 zenon_H55 zenon_H1cb zenon_He4 zenon_H156 zenon_H94 zenon_H22d zenon_H109 zenon_H100 zenon_Hb2 zenon_H4e zenon_H82 zenon_H189 zenon_H1a8 zenon_H186 zenon_H13c zenon_H5d zenon_Hcc zenon_H201 zenon_H13a zenon_Hb6 zenon_H47 zenon_H11a zenon_H6d zenon_Hf0 zenon_H40 zenon_H173 zenon_H2a zenon_H158 zenon_H121 zenon_H209 zenon_H177 zenon_Hc4 zenon_Ha0 zenon_H1c6 zenon_Ha9. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.76 apply (zenon_L251_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.76 apply (zenon_L147_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.76 apply (zenon_L253_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.76 apply (zenon_L116_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.76 apply (zenon_L272_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.76 apply (zenon_L469_); trivial. % 21.54/21.76 apply (zenon_L157_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.76 apply (zenon_L399_); trivial. % 21.54/21.76 exact (zenon_H209 zenon_H9d). % 21.54/21.76 apply (zenon_L401_); trivial. % 21.54/21.76 (* end of lemma zenon_L470_ *) % 21.54/21.76 assert (zenon_L471_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (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)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((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) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H1c6 zenon_H177 zenon_H121 zenon_H158 zenon_H40 zenon_Hf0 zenon_H6d zenon_H11a zenon_H201 zenon_Hcc zenon_H5d zenon_H13c zenon_H186 zenon_H1a8 zenon_H189 zenon_H82 zenon_H4e zenon_Hb2 zenon_H100 zenon_H109 zenon_H22d zenon_H94 zenon_H156 zenon_He4 zenon_H1cb zenon_H55 zenon_H164 zenon_H125 zenon_H117 zenon_H196 zenon_Hfa zenon_H73 zenon_H1ef zenon_H1a2 zenon_H6f zenon_H192 zenon_H111 zenon_Hf5 zenon_H15d zenon_H19d zenon_H190 zenon_H20b zenon_H163 zenon_H140 zenon_H1fe zenon_H1fb zenon_H1d8 zenon_H131 zenon_Heb zenon_H230 zenon_H1cd zenon_H139 zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha0 zenon_Hc4 zenon_H181 zenon_H120 zenon_H20f zenon_H1bb zenon_H1cf zenon_H104 zenon_H183 zenon_H19a zenon_H1b4 zenon_H77 zenon_H68 zenon_H1c3 zenon_H5c zenon_H48 zenon_H129 zenon_H212 zenon_H18a zenon_H7f zenon_H7d zenon_Hbc zenon_H209 zenon_H173 zenon_H2a zenon_H179 zenon_H13b zenon_Ha9. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.76 apply (zenon_L161_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.76 apply (zenon_L403_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.76 apply (zenon_L251_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.76 apply (zenon_L147_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.76 apply (zenon_L253_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.76 apply (zenon_L116_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.76 apply (zenon_L272_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.76 apply (zenon_L469_); trivial. % 21.54/21.76 apply (zenon_L422_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.76 apply (zenon_L67_); trivial. % 21.54/21.76 exact (zenon_H209 zenon_H9d). % 21.54/21.76 apply (zenon_L401_); trivial. % 21.54/21.76 apply (zenon_L423_); trivial. % 21.54/21.76 (* end of lemma zenon_L471_ *) % 21.54/21.76 assert (zenon_L472_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H13b zenon_Ha0 zenon_Ha6 zenon_H2a zenon_H173 zenon_Hc4 zenon_H1cb zenon_H120 zenon_H162 zenon_H1bb zenon_H6d zenon_H190 zenon_H68 zenon_Hfe zenon_Ha9 zenon_H1cf zenon_H48 zenon_H5c. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.76 apply (zenon_L116_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.76 apply (zenon_L272_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.76 apply (zenon_L425_); trivial. % 21.54/21.76 apply (zenon_L157_); trivial. % 21.54/21.76 (* end of lemma zenon_L472_ *) % 21.54/21.76 assert (zenon_L473_ : ((op (e1) (e0)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (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)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (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)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)))) -> (((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)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (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 (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H76 zenon_H7f zenon_H1cd zenon_H230 zenon_Heb zenon_H131 zenon_H40 zenon_H158 zenon_H6d zenon_Hf0 zenon_H2a zenon_H173 zenon_H1d8 zenon_H1fb zenon_H77 zenon_H1fe zenon_H104 zenon_H179 zenon_H140 zenon_H183 zenon_H1b4 zenon_H163 zenon_H129 zenon_H20b zenon_H190 zenon_H19a zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1bb zenon_H20f zenon_H1c3 zenon_H1cf zenon_H19d zenon_H15d zenon_Hf5 zenon_H111 zenon_H192 zenon_H6f zenon_H13a zenon_H13b zenon_H1a2 zenon_H1ef zenon_H68 zenon_H73 zenon_Hfa zenon_H196 zenon_H117 zenon_H121 zenon_H177 zenon_H11a zenon_Ha9 zenon_H1c6 zenon_Ha0 zenon_Hb6 zenon_H139 zenon_H125 zenon_H164 zenon_H55 zenon_H1cb zenon_He4 zenon_H156 zenon_H94 zenon_H22d zenon_H109 zenon_H100 zenon_Hb2 zenon_H4e zenon_H82 zenon_H189 zenon_H1a8 zenon_H186 zenon_H13c zenon_H5d zenon_Hcc zenon_H66 zenon_H201 zenon_H48 zenon_H5c. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.76 apply (zenon_L171_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.76 apply (zenon_L272_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.76 apply (zenon_L469_); trivial. % 21.54/21.76 apply (zenon_L157_); trivial. % 21.54/21.76 (* end of lemma zenon_L473_ *) % 21.54/21.76 assert (zenon_L474_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 21.54/21.76 do 0 intro. intros zenon_Hb2 zenon_Hb6 zenon_H47 zenon_H5c zenon_H48 zenon_H1cf zenon_Hfe zenon_H68 zenon_H190 zenon_H6d zenon_H1bb zenon_H162 zenon_H120 zenon_H1cb zenon_Hc4 zenon_H173 zenon_H2a zenon_H13b zenon_Ha0 zenon_H2d zenon_Ha9 zenon_H102. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.76 apply (zenon_L253_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.76 apply (zenon_L472_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.76 apply (zenon_L67_); trivial. % 21.54/21.76 apply (zenon_L91_); trivial. % 21.54/21.76 (* end of lemma zenon_L474_ *) % 21.54/21.76 assert (zenon_L475_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e2) (e1)) = (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))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H125 zenon_H77 zenon_H13a zenon_H2d zenon_Ha0 zenon_H13b zenon_H2a zenon_H173 zenon_Hc4 zenon_H1cb zenon_H120 zenon_H162 zenon_H1bb zenon_H6d zenon_H190 zenon_H68 zenon_H1cf zenon_H48 zenon_H5c zenon_H47 zenon_Hb6 zenon_Hb2 zenon_Ha9 zenon_Hf6. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.76 apply (zenon_L251_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.76 apply (zenon_L429_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.76 apply (zenon_L27_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.76 apply (zenon_L253_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.76 apply (zenon_L53_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.76 apply (zenon_L474_); trivial. % 21.54/21.76 apply (zenon_L92_); trivial. % 21.54/21.76 (* end of lemma zenon_L475_ *) % 21.54/21.76 assert (zenon_L476_ : (((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)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e3) (e2)) = (e3))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H231 zenon_H34 zenon_Hbc zenon_H105 zenon_H104 zenon_Hc4 zenon_H1cb zenon_H120 zenon_H162 zenon_H1bb zenon_H1a3. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H11d | zenon_intro zenon_H232 ]. % 21.54/21.76 apply (zenon_L328_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H106 | zenon_intro zenon_H233 ]. % 21.54/21.76 apply (zenon_L72_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H160 | zenon_intro zenon_Hbb ]. % 21.54/21.76 apply (zenon_L237_); trivial. % 21.54/21.76 exact (zenon_H1a3 zenon_Hbb). % 21.54/21.76 (* end of lemma zenon_L476_ *) % 21.54/21.76 assert (zenon_L477_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (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) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> False). % 21.54/21.76 do 0 intro. intros zenon_Hc2 zenon_Hbc zenon_H34 zenon_H104 zenon_H105 zenon_H1bb zenon_H1cb zenon_H120 zenon_H162 zenon_H1a3 zenon_H231. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.54/21.76 apply (zenon_L476_); trivial. % 21.54/21.76 apply (zenon_L476_); trivial. % 21.54/21.76 (* end of lemma zenon_L477_ *) % 21.54/21.76 assert (zenon_L478_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H13f zenon_H65 zenon_H77 zenon_H7f zenon_H1f1 zenon_H231 zenon_H1a3 zenon_H162 zenon_H120 zenon_H1cb zenon_H1bb zenon_H104 zenon_H34 zenon_Hbc zenon_Hc2 zenon_H195 zenon_H5c. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.54/21.76 apply (zenon_L30_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.54/21.76 apply (zenon_L284_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.54/21.76 apply (zenon_L477_); trivial. % 21.54/21.76 apply (zenon_L149_); trivial. % 21.54/21.76 (* end of lemma zenon_L478_ *) % 21.54/21.76 assert (zenon_L479_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H125 zenon_H77 zenon_Hf6 zenon_Ha9 zenon_H13b zenon_H2a zenon_H173 zenon_Hc4 zenon_H1cb zenon_H120 zenon_H162 zenon_H1bb zenon_H190 zenon_H1cf zenon_H48 zenon_H5c zenon_Ha0 zenon_H47 zenon_Hb6 zenon_H13a zenon_H6d zenon_H55 zenon_H34 zenon_H68. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.76 apply (zenon_L251_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.76 apply (zenon_L429_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.76 apply (zenon_L34_); trivial. % 21.54/21.76 apply (zenon_L291_); trivial. % 21.54/21.76 (* end of lemma zenon_L479_ *) % 21.54/21.76 assert (zenon_L480_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (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))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((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)) = (op (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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (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 (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) (e3)))) -> (((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)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (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 (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H1c3 zenon_H19a zenon_H18a zenon_H192 zenon_H164 zenon_H13f zenon_H7f zenon_H1f1 zenon_H231 zenon_H1a3 zenon_H104 zenon_Hbc zenon_Hc2 zenon_H195 zenon_H1cd zenon_H230 zenon_Heb zenon_H131 zenon_H40 zenon_H158 zenon_Hf0 zenon_H1d8 zenon_H1fb zenon_H1fe zenon_H179 zenon_H140 zenon_H183 zenon_H1b4 zenon_H163 zenon_H129 zenon_H20b zenon_H7d zenon_H212 zenon_H20f zenon_H19d zenon_H15d zenon_Hf5 zenon_H111 zenon_H6f zenon_H1a2 zenon_H1ef zenon_H73 zenon_Hfa zenon_H196 zenon_H117 zenon_H121 zenon_H177 zenon_H11a zenon_H1c6 zenon_H139 zenon_He4 zenon_H156 zenon_H94 zenon_H22d zenon_H109 zenon_H100 zenon_Hb2 zenon_H4e zenon_H82 zenon_H189 zenon_H1a8 zenon_H186 zenon_H13c zenon_H5d zenon_Hcc zenon_H201 zenon_H1d5 zenon_H125 zenon_H77 zenon_Ha9 zenon_H13b zenon_H2a zenon_H173 zenon_Hc4 zenon_H1cb zenon_H120 zenon_H162 zenon_H1bb zenon_H190 zenon_H1cf zenon_H48 zenon_H5c zenon_Ha0 zenon_H47 zenon_Hb6 zenon_H13a zenon_H6d zenon_H55 zenon_H68. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.76 apply (zenon_L13_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.76 apply (zenon_L251_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.76 apply (zenon_L21_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.76 apply (zenon_L396_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.76 apply (zenon_L251_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.76 apply (zenon_L171_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.76 apply (zenon_L34_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.76 apply (zenon_L253_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.76 apply (zenon_L53_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.76 apply (zenon_L253_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.76 apply (zenon_L472_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.76 apply (zenon_L427_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.76 apply (zenon_L61_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.76 apply (zenon_L53_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.54/21.76 apply (zenon_L151_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.54/21.76 apply (zenon_L56_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.54/21.76 apply (zenon_L431_); trivial. % 21.54/21.76 apply (zenon_L149_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.76 apply (zenon_L289_); trivial. % 21.54/21.76 apply (zenon_L394_); trivial. % 21.54/21.76 apply (zenon_L63_); trivial. % 21.54/21.76 apply (zenon_L91_); trivial. % 21.54/21.76 apply (zenon_L339_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.76 apply (zenon_L251_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.76 apply (zenon_L147_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.76 apply (zenon_L252_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.76 apply (zenon_L473_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.76 apply (zenon_L27_); trivial. % 21.54/21.76 apply (zenon_L340_); trivial. % 21.54/21.76 apply (zenon_L475_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.76 apply (zenon_L251_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.76 apply (zenon_L21_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.76 apply (zenon_L252_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.76 apply (zenon_L473_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.76 apply (zenon_L478_); trivial. % 21.54/21.76 apply (zenon_L340_); trivial. % 21.54/21.76 apply (zenon_L479_); trivial. % 21.54/21.76 (* end of lemma zenon_L480_ *) % 21.54/21.76 assert (zenon_L481_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (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) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((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)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H141 zenon_H120 zenon_H230 zenon_H131 zenon_H1d8 zenon_H1fb zenon_H104 zenon_H179 zenon_H140 zenon_H129 zenon_H20b zenon_H190 zenon_H19a zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1bb zenon_H20f zenon_H1c3 zenon_H1cf zenon_H15d zenon_Hf5 zenon_H111 zenon_H192 zenon_H6f zenon_H13b zenon_H1a2 zenon_H1ef zenon_Hfa zenon_H117 zenon_H121 zenon_H1c6 zenon_H164 zenon_H1cb zenon_H94 zenon_H22d zenon_H109 zenon_H100 zenon_H82 zenon_H1a8 zenon_H186 zenon_H13c zenon_H5d zenon_Hcc zenon_H1cd zenon_H201 zenon_H1f1 zenon_H231 zenon_H1d5 zenon_H195 zenon_H13f zenon_H55 zenon_H156 zenon_H77 zenon_Heb zenon_H19d zenon_H48 zenon_H125 zenon_Ha9 zenon_Hb2 zenon_H68 zenon_H4e zenon_H139 zenon_H183 zenon_H1b4 zenon_H163 zenon_He4 zenon_H73 zenon_H1fe zenon_H189 zenon_H11a zenon_H6d zenon_Hf0 zenon_H40 zenon_H173 zenon_H158 zenon_H196 zenon_H177 zenon_H2a zenon_Ha0 zenon_H47 zenon_Hb6 zenon_H13a. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.54/21.76 apply (zenon_L2_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.54/21.76 apply (zenon_L250_); trivial. % 21.54/21.76 apply (zenon_L389_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.76 apply (zenon_L251_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.76 apply (zenon_L147_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.76 apply (zenon_L252_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.76 apply (zenon_L171_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.76 apply (zenon_L34_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.76 apply (zenon_L253_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.76 apply (zenon_L53_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.76 apply (zenon_L193_); trivial. % 21.54/21.76 apply (zenon_L390_); trivial. % 21.54/21.76 apply (zenon_L303_); trivial. % 21.54/21.76 apply (zenon_L304_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.54/21.76 apply (zenon_L315_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.54/21.76 apply (zenon_L317_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.54/21.76 apply (zenon_L318_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.54/21.76 apply (zenon_L11_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.54/21.76 apply (zenon_L319_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.54/21.76 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.54/21.76 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.54/21.76 apply (zenon_L470_); trivial. % 21.54/21.76 apply (zenon_L470_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.54/21.76 apply (zenon_L471_); trivial. % 21.54/21.76 apply (zenon_L471_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.54/21.76 apply (zenon_L480_); trivial. % 21.54/21.76 apply (zenon_L480_); trivial. % 21.54/21.76 apply (zenon_L434_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.54/21.76 apply (zenon_L435_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.54/21.76 apply (zenon_L351_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.54/21.76 apply (zenon_L37_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.54/21.76 apply (zenon_L458_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.54/21.76 apply (zenon_L354_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.54/21.76 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.54/21.76 apply (zenon_L394_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.54/21.76 apply (zenon_L377_); trivial. % 21.54/21.76 apply (zenon_L51_); trivial. % 21.54/21.76 (* end of lemma zenon_L481_ *) % 21.54/21.76 assert (zenon_L482_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (e1)) = (e1)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H28 zenon_H3f. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.54/21.76 apply (zenon_L10_); trivial. % 21.54/21.76 (* end of lemma zenon_L482_ *) % 21.54/21.76 assert (zenon_L483_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H5a zenon_H3f zenon_Hf0. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.54/21.76 apply (zenon_L118_); trivial. % 21.54/21.76 (* end of lemma zenon_L483_ *) % 21.54/21.76 assert (zenon_L484_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H5c zenon_H3f zenon_H234. % 21.54/21.76 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H5e | zenon_intro zenon_H5f ]. % 21.54/21.76 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e1)) = (op (e1) (e3)))). % 21.54/21.76 intro zenon_D_pnotp. % 21.54/21.76 apply zenon_H234. % 21.54/21.76 rewrite <- zenon_D_pnotp. % 21.54/21.76 exact zenon_H5e. % 21.54/21.76 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.54/21.76 cut (((op (e1) (e3)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H235]. % 21.54/21.76 congruence. % 21.54/21.76 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e1)))). % 21.54/21.76 intro zenon_D_pnotp. % 21.54/21.76 apply zenon_H235. % 21.54/21.76 rewrite <- zenon_D_pnotp. % 21.54/21.76 exact zenon_H5c. % 21.54/21.76 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H170]. % 21.54/21.76 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 21.54/21.76 congruence. % 21.54/21.76 apply zenon_H5f. apply refl_equal. % 21.54/21.76 apply zenon_H170. apply sym_equal. exact zenon_H3f. % 21.54/21.76 apply zenon_H5f. apply refl_equal. % 21.54/21.76 apply zenon_H5f. apply refl_equal. % 21.54/21.76 (* end of lemma zenon_L484_ *) % 21.54/21.76 assert (zenon_L485_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H61 zenon_H3f zenon_H234. % 21.54/21.76 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.54/21.76 apply (zenon_L484_); trivial. % 21.54/21.76 (* end of lemma zenon_L485_ *) % 21.54/21.76 assert (zenon_L486_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H4d zenon_H3f zenon_H156. % 21.54/21.76 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H4f | zenon_intro zenon_H50 ]. % 21.54/21.76 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e1)) = (op (e1) (e2)))). % 21.54/21.76 intro zenon_D_pnotp. % 21.54/21.76 apply zenon_H156. % 21.54/21.76 rewrite <- zenon_D_pnotp. % 21.54/21.76 exact zenon_H4f. % 21.54/21.76 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.54/21.76 cut (((op (e1) (e2)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H157]. % 21.54/21.76 congruence. % 21.54/21.76 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e1)))). % 21.54/21.76 intro zenon_D_pnotp. % 21.54/21.76 apply zenon_H157. % 21.54/21.76 rewrite <- zenon_D_pnotp. % 21.54/21.76 exact zenon_H4d. % 21.54/21.76 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H170]. % 21.54/21.76 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 21.54/21.76 congruence. % 21.54/21.76 apply zenon_H50. apply refl_equal. % 21.54/21.76 apply zenon_H170. apply sym_equal. exact zenon_H3f. % 21.54/21.76 apply zenon_H50. apply refl_equal. % 21.54/21.76 apply zenon_H50. apply refl_equal. % 21.54/21.76 (* end of lemma zenon_L486_ *) % 21.54/21.76 assert (zenon_L487_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H236 zenon_H1f zenon_H48 zenon_H3d zenon_H237 zenon_H238. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 21.54/21.76 exact (zenon_H1f zenon_H1e). % 21.54/21.76 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 21.54/21.76 apply (zenon_L65_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 21.54/21.76 exact (zenon_H237 zenon_H31). % 21.54/21.76 exact (zenon_H238 zenon_H38). % 21.54/21.76 (* end of lemma zenon_L487_ *) % 21.54/21.76 assert (zenon_L488_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_Ha9 zenon_H66 zenon_H38 zenon_Ha0. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.76 exact (zenon_Ha4 zenon_H9f). % 21.54/21.76 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.76 apply (zenon_L55_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.76 apply (zenon_L193_); trivial. % 21.54/21.76 apply (zenon_L156_); trivial. % 21.54/21.76 (* end of lemma zenon_L488_ *) % 21.54/21.76 assert (zenon_L489_ : (((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)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H139 zenon_H2c zenon_H65 zenon_H77 zenon_Ha0 zenon_Ha9 zenon_H3d zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H38 zenon_H68. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.76 apply (zenon_L180_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.76 apply (zenon_L214_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.76 apply (zenon_L488_); trivial. % 21.54/21.76 apply (zenon_L165_); trivial. % 21.54/21.76 (* end of lemma zenon_L489_ *) % 21.54/21.76 assert (zenon_L490_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (((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)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H236 zenon_H1f zenon_H48 zenon_H237 zenon_H139 zenon_H2c zenon_H65 zenon_H77 zenon_Ha0 zenon_Ha9 zenon_H3d zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H68. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 21.54/21.76 exact (zenon_H1f zenon_H1e). % 21.54/21.76 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 21.54/21.76 apply (zenon_L65_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 21.54/21.76 exact (zenon_H237 zenon_H31). % 21.54/21.76 apply (zenon_L489_); trivial. % 21.54/21.76 (* end of lemma zenon_L490_ *) % 21.54/21.76 assert (zenon_L491_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H23b zenon_H139 zenon_H68 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H77 zenon_H65 zenon_H2c zenon_H1f zenon_H48 zenon_H3d zenon_H237 zenon_H236. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 21.54/21.76 apply (zenon_L487_); trivial. % 21.54/21.76 apply (zenon_L490_); trivial. % 21.54/21.76 (* end of lemma zenon_L491_ *) % 21.54/21.76 assert (zenon_L492_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H23c zenon_H3c zenon_H3f. % 21.54/21.76 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 21.54/21.76 intro zenon_D_pnotp. % 21.54/21.76 apply zenon_H23c. % 21.54/21.76 rewrite <- zenon_D_pnotp. % 21.54/21.76 exact zenon_H3c. % 21.54/21.76 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H170]. % 21.54/21.76 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H101]. % 21.54/21.76 congruence. % 21.54/21.76 apply zenon_H101. apply refl_equal. % 21.54/21.76 apply zenon_H170. apply sym_equal. exact zenon_H3f. % 21.54/21.76 (* end of lemma zenon_L492_ *) % 21.54/21.76 assert (zenon_L493_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H121 zenon_H33 zenon_H9f zenon_H171 zenon_Ha9 zenon_H106 zenon_Hb6 zenon_Hb9 zenon_H129. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.54/21.76 apply (zenon_L245_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.54/21.76 apply (zenon_L371_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.54/21.76 apply (zenon_L363_); trivial. % 21.54/21.76 apply (zenon_L189_); trivial. % 21.54/21.76 (* end of lemma zenon_L493_ *) % 21.54/21.76 assert (zenon_L494_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H13a zenon_H155 zenon_H17c zenon_Ha0 zenon_H2a zenon_Ha9 zenon_H66 zenon_Hb9 zenon_H196. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.76 apply (zenon_L444_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.76 apply (zenon_L53_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.76 apply (zenon_L193_); trivial. % 21.54/21.76 apply (zenon_L154_); trivial. % 21.54/21.76 (* end of lemma zenon_L494_ *) % 21.54/21.76 assert (zenon_L495_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (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) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H183 zenon_H68 zenon_H34 zenon_H129 zenon_Hb6 zenon_H9f zenon_H33 zenon_H121 zenon_H106 zenon_H77 zenon_H13a zenon_H155 zenon_Ha0 zenon_H2a zenon_Ha9 zenon_H66 zenon_Hb9 zenon_H196. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.54/21.76 apply (zenon_L291_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.54/21.76 apply (zenon_L493_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.54/21.76 apply (zenon_L367_); trivial. % 21.54/21.76 apply (zenon_L494_); trivial. % 21.54/21.76 (* end of lemma zenon_L495_ *) % 21.54/21.76 assert (zenon_L496_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H7f zenon_H66 zenon_H177 zenon_H155 zenon_H9f. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.54/21.76 apply (zenon_L291_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.54/21.76 apply (zenon_L169_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.54/21.76 apply (zenon_L122_); trivial. % 21.54/21.76 apply (zenon_L444_); trivial. % 21.54/21.76 (* end of lemma zenon_L496_ *) % 21.54/21.76 assert (zenon_L497_ : (((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)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H139 zenon_H2c zenon_H65 zenon_H68 zenon_H2a zenon_H153 zenon_H77 zenon_Ha9 zenon_H9e. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.76 apply (zenon_L180_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.76 apply (zenon_L147_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.76 apply (zenon_L94_); trivial. % 21.54/21.76 apply (zenon_L92_); trivial. % 21.54/21.76 (* end of lemma zenon_L497_ *) % 21.54/21.76 assert (zenon_L498_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H15d zenon_H4c zenon_H48 zenon_Ha9 zenon_H77 zenon_H2a zenon_H68 zenon_H65 zenon_H2c zenon_H139 zenon_Hb6 zenon_H9e. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.76 exact (zenon_H4c zenon_H47). % 21.54/21.76 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.76 apply (zenon_L65_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.76 apply (zenon_L497_); trivial. % 21.54/21.76 apply (zenon_L115_); trivial. % 21.54/21.76 (* end of lemma zenon_L498_ *) % 21.54/21.76 assert (zenon_L499_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> (((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)) = (e2)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H236 zenon_H1f zenon_Hb6 zenon_H139 zenon_H2c zenon_H65 zenon_H68 zenon_H77 zenon_Ha9 zenon_H48 zenon_H4c zenon_H15d zenon_H237 zenon_H9e zenon_Ha0. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 21.54/21.76 exact (zenon_H1f zenon_H1e). % 21.54/21.76 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 21.54/21.76 apply (zenon_L498_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 21.54/21.76 exact (zenon_H237 zenon_H31). % 21.54/21.76 apply (zenon_L156_); trivial. % 21.54/21.76 (* end of lemma zenon_L499_ *) % 21.54/21.76 assert (zenon_L500_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (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) (e0)) = (e1)) -> (~((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) (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 (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 (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> (((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)) = (e2)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((e0) = (e3))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H23b zenon_H177 zenon_H34 zenon_H183 zenon_H201 zenon_H4e zenon_H3c zenon_H190 zenon_H117 zenon_H14c zenon_H129 zenon_H33 zenon_H121 zenon_H13a zenon_H196 zenon_H23c zenon_He4 zenon_H2a zenon_H66 zenon_H236 zenon_H1f zenon_Hb6 zenon_H139 zenon_H2c zenon_H65 zenon_H68 zenon_H77 zenon_Ha9 zenon_H48 zenon_H4c zenon_H15d zenon_H237 zenon_Ha0. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.76 exact (zenon_H4c zenon_H47). % 21.54/21.76 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.76 apply (zenon_L491_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.76 apply (zenon_L94_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.76 apply (zenon_L65_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.76 apply (zenon_L492_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.76 apply (zenon_L94_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.76 apply (zenon_L14_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.76 apply (zenon_L143_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.76 apply (zenon_L43_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.76 apply (zenon_L113_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.76 apply (zenon_L278_); trivial. % 21.54/21.76 apply (zenon_L495_); trivial. % 21.54/21.76 apply (zenon_L496_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.76 apply (zenon_L53_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.76 apply (zenon_L193_); trivial. % 21.54/21.76 apply (zenon_L499_); trivial. % 21.54/21.76 (* end of lemma zenon_L500_ *) % 21.54/21.76 assert (zenon_L501_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (((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)) = (op (e2) (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (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 (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (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 (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.54/21.76 do 0 intro. intros zenon_H82 zenon_Ha0 zenon_H237 zenon_H15d zenon_H4c zenon_Ha9 zenon_H68 zenon_H2c zenon_H139 zenon_Hb6 zenon_H1f zenon_H236 zenon_H66 zenon_H2a zenon_He4 zenon_H23c zenon_H196 zenon_H13a zenon_H121 zenon_H33 zenon_H129 zenon_H14c zenon_H117 zenon_H190 zenon_H4e zenon_H201 zenon_H183 zenon_H177 zenon_H23b zenon_H65 zenon_H77 zenon_H34 zenon_H48. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.76 exact (zenon_H4c zenon_H47). % 21.54/21.76 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.76 apply (zenon_L500_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.76 apply (zenon_L30_); trivial. % 21.54/21.76 apply (zenon_L456_); trivial. % 21.54/21.76 (* end of lemma zenon_L501_ *) % 21.54/21.76 assert (zenon_L502_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H13a zenon_H33 zenon_H9d zenon_Ha0 zenon_H2a zenon_Ha9 zenon_H66 zenon_Hb6 zenon_H155. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.76 apply (zenon_L245_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.76 apply (zenon_L53_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.76 apply (zenon_L193_); trivial. % 21.54/21.76 apply (zenon_L115_); trivial. % 21.54/21.76 (* end of lemma zenon_L502_ *) % 21.54/21.76 assert (zenon_L503_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H82 zenon_H155 zenon_H13a zenon_H33 zenon_Ha0 zenon_H2a zenon_Ha9 zenon_H68 zenon_H139 zenon_H48 zenon_H25 zenon_H65 zenon_H77 zenon_Hb6 zenon_H9d. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.76 apply (zenon_L251_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.76 apply (zenon_L147_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.76 apply (zenon_L502_); trivial. % 21.54/21.76 apply (zenon_L98_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.76 apply (zenon_L25_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.76 apply (zenon_L30_); trivial. % 21.54/21.76 apply (zenon_L134_); trivial. % 21.54/21.76 (* end of lemma zenon_L503_ *) % 21.54/21.76 assert (zenon_L504_ : (((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)))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H183 zenon_H77 zenon_H7e zenon_Hac zenon_Ha9 zenon_H66 zenon_H177 zenon_H68 zenon_H167. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.54/21.76 apply (zenon_L71_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.54/21.76 apply (zenon_L371_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.54/21.76 apply (zenon_L122_); trivial. % 21.54/21.76 apply (zenon_L295_); trivial. % 21.54/21.76 (* end of lemma zenon_L504_ *) % 21.54/21.76 assert (zenon_L505_ : (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> False). % 21.54/21.76 do 0 intro. intros zenon_Ha0 zenon_Hc3 zenon_H167. % 21.54/21.76 cut (((op (e3) (e3)) = (e3)) = ((e0) = (e3))). % 21.54/21.76 intro zenon_D_pnotp. % 21.54/21.76 apply zenon_Ha0. % 21.54/21.76 rewrite <- zenon_D_pnotp. % 21.54/21.76 exact zenon_Hc3. % 21.54/21.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.76 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 21.54/21.76 congruence. % 21.54/21.76 exact (zenon_H162 zenon_H167). % 21.54/21.76 apply zenon_Ha2. apply refl_equal. % 21.54/21.76 (* end of lemma zenon_L505_ *) % 21.54/21.76 assert (zenon_L506_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((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)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (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 (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> False). % 21.54/21.76 do 0 intro. intros zenon_H121 zenon_H65 zenon_H25 zenon_H48 zenon_H139 zenon_H2a zenon_H33 zenon_H13a zenon_H155 zenon_H82 zenon_H68 zenon_H177 zenon_H66 zenon_Ha9 zenon_H7e zenon_H77 zenon_H183 zenon_H106 zenon_Hb6 zenon_Ha0 zenon_H167. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.54/21.76 apply (zenon_L503_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.54/21.76 apply (zenon_L504_); trivial. % 21.54/21.76 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.54/21.76 apply (zenon_L363_); trivial. % 21.54/21.76 apply (zenon_L505_); trivial. % 21.54/21.76 (* end of lemma zenon_L506_ *) % 21.54/21.76 assert (zenon_L507_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (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 (e2) (e0)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((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)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (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 (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H164 zenon_H23b zenon_H201 zenon_H4e zenon_H190 zenon_H117 zenon_H129 zenon_H196 zenon_H23c zenon_He4 zenon_H236 zenon_H1f zenon_H2c zenon_H4c zenon_H15d zenon_H237 zenon_H192 zenon_H14c zenon_H104 zenon_H121 zenon_H65 zenon_H25 zenon_H48 zenon_H139 zenon_H2a zenon_H33 zenon_H13a zenon_H155 zenon_H82 zenon_H68 zenon_H177 zenon_H66 zenon_Ha9 zenon_H7e zenon_H77 zenon_H183 zenon_H106 zenon_Hb6 zenon_Ha0. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.77 apply (zenon_L501_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.77 apply (zenon_L292_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.77 apply (zenon_L257_); trivial. % 21.54/21.77 apply (zenon_L506_); trivial. % 21.54/21.77 (* end of lemma zenon_L507_ *) % 21.54/21.77 assert (zenon_L508_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (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 (e2) (e0)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((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)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (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))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H156 zenon_H3f zenon_H1bf zenon_H164 zenon_H23b zenon_H201 zenon_H4e zenon_H190 zenon_H117 zenon_H129 zenon_H196 zenon_H23c zenon_He4 zenon_H236 zenon_H1f zenon_H2c zenon_H4c zenon_H15d zenon_H237 zenon_H192 zenon_H14c zenon_H104 zenon_H121 zenon_H65 zenon_H25 zenon_H48 zenon_H139 zenon_H2a zenon_H33 zenon_H13a zenon_H155 zenon_H82 zenon_H68 zenon_H177 zenon_H66 zenon_Ha9 zenon_H7e zenon_H77 zenon_H183 zenon_Hb6 zenon_Ha0. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.77 apply (zenon_L486_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_L507_); trivial. % 21.54/21.77 (* end of lemma zenon_L508_ *) % 21.54/21.77 assert (zenon_L509_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (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) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> False). % 21.54/21.77 do 0 intro. intros zenon_H201 zenon_H77 zenon_H156 zenon_H3f zenon_H1bf zenon_H117 zenon_Ha9 zenon_H65 zenon_H10c zenon_Hf0 zenon_H131 zenon_H66 zenon_H73 zenon_H163 zenon_H4e zenon_H25 zenon_H1ec zenon_Ha0 zenon_H115. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.77 apply (zenon_L486_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.77 apply (zenon_L43_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.77 apply (zenon_L74_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.77 apply (zenon_L286_); trivial. % 21.54/21.77 apply (zenon_L77_); trivial. % 21.54/21.77 (* end of lemma zenon_L509_ *) % 21.54/21.77 assert (zenon_L510_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((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 (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (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) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e3))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H141 zenon_H13f zenon_Hb6 zenon_H183 zenon_H7e zenon_H177 zenon_H68 zenon_H82 zenon_H155 zenon_H13a zenon_H33 zenon_H2a zenon_H139 zenon_H48 zenon_H121 zenon_H104 zenon_H192 zenon_H237 zenon_H15d zenon_H4c zenon_H2c zenon_H1f zenon_H236 zenon_He4 zenon_H23c zenon_H196 zenon_H129 zenon_H190 zenon_H23b zenon_H164 zenon_H201 zenon_H77 zenon_H156 zenon_H3f zenon_H1bf zenon_H117 zenon_Ha9 zenon_H65 zenon_H10c zenon_Hf0 zenon_H131 zenon_H66 zenon_H73 zenon_H163 zenon_H4e zenon_H25 zenon_H1ec zenon_Ha0. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.77 apply (zenon_L27_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.54/21.77 apply (zenon_L30_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.54/21.77 apply (zenon_L111_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.77 apply (zenon_L486_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.77 apply (zenon_L43_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.77 apply (zenon_L152_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.77 apply (zenon_L286_); trivial. % 21.54/21.77 apply (zenon_L182_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.77 apply (zenon_L508_); trivial. % 21.54/21.77 apply (zenon_L509_); trivial. % 21.54/21.77 (* end of lemma zenon_L510_ *) % 21.54/21.77 assert (zenon_L511_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (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)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (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) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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)) = (op (e2) (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 (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 (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H140 zenon_Ha0 zenon_Hb6 zenon_H183 zenon_H77 zenon_H7e zenon_Ha9 zenon_H177 zenon_H68 zenon_H82 zenon_H155 zenon_H13a zenon_H33 zenon_H2a zenon_H139 zenon_H48 zenon_H25 zenon_H65 zenon_H121 zenon_H192 zenon_H237 zenon_H15d zenon_H4c zenon_H2c zenon_H1f zenon_H236 zenon_He4 zenon_H23c zenon_H196 zenon_H129 zenon_H117 zenon_H190 zenon_H4e zenon_H201 zenon_H23b zenon_H164 zenon_H13e zenon_H104 zenon_H1bf zenon_H66 zenon_H111 zenon_H133 zenon_H131. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.77 exact (zenon_H237 zenon_H31). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.77 apply (zenon_L162_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.77 apply (zenon_L124_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_L507_); trivial. % 21.54/21.77 apply (zenon_L260_); trivial. % 21.54/21.77 (* end of lemma zenon_L511_ *) % 21.54/21.77 assert (zenon_L512_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> False). % 21.54/21.77 do 0 intro. intros zenon_H1a2 zenon_Ha9 zenon_H66 zenon_H186 zenon_Ha5 zenon_H190 zenon_H10d zenon_Hb6 zenon_H106. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.54/21.77 apply (zenon_L193_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.54/21.77 apply (zenon_L308_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.54/21.77 apply (zenon_L163_); trivial. % 21.54/21.77 apply (zenon_L363_); trivial. % 21.54/21.77 (* end of lemma zenon_L512_ *) % 21.54/21.77 assert (zenon_L513_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> False). % 21.54/21.77 do 0 intro. intros zenon_H3a zenon_H23c zenon_H3f. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 21.54/21.77 apply (zenon_L492_); trivial. % 21.54/21.77 (* end of lemma zenon_L513_ *) % 21.54/21.77 assert (zenon_L514_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 21.54/21.77 do 0 intro. intros zenon_H183 zenon_H7e zenon_Hac zenon_Ha9 zenon_H106 zenon_H77 zenon_H155 zenon_H9f. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.54/21.77 apply (zenon_L71_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.54/21.77 apply (zenon_L371_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.54/21.77 apply (zenon_L367_); trivial. % 21.54/21.77 apply (zenon_L444_); trivial. % 21.54/21.77 (* end of lemma zenon_L514_ *) % 21.54/21.77 assert (zenon_L515_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> (((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)) = (e2)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((e0) = (e3))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H13a zenon_H155 zenon_Hac zenon_H7e zenon_H183 zenon_H1bf zenon_H3f zenon_H156 zenon_H201 zenon_H2a zenon_H66 zenon_H236 zenon_H1f zenon_Hb6 zenon_H139 zenon_H2c zenon_H65 zenon_H68 zenon_H77 zenon_Ha9 zenon_H48 zenon_H4c zenon_H15d zenon_H237 zenon_Ha0. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.77 apply (zenon_L486_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_L514_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.77 apply (zenon_L53_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.77 apply (zenon_L193_); trivial. % 21.54/21.77 apply (zenon_L499_); trivial. % 21.54/21.77 (* end of lemma zenon_L515_ *) % 21.54/21.77 assert (zenon_L516_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H82 zenon_H4c zenon_H3f zenon_H23c zenon_H65 zenon_H77 zenon_H34 zenon_H48. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.77 exact (zenon_H4c zenon_H47). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.77 apply (zenon_L492_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.77 apply (zenon_L30_); trivial. % 21.54/21.77 apply (zenon_L456_); trivial. % 21.54/21.77 (* end of lemma zenon_L516_ *) % 21.54/21.77 assert (zenon_L517_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> False). % 21.54/21.77 do 0 intro. intros zenon_H23d zenon_H1f zenon_H4c zenon_H6c zenon_H17c zenon_H155. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1e | zenon_intro zenon_H23e ]. % 21.54/21.77 exact (zenon_H1f zenon_H1e). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H47 | zenon_intro zenon_H23f ]. % 21.54/21.77 exact (zenon_H4c zenon_H47). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H67 | zenon_intro zenon_H9f ]. % 21.54/21.77 exact (zenon_H6c zenon_H67). % 21.54/21.77 apply (zenon_L444_); trivial. % 21.54/21.77 (* end of lemma zenon_L517_ *) % 21.54/21.77 assert (zenon_L518_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.54/21.77 do 0 intro. intros zenon_H183 zenon_H7e zenon_Hef zenon_H11a zenon_H106 zenon_H77 zenon_H23d zenon_H1f zenon_H4c zenon_H6c zenon_H155. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.54/21.77 apply (zenon_L71_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.54/21.77 apply (zenon_L119_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.54/21.77 apply (zenon_L367_); trivial. % 21.54/21.77 apply (zenon_L517_); trivial. % 21.54/21.77 (* end of lemma zenon_L518_ *) % 21.54/21.77 assert (zenon_L519_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.54/21.77 do 0 intro. intros zenon_H201 zenon_H66 zenon_H156 zenon_H3f zenon_H1bf zenon_H183 zenon_H7e zenon_Hef zenon_H11a zenon_H77 zenon_H23d zenon_H1f zenon_H4c zenon_H6c zenon_H155. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.77 apply (zenon_L486_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_L518_); trivial. % 21.54/21.77 (* end of lemma zenon_L519_ *) % 21.54/21.77 assert (zenon_L520_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H1fe zenon_Hac zenon_Ha9 zenon_H55 zenon_H13c zenon_Ha0 zenon_H6c zenon_H1f zenon_H23d zenon_H11a zenon_H183 zenon_H1bf zenon_Hb6 zenon_H66 zenon_H201 zenon_H2a zenon_H1a8 zenon_H73 zenon_H156 zenon_Hfa zenon_H15d zenon_H68 zenon_H82 zenon_H4c zenon_H3f zenon_H23c zenon_H65 zenon_H77 zenon_H48. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.77 exact (zenon_H1f zenon_H1e). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.77 exact (zenon_H4c zenon_H47). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.77 apply (zenon_L65_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.77 exact (zenon_H4c zenon_H47). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.77 apply (zenon_L492_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.77 apply (zenon_L30_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.77 apply (zenon_L171_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.77 apply (zenon_L519_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.77 apply (zenon_L22_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.54/21.77 apply (zenon_L147_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.77 apply (zenon_L116_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.77 apply (zenon_L79_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.77 apply (zenon_L124_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_L518_); trivial. % 21.54/21.77 apply (zenon_L299_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.54/21.77 apply (zenon_L34_); trivial. % 21.54/21.77 apply (zenon_L371_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.77 apply (zenon_L27_); trivial. % 21.54/21.77 apply (zenon_L516_); trivial. % 21.54/21.77 (* end of lemma zenon_L520_ *) % 21.54/21.77 assert (zenon_L521_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (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))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (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)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((op (e0) (e1)) = (e0)) -> False). % 21.54/21.77 do 0 intro. intros zenon_H204 zenon_H1fe zenon_H23c zenon_H48 zenon_H77 zenon_H66 zenon_H82 zenon_H201 zenon_Ha9 zenon_Hac zenon_H183 zenon_H1bf zenon_H3f zenon_H156 zenon_Ha0 zenon_H236 zenon_H139 zenon_H68 zenon_H2c zenon_Hb6 zenon_H15d zenon_H13a zenon_H65 zenon_H1f zenon_H11a zenon_H23d zenon_H73 zenon_H1a8 zenon_H55 zenon_H13c zenon_Hfa zenon_H240 zenon_H2a. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 21.54/21.77 exact (zenon_H205 zenon_H2a). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.77 exact (zenon_H1f zenon_H1e). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.77 exact (zenon_H4c zenon_H47). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.77 apply (zenon_L65_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.77 exact (zenon_H4c zenon_H47). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.77 apply (zenon_L25_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.77 apply (zenon_L30_); trivial. % 21.54/21.77 apply (zenon_L515_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.77 apply (zenon_L27_); trivial. % 21.54/21.77 apply (zenon_L516_); trivial. % 21.54/21.77 apply (zenon_L520_); trivial. % 21.54/21.77 (* end of lemma zenon_L521_ *) % 21.54/21.77 assert (zenon_L522_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (e1)) = (e1)) -> False). % 21.54/21.77 do 0 intro. intros zenon_H87 zenon_H3f. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.54/21.77 apply (zenon_L10_); trivial. % 21.54/21.77 (* end of lemma zenon_L522_ *) % 21.54/21.77 assert (zenon_L523_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H13e zenon_H11d zenon_H1bf zenon_H104 zenon_H99 zenon_H133 zenon_H131. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H14c | zenon_intro zenon_H151 ]. % 21.54/21.77 apply (zenon_L257_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H105 | zenon_intro zenon_H152 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H8a | zenon_intro zenon_H110 ]. % 21.54/21.77 apply (zenon_L232_); trivial. % 21.54/21.77 apply (zenon_L259_); trivial. % 21.54/21.77 (* end of lemma zenon_L523_ *) % 21.54/21.77 assert (zenon_L524_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H140 zenon_H1d8 zenon_H2a zenon_Ha0 zenon_Hef zenon_H13e zenon_H1bf zenon_H104 zenon_H99 zenon_H133 zenon_H131. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.77 apply (zenon_L254_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.77 apply (zenon_L162_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.77 apply (zenon_L265_); trivial. % 21.54/21.77 apply (zenon_L523_); trivial. % 21.54/21.77 (* end of lemma zenon_L524_ *) % 21.54/21.77 assert (zenon_L525_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H1ec zenon_H25 zenon_H4e zenon_H156 zenon_H3f zenon_H160 zenon_H163 zenon_Ha5 zenon_H186. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1ed ]. % 21.54/21.77 apply (zenon_L274_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H4d | zenon_intro zenon_H1ee ]. % 21.54/21.77 apply (zenon_L486_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H72 | zenon_intro zenon_H133 ]. % 21.54/21.77 apply (zenon_L227_); trivial. % 21.54/21.77 apply (zenon_L308_); trivial. % 21.54/21.77 (* end of lemma zenon_L525_ *) % 21.54/21.77 assert (zenon_L526_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.54/21.77 do 0 intro. intros zenon_H13f zenon_H48 zenon_H2d zenon_Hf0 zenon_H3f zenon_H1bf zenon_H77 zenon_H93. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.54/21.77 apply (zenon_L217_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.54/21.77 apply (zenon_L118_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_L218_); trivial. % 21.54/21.77 (* end of lemma zenon_L526_ *) % 21.54/21.77 assert (zenon_L527_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H1bb zenon_H209 zenon_H160 zenon_Hbc zenon_H7d zenon_H7f zenon_H18a zenon_H212 zenon_H120 zenon_H129 zenon_H93 zenon_Hc4. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.54/21.77 apply (zenon_L417_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.54/21.77 exact (zenon_H120 zenon_H11f). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.54/21.77 apply (zenon_L126_); trivial. % 21.54/21.77 exact (zenon_Hc4 zenon_Hc3). % 21.54/21.77 (* end of lemma zenon_L527_ *) % 21.54/21.77 assert (zenon_L528_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H12e zenon_H48 zenon_H34 zenon_Hc4 zenon_H93 zenon_H129 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H160 zenon_H77 zenon_H120. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.77 apply (zenon_L456_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.77 apply (zenon_L527_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.77 apply (zenon_L367_); trivial. % 21.54/21.77 exact (zenon_H120 zenon_H11f). % 21.54/21.77 (* end of lemma zenon_L528_ *) % 21.54/21.77 assert (zenon_L529_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H1fe zenon_H19d zenon_H195 zenon_H163 zenon_H13c zenon_H11a zenon_Hac zenon_H131 zenon_H99 zenon_H104 zenon_H13e zenon_Ha0 zenon_H2a zenon_H1d8 zenon_H140 zenon_H1ec zenon_H4e zenon_H156 zenon_H186 zenon_H68 zenon_Hfa zenon_H1bf zenon_H3f zenon_Hf0 zenon_H13f zenon_H12e zenon_H48 zenon_Hc4 zenon_H93 zenon_H129 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H160 zenon_H77 zenon_H120. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.77 apply (zenon_L161_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.77 apply (zenon_L171_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.77 apply (zenon_L116_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.77 apply (zenon_L79_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.77 apply (zenon_L524_); trivial. % 21.54/21.77 apply (zenon_L525_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.77 apply (zenon_L227_); trivial. % 21.54/21.77 apply (zenon_L228_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.77 apply (zenon_L526_); trivial. % 21.54/21.77 apply (zenon_L528_); trivial. % 21.54/21.77 (* end of lemma zenon_L529_ *) % 21.54/21.77 assert (zenon_L530_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 21.54/21.77 do 0 intro. intros zenon_Hca zenon_H1bb zenon_H160 zenon_H1cb zenon_H162 zenon_Hc2 zenon_Hac. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.54/21.77 exact (zenon_H1c7 zenon_Hac). % 21.54/21.77 apply (zenon_L238_); trivial. % 21.54/21.77 (* end of lemma zenon_L530_ *) % 21.54/21.77 assert (zenon_L531_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (e1)) = (e1)) -> False). % 21.54/21.77 do 0 intro. intros zenon_Hb1 zenon_H3f. % 21.54/21.77 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.54/21.77 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.54/21.77 apply (zenon_L10_); trivial. % 21.54/21.77 (* end of lemma zenon_L531_ *) % 21.54/21.77 assert (zenon_L532_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((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) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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 (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (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) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (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) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 21.54/21.77 do 0 intro. intros zenon_Hcc zenon_H1fb zenon_H234 zenon_H23c zenon_H82 zenon_H201 zenon_Ha9 zenon_H183 zenon_H236 zenon_H139 zenon_H2c zenon_Hb6 zenon_H15d zenon_H13a zenon_H23d zenon_H73 zenon_H1a8 zenon_H55 zenon_H1fe zenon_H1bb zenon_H129 zenon_H18a zenon_Hbc zenon_H212 zenon_H12e zenon_H48 zenon_Hf0 zenon_H77 zenon_H13f zenon_H68 zenon_H13c zenon_H4e zenon_H156 zenon_H163 zenon_H186 zenon_H1ec zenon_H1d8 zenon_H13e zenon_H131 zenon_H1bf zenon_H104 zenon_H140 zenon_H11a zenon_Ha0 zenon_H195 zenon_Hfa zenon_H2a zenon_H19d zenon_H1cb zenon_H7d zenon_H3f zenon_H1cd zenon_Hac. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.54/21.77 apply (zenon_L2_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.54/21.77 apply (zenon_L482_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.54/21.77 apply (zenon_L315_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.54/21.77 apply (zenon_L317_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.54/21.77 apply (zenon_L513_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.54/21.77 apply (zenon_L11_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.54/21.77 apply (zenon_L483_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.54/21.77 apply (zenon_L485_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 21.54/21.77 apply (zenon_L521_); trivial. % 21.54/21.77 apply (zenon_L521_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.54/21.77 apply (zenon_L522_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.54/21.77 apply (zenon_L37_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.54/21.77 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.54/21.77 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.54/21.77 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.54/21.77 exact (zenon_H1c7 zenon_Hac). % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.54/21.77 apply (zenon_L529_); trivial. % 21.54/21.77 apply (zenon_L529_); trivial. % 21.54/21.77 apply (zenon_L530_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.54/21.77 apply (zenon_L387_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.54/21.77 apply (zenon_L531_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.54/21.77 apply (zenon_L388_); trivial. % 21.54/21.77 apply (zenon_L51_); trivial. % 21.54/21.77 (* end of lemma zenon_L532_ *) % 21.54/21.77 assert (zenon_L533_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H8a zenon_H65 zenon_H1ef. % 21.54/21.77 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H112 | zenon_intro zenon_H108 ]. % 21.54/21.77 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 21.54/21.77 intro zenon_D_pnotp. % 21.54/21.77 apply zenon_H1ef. % 21.54/21.77 rewrite <- zenon_D_pnotp. % 21.54/21.77 exact zenon_H112. % 21.54/21.77 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.54/21.77 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f0]. % 21.54/21.77 congruence. % 21.54/21.77 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 21.54/21.77 intro zenon_D_pnotp. % 21.54/21.77 apply zenon_H1f0. % 21.54/21.77 rewrite <- zenon_D_pnotp. % 21.54/21.77 exact zenon_H8a. % 21.54/21.77 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 21.54/21.77 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 21.54/21.77 congruence. % 21.54/21.77 apply zenon_H108. apply refl_equal. % 21.54/21.77 apply zenon_H98. apply sym_equal. exact zenon_H65. % 21.54/21.77 apply zenon_H108. apply refl_equal. % 21.54/21.77 apply zenon_H108. apply refl_equal. % 21.54/21.77 (* end of lemma zenon_L533_ *) % 21.54/21.77 assert (zenon_L534_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H125 zenon_H6c zenon_H68 zenon_H25 zenon_H1ef zenon_H8a zenon_H7e zenon_H77. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.77 exact (zenon_H6c zenon_H67). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.77 apply (zenon_L171_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.77 apply (zenon_L533_); trivial. % 21.54/21.77 apply (zenon_L71_); trivial. % 21.54/21.77 (* end of lemma zenon_L534_ *) % 21.54/21.77 assert (zenon_L535_ : (((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))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H13e zenon_H11d zenon_H104 zenon_H1bf zenon_H77 zenon_H7e zenon_H1ef zenon_H25 zenon_H68 zenon_H6c zenon_H125 zenon_H10d zenon_H190. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H14c | zenon_intro zenon_H151 ]. % 21.54/21.77 apply (zenon_L257_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H105 | zenon_intro zenon_H152 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H8a | zenon_intro zenon_H110 ]. % 21.54/21.77 apply (zenon_L534_); trivial. % 21.54/21.77 apply (zenon_L163_); trivial. % 21.54/21.77 (* end of lemma zenon_L535_ *) % 21.54/21.77 assert (zenon_L536_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (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 (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((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)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (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 (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H164 zenon_H23c zenon_H3f zenon_H4c zenon_H192 zenon_H190 zenon_H10d zenon_H125 zenon_H6c zenon_H1ef zenon_H1bf zenon_H104 zenon_H13e zenon_H121 zenon_H65 zenon_H25 zenon_H48 zenon_H139 zenon_H2a zenon_H33 zenon_H13a zenon_H155 zenon_H82 zenon_H68 zenon_H177 zenon_H66 zenon_Ha9 zenon_H7e zenon_H77 zenon_H183 zenon_H106 zenon_Hb6 zenon_Ha0. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.77 apply (zenon_L516_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.77 apply (zenon_L292_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.77 apply (zenon_L535_); trivial. % 21.54/21.77 apply (zenon_L506_); trivial. % 21.54/21.77 (* end of lemma zenon_L536_ *) % 21.54/21.77 assert (zenon_L537_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (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)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((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 (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (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) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (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 (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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 (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((op (e0) (e1)) = (e0)) -> False). % 21.54/21.77 do 0 intro. intros zenon_H204 zenon_H48 zenon_H77 zenon_H66 zenon_Ha0 zenon_H141 zenon_Hf0 zenon_H164 zenon_H104 zenon_H192 zenon_He4 zenon_H177 zenon_H190 zenon_H121 zenon_H129 zenon_H33 zenon_H196 zenon_H183 zenon_H23c zenon_H15d zenon_H236 zenon_H2c zenon_H13a zenon_H139 zenon_H23b zenon_H82 zenon_H1bf zenon_H201 zenon_Ha9 zenon_H1ec zenon_H131 zenon_H73 zenon_H163 zenon_H4e zenon_Hb6 zenon_H117 zenon_H3f zenon_H156 zenon_H13f zenon_H68 zenon_H140 zenon_H111 zenon_H13e zenon_H1c6 zenon_H1d8 zenon_H1fb zenon_H234 zenon_H1fe zenon_H11a zenon_H23d zenon_H1a8 zenon_H55 zenon_H13c zenon_Hfa zenon_H1bb zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H12e zenon_H195 zenon_H19d zenon_H1cb zenon_H1cd zenon_Hcc zenon_H1a2 zenon_H186 zenon_H65 zenon_H1f zenon_H1ef zenon_H125 zenon_H240 zenon_H2a. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 21.54/21.77 exact (zenon_H205 zenon_H2a). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.77 exact (zenon_H1f zenon_H1e). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.77 exact (zenon_H4c zenon_H47). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.77 apply (zenon_L65_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.77 exact (zenon_H4c zenon_H47). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.77 apply (zenon_L25_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.77 apply (zenon_L30_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.77 apply (zenon_L116_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.77 apply (zenon_L510_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.77 apply (zenon_L511_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.77 apply (zenon_L53_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.77 apply (zenon_L510_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.77 apply (zenon_L486_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_L512_); trivial. % 21.54/21.77 apply (zenon_L532_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.77 apply (zenon_L27_); trivial. % 21.54/21.77 apply (zenon_L516_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.77 exact (zenon_H1f zenon_H1e). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.77 exact (zenon_H4c zenon_H47). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.77 apply (zenon_L65_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.77 exact (zenon_H4c zenon_H47). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.77 apply (zenon_L492_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.77 apply (zenon_L30_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.54/21.77 apply (zenon_L147_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.54/21.77 apply (zenon_L519_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.54/21.77 apply (zenon_L34_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.77 apply (zenon_L94_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.77 apply (zenon_L486_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.77 exact (zenon_H1bf zenon_H105). % 21.54/21.77 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.77 apply (zenon_L43_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.77 apply (zenon_L536_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.77 apply (zenon_L286_); trivial. % 21.54/21.77 apply (zenon_L493_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.77 apply (zenon_L53_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.77 apply (zenon_L193_); trivial. % 21.54/21.77 apply (zenon_L115_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.77 apply (zenon_L27_); trivial. % 21.54/21.77 apply (zenon_L516_); trivial. % 21.54/21.77 (* end of lemma zenon_L537_ *) % 21.54/21.77 assert (zenon_L538_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.54/21.77 do 0 intro. intros zenon_H121 zenon_H33 zenon_H9f zenon_H11a zenon_H10c zenon_H1a3 zenon_Hc4. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.54/21.77 apply (zenon_L245_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.54/21.77 apply (zenon_L79_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.54/21.77 exact (zenon_H1a3 zenon_Hbb). % 21.54/21.77 exact (zenon_Hc4 zenon_Hc3). % 21.54/21.77 (* end of lemma zenon_L538_ *) % 21.54/21.77 assert (zenon_L539_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((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) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (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)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.77 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H186 zenon_H3f zenon_H156 zenon_H4e zenon_H25 zenon_H1ec zenon_H140 zenon_H1d8 zenon_H2a zenon_Ha0 zenon_H13e zenon_H1bf zenon_H104 zenon_H99 zenon_H131 zenon_H121 zenon_H33 zenon_H9f zenon_H11a zenon_H1a3 zenon_Hc4 zenon_H13c zenon_H160 zenon_H163 zenon_H93 zenon_H195. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.77 apply (zenon_L171_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.77 apply (zenon_L116_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.77 apply (zenon_L538_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.77 apply (zenon_L524_); trivial. % 21.54/21.77 apply (zenon_L525_); trivial. % 21.54/21.77 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.78 apply (zenon_L227_); trivial. % 21.54/21.78 apply (zenon_L228_); trivial. % 21.54/21.78 (* end of lemma zenon_L539_ *) % 21.54/21.78 assert (zenon_L540_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H18d zenon_H9e zenon_Hb6 zenon_H234 zenon_H3f zenon_H93 zenon_H77 zenon_H120. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.54/21.78 apply (zenon_L115_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.54/21.78 apply (zenon_L484_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.54/21.78 apply (zenon_L218_); trivial. % 21.54/21.78 exact (zenon_H120 zenon_H11f). % 21.54/21.78 (* end of lemma zenon_L540_ *) % 21.54/21.78 assert (zenon_L541_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H125 zenon_H77 zenon_H47 zenon_H68 zenon_H25 zenon_H94 zenon_H93 zenon_H160 zenon_Hbc. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.78 apply (zenon_L251_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.78 apply (zenon_L171_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.78 apply (zenon_L38_); trivial. % 21.54/21.78 apply (zenon_L104_); trivial. % 21.54/21.78 (* end of lemma zenon_L541_ *) % 21.54/21.78 assert (zenon_L542_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (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)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (e3))) -> False). % 21.54/21.78 do 0 intro. intros zenon_Hb2 zenon_H186 zenon_H163 zenon_H160 zenon_H3f zenon_H156 zenon_H4e zenon_H1ec zenon_H73 zenon_Hfe zenon_H121 zenon_H33 zenon_H11a zenon_H1a3 zenon_Hc4 zenon_H13c zenon_Ha0 zenon_H25 zenon_Hb6 zenon_H54 zenon_H209. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.78 apply (zenon_L116_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.78 apply (zenon_L538_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.78 apply (zenon_L89_); trivial. % 21.54/21.78 apply (zenon_L525_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.78 apply (zenon_L116_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.78 apply (zenon_L151_); trivial. % 21.54/21.78 exact (zenon_H209 zenon_H9d). % 21.54/21.78 (* end of lemma zenon_L542_ *) % 21.54/21.78 assert (zenon_L543_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H121 zenon_H209 zenon_He0 zenon_Ha0 zenon_H1a3 zenon_Hc4. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.54/21.78 exact (zenon_H209 zenon_H9d). % 21.54/21.78 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.54/21.78 apply (zenon_L107_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.54/21.78 exact (zenon_H1a3 zenon_Hbb). % 21.54/21.78 exact (zenon_Hc4 zenon_Hc3). % 21.54/21.78 (* end of lemma zenon_L543_ *) % 21.54/21.78 assert (zenon_L544_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))) -> ((op (e3) (e3)) = (e0)) -> False). % 21.54/21.78 do 0 intro. intros zenon_H241 zenon_H167. % 21.54/21.78 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 21.54/21.78 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 21.54/21.78 congruence. % 21.54/21.78 exact (zenon_H162 zenon_H167). % 21.54/21.78 exact (zenon_H162 zenon_H167). % 21.54/21.78 (* end of lemma zenon_L544_ *) % 21.54/21.78 assert (zenon_L545_ : (~((op (e3) (op (e3) (e3))) = (op (e3) (e0)))) -> ((op (e3) (e3)) = (e0)) -> False). % 21.54/21.78 do 0 intro. intros zenon_H242 zenon_H167. % 21.54/21.78 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 21.54/21.78 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.78 congruence. % 21.54/21.78 apply zenon_Ha2. apply refl_equal. % 21.54/21.78 exact (zenon_H162 zenon_H167). % 21.54/21.78 (* end of lemma zenon_L545_ *) % 21.54/21.78 assert (zenon_L546_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((e1) = (op (e3) (op (e3) (e3))))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H7e zenon_H167 zenon_H243. % 21.54/21.78 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H244 | zenon_intro zenon_H245 ]. % 21.54/21.78 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((e1) = (op (e3) (op (e3) (e3))))). % 21.54/21.78 intro zenon_D_pnotp. % 21.54/21.78 apply zenon_H243. % 21.54/21.78 rewrite <- zenon_D_pnotp. % 21.54/21.78 exact zenon_H244. % 21.54/21.78 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 21.54/21.78 cut (((op (e3) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H246]. % 21.54/21.78 congruence. % 21.54/21.78 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (op (e3) (e3))) = (e1))). % 21.54/21.78 intro zenon_D_pnotp. % 21.54/21.78 apply zenon_H246. % 21.54/21.78 rewrite <- zenon_D_pnotp. % 21.54/21.78 exact zenon_H7e. % 21.54/21.78 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.78 cut (((op (e3) (e0)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H247]. % 21.54/21.78 congruence. % 21.54/21.78 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H244 | zenon_intro zenon_H245 ]. % 21.54/21.78 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e0)) = (op (e3) (op (e3) (e3))))). % 21.54/21.78 intro zenon_D_pnotp. % 21.54/21.78 apply zenon_H247. % 21.54/21.78 rewrite <- zenon_D_pnotp. % 21.54/21.78 exact zenon_H244. % 21.54/21.78 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 21.54/21.78 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H242]. % 21.54/21.78 congruence. % 21.54/21.78 apply (zenon_L545_); trivial. % 21.54/21.78 apply zenon_H245. apply refl_equal. % 21.54/21.78 apply zenon_H245. apply refl_equal. % 21.54/21.78 apply zenon_H4a. apply refl_equal. % 21.54/21.78 apply zenon_H245. apply refl_equal. % 21.54/21.78 apply zenon_H245. apply refl_equal. % 21.54/21.78 (* end of lemma zenon_L546_ *) % 21.54/21.78 assert (zenon_L547_ : ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> False). % 21.54/21.78 do 0 intro. intros zenon_H67 zenon_H7e zenon_H167. % 21.54/21.78 apply (zenon_notand_s _ _ ax19); [ zenon_intro zenon_H249 | zenon_intro zenon_H248 ]. % 21.54/21.78 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H24b ]. % 21.54/21.78 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e2) = (op (op (e3) (e3)) (op (e3) (e3))))). % 21.54/21.78 intro zenon_D_pnotp. % 21.54/21.78 apply zenon_H249. % 21.54/21.78 rewrite <- zenon_D_pnotp. % 21.54/21.78 exact zenon_H24a. % 21.54/21.78 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 21.54/21.78 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H24c]. % 21.54/21.78 congruence. % 21.54/21.78 cut (((op (e0) (e0)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))). % 21.54/21.78 intro zenon_D_pnotp. % 21.54/21.78 apply zenon_H24c. % 21.54/21.78 rewrite <- zenon_D_pnotp. % 21.54/21.78 exact zenon_H67. % 21.54/21.78 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.54/21.78 cut (((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24d]. % 21.54/21.78 congruence. % 21.54/21.78 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H24b ]. % 21.54/21.78 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))))). % 21.54/21.78 intro zenon_D_pnotp. % 21.54/21.78 apply zenon_H24d. % 21.54/21.78 rewrite <- zenon_D_pnotp. % 21.54/21.78 exact zenon_H24a. % 21.54/21.78 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 21.54/21.78 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 21.54/21.78 congruence. % 21.54/21.78 apply (zenon_L544_); trivial. % 21.54/21.78 apply zenon_H24b. apply refl_equal. % 21.54/21.78 apply zenon_H24b. apply refl_equal. % 21.54/21.78 apply zenon_H6a. apply refl_equal. % 21.54/21.78 apply zenon_H24b. apply refl_equal. % 21.54/21.78 apply zenon_H24b. apply refl_equal. % 21.54/21.78 apply (zenon_notand_s _ _ zenon_H248); [ zenon_intro zenon_H20e | zenon_intro zenon_H243 ]. % 21.54/21.78 apply zenon_H20e. apply sym_equal. exact zenon_H167. % 21.54/21.78 apply (zenon_L546_); trivial. % 21.54/21.78 (* end of lemma zenon_L547_ *) % 21.54/21.78 assert (zenon_L548_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.54/21.78 do 0 intro. intros zenon_H164 zenon_H48 zenon_Hc4 zenon_H1a3 zenon_Ha0 zenon_H209 zenon_H121 zenon_H31 zenon_H177 zenon_H67 zenon_H7e. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.78 apply (zenon_L456_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.78 apply (zenon_L543_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.78 apply (zenon_L406_); trivial. % 21.54/21.78 apply (zenon_L547_); trivial. % 21.54/21.78 (* end of lemma zenon_L548_ *) % 21.54/21.78 assert (zenon_L549_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.54/21.78 do 0 intro. intros zenon_H19a zenon_H48 zenon_H155 zenon_Ha5 zenon_Ha0 zenon_H93 zenon_H68 zenon_H67 zenon_H7e. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.54/21.78 apply (zenon_L246_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.54/21.78 apply (zenon_L90_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.54/21.78 apply (zenon_L158_); trivial. % 21.54/21.78 apply (zenon_L547_); trivial. % 21.54/21.78 (* end of lemma zenon_L549_ *) % 21.54/21.78 assert (zenon_L550_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((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 (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.54/21.78 do 0 intro. intros zenon_H13c zenon_H25 zenon_Hc4 zenon_H177 zenon_H11a zenon_H209 zenon_H121 zenon_Hfe zenon_H73 zenon_H19a zenon_H48 zenon_H155 zenon_Ha0 zenon_H93 zenon_H68 zenon_H67 zenon_H7e. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.78 apply (zenon_L116_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.78 apply (zenon_L393_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.78 apply (zenon_L89_); trivial. % 21.54/21.78 apply (zenon_L549_); trivial. % 21.54/21.78 (* end of lemma zenon_L550_ *) % 21.54/21.78 assert (zenon_L551_ : (((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 (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((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) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H13a zenon_H195 zenon_H163 zenon_H160 zenon_H33 zenon_H131 zenon_H99 zenon_H104 zenon_H1bf zenon_H13e zenon_H164 zenon_H1a3 zenon_H140 zenon_Hfa zenon_H2a zenon_H7e zenon_H67 zenon_H68 zenon_Ha0 zenon_H155 zenon_H48 zenon_H19a zenon_H73 zenon_H121 zenon_H209 zenon_H11a zenon_H177 zenon_Hc4 zenon_H25 zenon_H13c zenon_H18d zenon_Hb6 zenon_H234 zenon_H3f zenon_H93 zenon_H77 zenon_H120. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.78 apply (zenon_L171_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.78 apply (zenon_L116_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.78 apply (zenon_L538_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.78 apply (zenon_L548_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.78 apply (zenon_L162_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.78 apply (zenon_L265_); trivial. % 21.54/21.78 apply (zenon_L523_); trivial. % 21.54/21.78 apply (zenon_L549_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.78 apply (zenon_L227_); trivial. % 21.54/21.78 apply (zenon_L228_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.78 apply (zenon_L53_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.78 apply (zenon_L550_); trivial. % 21.54/21.78 apply (zenon_L540_); trivial. % 21.54/21.78 (* end of lemma zenon_L551_ *) % 21.54/21.78 assert (zenon_L552_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 21.54/21.78 do 0 intro. intros zenon_H11a zenon_H3f zenon_H7f. % 21.54/21.78 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 21.54/21.78 intro zenon_D_pnotp. % 21.54/21.78 apply zenon_H11a. % 21.54/21.78 rewrite <- zenon_D_pnotp. % 21.54/21.78 exact zenon_H3f. % 21.54/21.78 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 21.54/21.78 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 21.54/21.78 congruence. % 21.54/21.78 apply zenon_H10f. apply refl_equal. % 21.54/21.78 apply zenon_H80. apply sym_equal. exact zenon_H7f. % 21.54/21.78 (* end of lemma zenon_L552_ *) % 21.54/21.78 assert (zenon_L553_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H12e zenon_H48 zenon_H34 zenon_H3f zenon_H11a zenon_H160 zenon_H77 zenon_H120. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.78 apply (zenon_L456_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.78 apply (zenon_L552_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.78 apply (zenon_L367_); trivial. % 21.54/21.78 exact (zenon_H120 zenon_H11f). % 21.54/21.78 (* end of lemma zenon_L553_ *) % 21.54/21.78 assert (zenon_L554_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (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 (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e2) (e2)) = (op (e3) (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 (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (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 (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H1fe zenon_H19d zenon_H177 zenon_H2a zenon_H68 zenon_H13a zenon_H195 zenon_H163 zenon_H33 zenon_H131 zenon_H99 zenon_H104 zenon_H13e zenon_H164 zenon_H1a3 zenon_H140 zenon_Hfa zenon_Ha0 zenon_H19a zenon_H73 zenon_H121 zenon_H209 zenon_Hc4 zenon_H13c zenon_H18d zenon_Hb6 zenon_H234 zenon_H139 zenon_H1d8 zenon_H1ec zenon_H4e zenon_H156 zenon_H186 zenon_Hb2 zenon_H125 zenon_H94 zenon_Hbc zenon_H82 zenon_H196 zenon_H15d zenon_H93 zenon_H1bf zenon_Hf0 zenon_H13f zenon_H12e zenon_H48 zenon_H3f zenon_H11a zenon_H160 zenon_H77 zenon_H120. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.78 apply (zenon_L161_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.78 apply (zenon_L352_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.78 apply (zenon_L65_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.78 apply (zenon_L539_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.78 apply (zenon_L53_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.78 apply (zenon_L95_); trivial. % 21.54/21.78 apply (zenon_L540_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.78 apply (zenon_L541_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.78 apply (zenon_L25_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.78 apply (zenon_L539_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.78 apply (zenon_L53_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.78 apply (zenon_L542_); trivial. % 21.54/21.78 apply (zenon_L115_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.78 apply (zenon_L551_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.78 apply (zenon_L147_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.78 apply (zenon_L122_); trivial. % 21.54/21.78 apply (zenon_L98_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.78 apply (zenon_L526_); trivial. % 21.54/21.78 apply (zenon_L553_); trivial. % 21.54/21.78 (* end of lemma zenon_L554_ *) % 21.54/21.78 assert (zenon_L555_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H93 zenon_H77 zenon_H120. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.54/21.78 apply (zenon_L246_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.54/21.78 apply (zenon_L413_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.54/21.78 apply (zenon_L218_); trivial. % 21.54/21.78 exact (zenon_H120 zenon_H11f). % 21.54/21.78 (* end of lemma zenon_L555_ *) % 21.54/21.78 assert (zenon_L556_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H167 zenon_He0 zenon_H1b7. % 21.54/21.78 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.54/21.78 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 21.54/21.78 intro zenon_D_pnotp. % 21.54/21.78 apply zenon_H1b7. % 21.54/21.78 rewrite <- zenon_D_pnotp. % 21.54/21.78 exact zenon_H12a. % 21.54/21.78 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.78 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 21.54/21.78 congruence. % 21.54/21.78 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 21.54/21.78 intro zenon_D_pnotp. % 21.54/21.78 apply zenon_H1b8. % 21.54/21.78 rewrite <- zenon_D_pnotp. % 21.54/21.78 exact zenon_H167. % 21.54/21.78 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 21.54/21.78 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.78 congruence. % 21.54/21.78 apply zenon_H12b. apply refl_equal. % 21.54/21.78 apply zenon_H1f2. apply sym_equal. exact zenon_He0. % 21.54/21.78 apply zenon_H12b. apply refl_equal. % 21.54/21.78 apply zenon_H12b. apply refl_equal. % 21.54/21.78 (* end of lemma zenon_L556_ *) % 21.54/21.78 assert (zenon_L557_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H19a zenon_H77 zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H120 zenon_H20f zenon_H1bb zenon_H93 zenon_H68 zenon_He0 zenon_H1b7. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.54/21.78 apply (zenon_L555_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.54/21.78 apply (zenon_L422_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.54/21.78 apply (zenon_L158_); trivial. % 21.54/21.78 apply (zenon_L556_); trivial. % 21.54/21.78 (* end of lemma zenon_L557_ *) % 21.54/21.78 assert (zenon_L558_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((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 (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H12e zenon_H67 zenon_H209 zenon_Hbc zenon_H7d zenon_H167 zenon_H18a zenon_H212 zenon_H160 zenon_H77 zenon_H120. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.78 apply (zenon_L547_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.78 apply (zenon_L417_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.78 apply (zenon_L367_); trivial. % 21.54/21.78 exact (zenon_H120 zenon_H11f). % 21.54/21.78 (* end of lemma zenon_L558_ *) % 21.54/21.78 assert (zenon_L559_ : (((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)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H164 zenon_H25 zenon_H179 zenon_H1b7 zenon_H68 zenon_H93 zenon_H1bb zenon_H20f zenon_H181 zenon_Hc4 zenon_H18d zenon_H48 zenon_H129 zenon_H1b4 zenon_H19a zenon_H31 zenon_H177 zenon_H12e zenon_H67 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H160 zenon_H77 zenon_H120. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.78 apply (zenon_L297_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.78 apply (zenon_L557_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.78 apply (zenon_L406_); trivial. % 21.54/21.78 apply (zenon_L558_); trivial. % 21.54/21.78 (* end of lemma zenon_L559_ *) % 21.54/21.78 assert (zenon_L560_ : (((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)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((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 (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H24e zenon_H1b7 zenon_H209 zenon_Hbc zenon_H7d zenon_H167 zenon_H18a zenon_H212 zenon_H160 zenon_Hbb zenon_H1cd. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_He0 | zenon_intro zenon_H24f ]. % 21.54/21.78 apply (zenon_L556_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H7f | zenon_intro zenon_H250 ]. % 21.54/21.78 apply (zenon_L417_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H171 | zenon_intro zenon_Hac ]. % 21.54/21.78 apply (zenon_L240_); trivial. % 21.54/21.78 apply (zenon_L360_); trivial. % 21.54/21.78 (* end of lemma zenon_L560_ *) % 21.54/21.78 assert (zenon_L561_ : (((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)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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 (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H121 zenon_H11a zenon_H10c zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H167 zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_Hc4. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.54/21.78 exact (zenon_H209 zenon_H9d). % 21.54/21.78 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.54/21.78 apply (zenon_L79_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.54/21.78 apply (zenon_L560_); trivial. % 21.54/21.78 exact (zenon_Hc4 zenon_Hc3). % 21.54/21.78 (* end of lemma zenon_L561_ *) % 21.54/21.78 assert (zenon_L562_ : (((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) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((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 (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H164 zenon_H12e zenon_H68 zenon_H93 zenon_H1bb zenon_H20f zenon_H120 zenon_H181 zenon_H18d zenon_H48 zenon_H129 zenon_H1b4 zenon_H77 zenon_H19a zenon_H14c zenon_H104 zenon_H121 zenon_H11a zenon_H10c zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_Hc4. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.78 apply (zenon_L528_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.78 apply (zenon_L557_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.78 apply (zenon_L257_); trivial. % 21.54/21.78 apply (zenon_L561_); trivial. % 21.54/21.78 (* end of lemma zenon_L562_ *) % 21.54/21.78 assert (zenon_L563_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H19a zenon_H77 zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H120 zenon_H20f zenon_H1bb zenon_H93 zenon_H68 zenon_H11d zenon_H1cb. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.54/21.78 apply (zenon_L555_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.54/21.78 apply (zenon_L422_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.54/21.78 apply (zenon_L158_); trivial. % 21.54/21.78 apply (zenon_L266_); trivial. % 21.54/21.78 (* end of lemma zenon_L563_ *) % 21.54/21.78 assert (zenon_L564_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (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)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H1fe zenon_H19d zenon_H196 zenon_H177 zenon_H2a zenon_H68 zenon_Hfa zenon_H186 zenon_H156 zenon_H4e zenon_H1ec zenon_H140 zenon_H1d8 zenon_Ha0 zenon_H13e zenon_H104 zenon_H99 zenon_H131 zenon_H179 zenon_H24e zenon_H1b7 zenon_H1cd zenon_H11a zenon_H121 zenon_H164 zenon_H19a zenon_H1b4 zenon_H18d zenon_H181 zenon_H20f zenon_H1cb zenon_H13c zenon_H163 zenon_H195 zenon_H139 zenon_H1bf zenon_H3f zenon_Hf0 zenon_H13f zenon_H12e zenon_H48 zenon_Hc4 zenon_H93 zenon_H129 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H160 zenon_H77 zenon_H120. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.78 apply (zenon_L161_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.78 apply (zenon_L171_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.78 apply (zenon_L116_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.78 apply (zenon_L559_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.78 apply (zenon_L274_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.78 apply (zenon_L562_); trivial. % 21.54/21.78 apply (zenon_L563_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.78 apply (zenon_L524_); trivial. % 21.54/21.78 apply (zenon_L525_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.78 apply (zenon_L227_); trivial. % 21.54/21.78 apply (zenon_L228_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.78 apply (zenon_L147_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.78 apply (zenon_L122_); trivial. % 21.54/21.78 apply (zenon_L167_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.78 apply (zenon_L526_); trivial. % 21.54/21.78 apply (zenon_L528_); trivial. % 21.54/21.78 (* end of lemma zenon_L564_ *) % 21.54/21.78 assert (zenon_L565_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 21.54/21.78 do 0 intro. intros zenon_Hc2 zenon_H19d zenon_H2a zenon_H139 zenon_H196 zenon_H68 zenon_H13c zenon_H156 zenon_H3f zenon_H163 zenon_H186 zenon_H1ec zenon_H1d8 zenon_H13e zenon_H131 zenon_H99 zenon_H1bf zenon_H164 zenon_H212 zenon_H209 zenon_H160 zenon_Hbc zenon_H7d zenon_H18a zenon_H12e zenon_H177 zenon_H18d zenon_H120 zenon_H77 zenon_H1b4 zenon_H20f zenon_H129 zenon_H93 zenon_H1bb zenon_H48 zenon_H181 zenon_H1b7 zenon_H19a zenon_H179 zenon_H4e zenon_H11a zenon_H24e zenon_H1cd zenon_H121 zenon_H104 zenon_H1cb zenon_H140 zenon_Ha0 zenon_H195 zenon_Hfa zenon_H13f zenon_Hf0 zenon_H1fe. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.54/21.78 apply (zenon_L564_); trivial. % 21.54/21.78 apply (zenon_L564_); trivial. % 21.54/21.78 (* end of lemma zenon_L565_ *) % 21.54/21.78 assert (zenon_L566_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 21.54/21.78 do 0 intro. intros zenon_H177 zenon_H153 zenon_H106. % 21.54/21.78 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 21.54/21.78 intro zenon_D_pnotp. % 21.54/21.78 apply zenon_H177. % 21.54/21.78 rewrite <- zenon_D_pnotp. % 21.54/21.78 exact zenon_H153. % 21.54/21.78 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 21.54/21.78 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 21.54/21.78 congruence. % 21.54/21.78 apply zenon_H135. apply refl_equal. % 21.54/21.78 apply zenon_H107. apply sym_equal. exact zenon_H106. % 21.54/21.78 (* end of lemma zenon_L566_ *) % 21.54/21.78 assert (zenon_L567_ : (((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 (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 21.54/21.78 do 0 intro. intros zenon_H15d zenon_H4c zenon_H48 zenon_H2a zenon_H120 zenon_H177 zenon_H11a zenon_H3f zenon_H9d zenon_H12e zenon_Hb6 zenon_H9e. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.78 exact (zenon_H4c zenon_H47). % 21.54/21.78 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.78 apply (zenon_L65_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.78 apply (zenon_L134_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.78 apply (zenon_L552_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.78 apply (zenon_L566_); trivial. % 21.54/21.78 exact (zenon_H120 zenon_H11f). % 21.54/21.78 apply (zenon_L115_); trivial. % 21.54/21.78 (* end of lemma zenon_L567_ *) % 21.54/21.78 assert (zenon_L568_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H1cf zenon_H153 zenon_H156 zenon_Hef zenon_H8b zenon_H12e zenon_H48 zenon_H34 zenon_H3f zenon_H11a zenon_H77 zenon_H120. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.78 apply (zenon_L94_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.78 apply (zenon_L100_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.78 exact (zenon_H8b zenon_H8a). % 21.54/21.78 apply (zenon_L553_); trivial. % 21.54/21.78 (* end of lemma zenon_L568_ *) % 21.54/21.78 assert (zenon_L569_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (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 (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 21.54/21.78 do 0 intro. intros zenon_H201 zenon_H120 zenon_H77 zenon_H11a zenon_H34 zenon_H48 zenon_H12e zenon_H8b zenon_Hef zenon_H1cf zenon_H156 zenon_H3f zenon_H1bf zenon_Hb6 zenon_Hbb. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.78 apply (zenon_L568_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.78 apply (zenon_L486_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.78 exact (zenon_H1bf zenon_H105). % 21.54/21.78 apply (zenon_L363_); trivial. % 21.54/21.78 (* end of lemma zenon_L569_ *) % 21.54/21.78 assert (zenon_L570_ : ((op (e3) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H17c zenon_Hf7 zenon_H20f. % 21.54/21.78 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.54/21.78 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 21.54/21.78 intro zenon_D_pnotp. % 21.54/21.78 apply zenon_H20f. % 21.54/21.78 rewrite <- zenon_D_pnotp. % 21.54/21.78 exact zenon_H12a. % 21.54/21.78 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.78 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 21.54/21.78 congruence. % 21.54/21.78 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 21.54/21.78 intro zenon_D_pnotp. % 21.54/21.78 apply zenon_H210. % 21.54/21.78 rewrite <- zenon_D_pnotp. % 21.54/21.78 exact zenon_H17c. % 21.54/21.78 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 21.54/21.78 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.78 congruence. % 21.54/21.78 apply zenon_H12b. apply refl_equal. % 21.54/21.78 apply zenon_Hf8. apply sym_equal. exact zenon_Hf7. % 21.54/21.78 apply zenon_H12b. apply refl_equal. % 21.54/21.78 apply zenon_H12b. apply refl_equal. % 21.54/21.78 (* end of lemma zenon_L570_ *) % 21.54/21.78 assert (zenon_L571_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H1bb zenon_H10c zenon_H120 zenon_H20f zenon_Hf7 zenon_Hc0 zenon_H129. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.54/21.78 apply (zenon_L294_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.54/21.78 exact (zenon_H120 zenon_H11f). % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.54/21.78 apply (zenon_L570_); trivial. % 21.54/21.78 apply (zenon_L190_); trivial. % 21.54/21.78 (* end of lemma zenon_L571_ *) % 21.54/21.78 assert (zenon_L572_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e1)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H1c3 zenon_H77 zenon_H155 zenon_H129 zenon_Hc0 zenon_H20f zenon_H120 zenon_H10c zenon_H1bb zenon_H189 zenon_H6d zenon_H160 zenon_H1cb. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.54/21.78 apply (zenon_L98_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.54/21.78 apply (zenon_L571_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.54/21.78 apply (zenon_L439_); trivial. % 21.54/21.78 apply (zenon_L236_); trivial. % 21.54/21.78 (* end of lemma zenon_L572_ *) % 21.54/21.78 assert (zenon_L573_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H1cf zenon_H153 zenon_H4e zenon_H76 zenon_H8b zenon_H18d zenon_H1cb zenon_H6d zenon_H189 zenon_H1bb zenon_H10c zenon_H20f zenon_Hc0 zenon_H129 zenon_H77 zenon_H1c3 zenon_H234 zenon_H3f zenon_Hb9 zenon_Hb6 zenon_H120. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.78 apply (zenon_L94_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.78 apply (zenon_L83_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.78 exact (zenon_H8b zenon_H8a). % 21.54/21.78 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.54/21.78 apply (zenon_L572_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.54/21.78 apply (zenon_L484_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.54/21.78 apply (zenon_L182_); trivial. % 21.54/21.78 exact (zenon_H120 zenon_H11f). % 21.54/21.78 (* end of lemma zenon_L573_ *) % 21.54/21.78 assert (zenon_L574_ : (((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))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H1c6 zenon_Ha0 zenon_H2a zenon_H120 zenon_Hb6 zenon_Hb9 zenon_H3f zenon_H234 zenon_H1c3 zenon_H77 zenon_H129 zenon_Hc0 zenon_H20f zenon_H1bb zenon_H189 zenon_H1cb zenon_H18d zenon_H8b zenon_H76 zenon_H4e zenon_H153 zenon_H1cf zenon_Ha9 zenon_H6d zenon_Hbb zenon_H1cd. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.78 apply (zenon_L53_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.78 apply (zenon_L573_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.78 apply (zenon_L289_); trivial. % 21.54/21.78 apply (zenon_L360_); trivial. % 21.54/21.78 (* end of lemma zenon_L574_ *) % 21.54/21.78 assert (zenon_L575_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 21.54/21.78 do 0 intro. intros zenon_H201 zenon_H1cd zenon_H171 zenon_H8b zenon_H68 zenon_H77 zenon_H1cf zenon_Hf3 zenon_H48 zenon_H1bf zenon_Hb6 zenon_Hbb. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.78 apply (zenon_L241_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.78 apply (zenon_L117_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.78 exact (zenon_H1bf zenon_H105). % 21.54/21.78 apply (zenon_L363_); trivial. % 21.54/21.78 (* end of lemma zenon_L575_ *) % 21.54/21.78 assert (zenon_L576_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H1c6 zenon_Ha0 zenon_H2a zenon_H129 zenon_Hc0 zenon_Hf7 zenon_H20f zenon_H120 zenon_H1bb zenon_Ha9 zenon_H6d zenon_Hbb zenon_H1cd. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.78 apply (zenon_L53_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.78 apply (zenon_L571_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.78 apply (zenon_L289_); trivial. % 21.54/21.78 apply (zenon_L360_); trivial. % 21.54/21.78 (* end of lemma zenon_L576_ *) % 21.54/21.78 assert (zenon_L577_ : (((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 (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.78 do 0 intro. intros zenon_Hfa zenon_H1cf zenon_H153 zenon_H4e zenon_H8b zenon_H18d zenon_H1cb zenon_H189 zenon_H77 zenon_H1c3 zenon_H234 zenon_H3f zenon_Hb9 zenon_Hb6 zenon_Hf0 zenon_Hf3 zenon_H68 zenon_H1c6 zenon_Ha0 zenon_H2a zenon_H129 zenon_Hc0 zenon_H20f zenon_H120 zenon_H1bb zenon_Ha9 zenon_H6d zenon_Hbb zenon_H1cd. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.78 apply (zenon_L574_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.78 apply (zenon_L61_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.78 apply (zenon_L62_); trivial. % 21.54/21.78 apply (zenon_L576_); trivial. % 21.54/21.78 (* end of lemma zenon_L577_ *) % 21.54/21.78 assert (zenon_L578_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.78 do 0 intro. intros zenon_H12e zenon_Hb9 zenon_H48 zenon_H136 zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H72 zenon_H163 zenon_H9f zenon_H18d zenon_Hbb zenon_Hb6 zenon_H120. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.78 apply (zenon_L456_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.54/21.78 apply (zenon_L449_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.54/21.78 apply (zenon_L157_); trivial. % 21.54/21.78 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.54/21.78 apply (zenon_L182_); trivial. % 21.54/21.79 exact (zenon_H120 zenon_H11f). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.79 apply (zenon_L363_); trivial. % 21.54/21.79 exact (zenon_H120 zenon_H11f). % 21.54/21.79 (* end of lemma zenon_L578_ *) % 21.54/21.79 assert (zenon_L579_ : (((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)) = (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 (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e3)) -> (((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 (e0) (e1)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H13b zenon_H179 zenon_H173 zenon_Hfa zenon_H1cf zenon_H153 zenon_H4e zenon_H8b zenon_H1cb zenon_H189 zenon_H1c3 zenon_H234 zenon_H3f zenon_Hf0 zenon_Hb6 zenon_H18d zenon_H9f zenon_H163 zenon_H77 zenon_H34 zenon_H68 zenon_H183 zenon_H48 zenon_Hb9 zenon_H12e zenon_H1c6 zenon_Ha0 zenon_H2a zenon_H129 zenon_Hc0 zenon_H20f zenon_H120 zenon_H1bb zenon_Ha9 zenon_H6d zenon_Hbb zenon_H1cd. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.79 apply (zenon_L297_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.79 apply (zenon_L272_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.79 apply (zenon_L577_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.79 apply (zenon_L574_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.79 apply (zenon_L61_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.79 apply (zenon_L578_); trivial. % 21.54/21.79 apply (zenon_L576_); trivial. % 21.54/21.79 (* end of lemma zenon_L579_ *) % 21.54/21.79 assert (zenon_L580_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (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) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (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) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H16a zenon_H7b zenon_H1cd zenon_Hbb zenon_Ha9 zenon_H1bb zenon_H120 zenon_H20f zenon_Hc0 zenon_H129 zenon_H2a zenon_Ha0 zenon_H1c6 zenon_H12e zenon_Hb9 zenon_H48 zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H163 zenon_H9f zenon_H18d zenon_Hb6 zenon_Hf0 zenon_H3f zenon_H234 zenon_H1c3 zenon_H189 zenon_H1cb zenon_H4e zenon_H153 zenon_H1cf zenon_Hfa zenon_H173 zenon_H179 zenon_H13b zenon_H8b zenon_Hf7 zenon_H195. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.79 exact (zenon_H7b zenon_H65). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.79 apply (zenon_L579_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.79 exact (zenon_H8b zenon_H8a). % 21.54/21.79 apply (zenon_L228_); trivial. % 21.54/21.79 (* end of lemma zenon_L580_ *) % 21.54/21.79 assert (zenon_L581_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H117 zenon_Hb6 zenon_H54 zenon_H10c zenon_Hf0 zenon_H14c zenon_Ha0 zenon_H9e zenon_H196. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.79 apply (zenon_L151_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.79 apply (zenon_L74_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.79 apply (zenon_L278_); trivial. % 21.54/21.79 apply (zenon_L154_); trivial. % 21.54/21.79 (* end of lemma zenon_L581_ *) % 21.54/21.79 assert (zenon_L582_ : (((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)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> False). % 21.54/21.79 do 0 intro. intros zenon_H117 zenon_Hb6 zenon_H54 zenon_H6d zenon_H8a zenon_Ha9 zenon_Ha0 zenon_H115. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.79 apply (zenon_L151_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.79 apply (zenon_L289_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.79 apply (zenon_L153_); trivial. % 21.54/21.79 apply (zenon_L77_); trivial. % 21.54/21.79 (* end of lemma zenon_L582_ *) % 21.54/21.79 assert (zenon_L583_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H12e zenon_H9d zenon_Hb6 zenon_H3f zenon_H11a zenon_H160 zenon_H77 zenon_H120. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.79 apply (zenon_L134_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.79 apply (zenon_L552_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.79 apply (zenon_L367_); trivial. % 21.54/21.79 exact (zenon_H120 zenon_H11f). % 21.54/21.79 (* end of lemma zenon_L583_ *) % 21.54/21.79 assert (zenon_L584_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H1cf zenon_H1d5 zenon_H67 zenon_Hf7 zenon_H186 zenon_H115 zenon_Ha0 zenon_Ha9 zenon_H6d zenon_H54 zenon_H117 zenon_H12e zenon_H9d zenon_Hb6 zenon_H3f zenon_H11a zenon_H77 zenon_H120. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.79 apply (zenon_L252_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.79 apply (zenon_L438_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.79 apply (zenon_L582_); trivial. % 21.54/21.79 apply (zenon_L583_); trivial. % 21.54/21.79 (* end of lemma zenon_L584_ *) % 21.54/21.79 assert (zenon_L585_ : (((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) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H24e zenon_H2a zenon_H192 zenon_H106 zenon_H1cd zenon_H1b7 zenon_H17c zenon_H9d zenon_H7d. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_He0 | zenon_intro zenon_H24f ]. % 21.54/21.79 apply (zenon_L292_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H7f | zenon_intro zenon_H250 ]. % 21.54/21.79 apply (zenon_L331_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H171 | zenon_intro zenon_Hac ]. % 21.54/21.79 apply (zenon_L188_); trivial. % 21.54/21.79 apply (zenon_L44_); trivial. % 21.54/21.79 (* end of lemma zenon_L585_ *) % 21.54/21.79 assert (zenon_L586_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 21.54/21.79 do 0 intro. intros zenon_H82 zenon_H4c zenon_H3f zenon_H23c zenon_H48 zenon_H2d zenon_Hb6 zenon_H9d. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.79 exact (zenon_H4c zenon_H47). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.79 apply (zenon_L492_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.79 apply (zenon_L217_); trivial. % 21.54/21.79 apply (zenon_L134_); trivial. % 21.54/21.79 (* end of lemma zenon_L586_ *) % 21.54/21.79 assert (zenon_L587_ : (((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)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H117 zenon_H109 zenon_H9d zenon_Ha0 zenon_Hdd zenon_H131 zenon_H133 zenon_H9e zenon_H196. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.79 apply (zenon_L73_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.79 apply (zenon_L152_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.79 apply (zenon_L259_); trivial. % 21.54/21.79 apply (zenon_L154_); trivial. % 21.54/21.79 (* end of lemma zenon_L587_ *) % 21.54/21.79 assert (zenon_L588_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 21.54/21.79 do 0 intro. intros zenon_Hcc zenon_H1d8 zenon_H1fb zenon_H48 zenon_H2a zenon_H77 zenon_H234 zenon_H55 zenon_H189 zenon_H6d zenon_H7d zenon_H3f zenon_H1cd zenon_Hac. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.54/21.79 apply (zenon_L2_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.54/21.79 apply (zenon_L482_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.54/21.79 apply (zenon_L315_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.54/21.79 apply (zenon_L317_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.54/21.79 apply (zenon_L318_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.54/21.79 apply (zenon_L11_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.54/21.79 apply (zenon_L319_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.54/21.79 apply (zenon_L485_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.54/21.79 apply (zenon_L435_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.54/21.79 apply (zenon_L522_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.54/21.79 apply (zenon_L37_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.54/21.79 apply (zenon_L458_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.54/21.79 apply (zenon_L387_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.54/21.79 apply (zenon_L531_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.54/21.79 apply (zenon_L388_); trivial. % 21.54/21.79 apply (zenon_L51_); trivial. % 21.54/21.79 (* end of lemma zenon_L588_ *) % 21.54/21.79 assert (zenon_L589_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H15d zenon_H4c zenon_H48 zenon_H77 zenon_H13a zenon_H33 zenon_H9d zenon_Ha0 zenon_H2a zenon_Ha9 zenon_H66 zenon_Hb6. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.79 exact (zenon_H4c zenon_H47). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.79 apply (zenon_L65_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.79 apply (zenon_L94_); trivial. % 21.54/21.79 apply (zenon_L502_); trivial. % 21.54/21.79 (* end of lemma zenon_L589_ *) % 21.54/21.79 assert (zenon_L590_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H236 zenon_H1f zenon_Hb6 zenon_H66 zenon_Ha9 zenon_Ha0 zenon_H9d zenon_H33 zenon_H13a zenon_H77 zenon_H48 zenon_H4c zenon_H15d zenon_H237 zenon_H238. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 21.54/21.79 exact (zenon_H1f zenon_H1e). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 21.54/21.79 apply (zenon_L589_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 21.54/21.79 exact (zenon_H237 zenon_H31). % 21.54/21.79 exact (zenon_H238 zenon_H38). % 21.54/21.79 (* end of lemma zenon_L590_ *) % 21.54/21.79 assert (zenon_L591_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H1cf zenon_H1d5 zenon_H67 zenon_Hf3 zenon_H68 zenon_H115 zenon_Ha0 zenon_Ha9 zenon_H6d zenon_H54 zenon_H117 zenon_H12e zenon_H9d zenon_Hb6 zenon_H3f zenon_H11a zenon_H77 zenon_H120. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.79 apply (zenon_L252_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.79 apply (zenon_L62_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.79 apply (zenon_L582_); trivial. % 21.54/21.79 apply (zenon_L583_); trivial. % 21.54/21.79 (* end of lemma zenon_L591_ *) % 21.54/21.79 assert (zenon_L592_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> False). % 21.54/21.79 do 0 intro. intros zenon_H117 zenon_H109 zenon_H9d zenon_Ha9 zenon_H6d zenon_H14c zenon_Ha0 zenon_H115. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.79 apply (zenon_L73_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.79 apply (zenon_L289_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.79 apply (zenon_L278_); trivial. % 21.54/21.79 apply (zenon_L77_); trivial. % 21.54/21.79 (* end of lemma zenon_L592_ *) % 21.54/21.79 assert (zenon_L593_ : (((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) (e1)) = (op (e2) (e1)))) -> ((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 (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (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 (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 21.54/21.79 do 0 intro. intros zenon_H141 zenon_H196 zenon_H9e zenon_Hf0 zenon_H10c zenon_H140 zenon_H237 zenon_H120 zenon_H77 zenon_H11a zenon_H3f zenon_Hb6 zenon_H12e zenon_H54 zenon_H68 zenon_H67 zenon_H1d5 zenon_H1cf zenon_Ha0 zenon_H6d zenon_Ha9 zenon_H9d zenon_H109 zenon_H117 zenon_Hbc zenon_H34. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.79 apply (zenon_L359_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.79 apply (zenon_L54_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.79 apply (zenon_L581_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.79 exact (zenon_H237 zenon_H31). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.79 apply (zenon_L591_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.79 apply (zenon_L592_); trivial. % 21.54/21.79 apply (zenon_L328_); trivial. % 21.54/21.79 (* end of lemma zenon_L593_ *) % 21.54/21.79 assert (zenon_L594_ : (((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) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H1c6 zenon_H2a zenon_H34 zenon_Hbc zenon_H117 zenon_H109 zenon_Ha0 zenon_H133 zenon_H237 zenon_H140 zenon_Hb6 zenon_H54 zenon_Hf0 zenon_H9e zenon_H196 zenon_H131 zenon_H48 zenon_H141 zenon_Ha9 zenon_H6d zenon_H9d zenon_H7d. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.79 apply (zenon_L53_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.79 apply (zenon_L217_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.79 apply (zenon_L587_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.79 apply (zenon_L581_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.79 exact (zenon_H237 zenon_H31). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.79 apply (zenon_L162_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.79 apply (zenon_L592_); trivial. % 21.54/21.79 apply (zenon_L328_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.79 apply (zenon_L289_); trivial. % 21.54/21.79 apply (zenon_L44_); trivial. % 21.54/21.79 (* end of lemma zenon_L594_ *) % 21.54/21.79 assert (zenon_L595_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 21.54/21.79 do 0 intro. intros zenon_Hb2 zenon_Ha4 zenon_Ha0 zenon_H25 zenon_H1ef zenon_H110 zenon_Hb6 zenon_H7e. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.79 exact (zenon_Ha4 zenon_H9f). % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.79 apply (zenon_L116_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.79 apply (zenon_L282_); trivial. % 21.54/21.79 apply (zenon_L134_); trivial. % 21.54/21.79 (* end of lemma zenon_L595_ *) % 21.54/21.79 assert (zenon_L596_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.54/21.79 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha0 zenon_H2a zenon_H111 zenon_H110 zenon_Hb6 zenon_H155. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.79 exact (zenon_Ha4 zenon_H9f). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.79 apply (zenon_L53_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.79 apply (zenon_L75_); trivial. % 21.54/21.79 apply (zenon_L115_); trivial. % 21.54/21.79 (* end of lemma zenon_L596_ *) % 21.54/21.79 assert (zenon_L597_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 21.54/21.79 do 0 intro. intros zenon_Hb2 zenon_Ha4 zenon_Ha0 zenon_H25 zenon_H1ef zenon_H110 zenon_Ha9 zenon_H102. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.54/21.79 exact (zenon_Ha4 zenon_H9f). % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.54/21.79 apply (zenon_L116_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.54/21.79 apply (zenon_L282_); trivial. % 21.54/21.79 apply (zenon_L91_); trivial. % 21.54/21.79 (* end of lemma zenon_L597_ *) % 21.54/21.79 assert (zenon_L598_ : (((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)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.54/21.79 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H173 zenon_H10c zenon_Hb6 zenon_H153 zenon_Ha9 zenon_Hf6. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.79 exact (zenon_Ha4 zenon_H9f). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.79 apply (zenon_L120_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.79 apply (zenon_L95_); trivial. % 21.54/21.79 apply (zenon_L92_); trivial. % 21.54/21.79 (* end of lemma zenon_L598_ *) % 21.54/21.79 assert (zenon_L599_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((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) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H1c3 zenon_Ha9 zenon_H153 zenon_Hb6 zenon_H10c zenon_H173 zenon_Ha4 zenon_H13a zenon_H72 zenon_H186 zenon_H128 zenon_H77 zenon_H171 zenon_H1b7. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.54/21.79 apply (zenon_L598_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.54/21.79 apply (zenon_L438_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.54/21.79 apply (zenon_L218_); trivial. % 21.54/21.79 apply (zenon_L188_); trivial. % 21.54/21.79 (* end of lemma zenon_L599_ *) % 21.54/21.79 assert (zenon_L600_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha0 zenon_H2a zenon_Hb6 zenon_H153 zenon_Ha5 zenon_Hf5. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.79 exact (zenon_Ha4 zenon_H9f). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.79 apply (zenon_L53_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.79 apply (zenon_L95_); trivial. % 21.54/21.79 apply (zenon_L262_); trivial. % 21.54/21.79 (* end of lemma zenon_L600_ *) % 21.54/21.79 assert (zenon_L601_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e3))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H23d zenon_H1f zenon_H4c zenon_H1d5 zenon_H66 zenon_Ha4. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1e | zenon_intro zenon_H23e ]. % 21.54/21.79 exact (zenon_H1f zenon_H1e). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H47 | zenon_intro zenon_H23f ]. % 21.54/21.79 exact (zenon_H4c zenon_H47). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H67 | zenon_intro zenon_H9f ]. % 21.54/21.79 apply (zenon_L252_); trivial. % 21.54/21.79 exact (zenon_Ha4 zenon_H9f). % 21.54/21.79 (* end of lemma zenon_L601_ *) % 21.54/21.79 assert (zenon_L602_ : ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_Hc3 zenon_H9e zenon_H1b4. % 21.54/21.79 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.54/21.79 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 21.54/21.79 intro zenon_D_pnotp. % 21.54/21.79 apply zenon_H1b4. % 21.54/21.79 rewrite <- zenon_D_pnotp. % 21.54/21.79 exact zenon_H12a. % 21.54/21.79 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.79 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 21.54/21.79 congruence. % 21.54/21.79 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 21.54/21.79 intro zenon_D_pnotp. % 21.54/21.79 apply zenon_H1b5. % 21.54/21.79 rewrite <- zenon_D_pnotp. % 21.54/21.79 exact zenon_Hc3. % 21.54/21.79 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 21.54/21.79 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.79 congruence. % 21.54/21.79 apply zenon_H12b. apply refl_equal. % 21.54/21.79 apply zenon_H198. apply sym_equal. exact zenon_H9e. % 21.54/21.79 apply zenon_H12b. apply refl_equal. % 21.54/21.79 apply zenon_H12b. apply refl_equal. % 21.54/21.79 (* end of lemma zenon_L602_ *) % 21.54/21.79 assert (zenon_L603_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha0 zenon_H2a zenon_Hb6 zenon_H153 zenon_Hc3 zenon_H1b4. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.79 exact (zenon_Ha4 zenon_H9f). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.79 apply (zenon_L53_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.79 apply (zenon_L95_); trivial. % 21.54/21.79 apply (zenon_L602_); trivial. % 21.54/21.79 (* end of lemma zenon_L603_ *) % 21.54/21.79 assert (zenon_L604_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H1bb zenon_H68 zenon_H77 zenon_H128 zenon_H10c zenon_Ha9 zenon_H9e zenon_H1c3 zenon_H120 zenon_H1cb zenon_H160 zenon_H13a zenon_Ha4 zenon_Ha0 zenon_H2a zenon_Hb6 zenon_H153 zenon_H1b4. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.54/21.79 apply (zenon_L296_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.54/21.79 exact (zenon_H120 zenon_H11f). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.54/21.79 apply (zenon_L236_); trivial. % 21.54/21.79 apply (zenon_L603_); trivial. % 21.54/21.79 (* end of lemma zenon_L604_ *) % 21.54/21.79 assert (zenon_L605_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H141 zenon_H48 zenon_H1cf zenon_H1d5 zenon_H4c zenon_H1f zenon_H23d zenon_H186 zenon_H6d zenon_H117 zenon_H54 zenon_Hf0 zenon_H120 zenon_H1bb zenon_H68 zenon_H77 zenon_H10c zenon_Ha9 zenon_H1c3 zenon_H1cb zenon_H13a zenon_Ha4 zenon_Ha0 zenon_H2a zenon_Hb6 zenon_H153 zenon_H1b4 zenon_Hf7 zenon_H111 zenon_H18d zenon_H9e zenon_H196. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.79 apply (zenon_L217_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.79 apply (zenon_L54_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.79 apply (zenon_L581_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.79 apply (zenon_L601_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.79 apply (zenon_L438_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.79 apply (zenon_L582_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.79 apply (zenon_L151_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.79 apply (zenon_L74_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.54/21.79 apply (zenon_L596_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.54/21.79 apply (zenon_L206_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.54/21.79 apply (zenon_L604_); trivial. % 21.54/21.79 exact (zenon_H120 zenon_H11f). % 21.54/21.79 apply (zenon_L154_); trivial. % 21.54/21.79 (* end of lemma zenon_L605_ *) % 21.54/21.79 assert (zenon_L606_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (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))))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.79 do 0 intro. intros zenon_H1c6 zenon_H196 zenon_H9e zenon_H18d zenon_H111 zenon_Hf7 zenon_H1b4 zenon_H153 zenon_Hb6 zenon_Ha0 zenon_Ha4 zenon_H13a zenon_H1cb zenon_H1c3 zenon_H68 zenon_H1bb zenon_H120 zenon_Hf0 zenon_H54 zenon_H117 zenon_H186 zenon_H23d zenon_H1f zenon_H4c zenon_H1d5 zenon_H1cf zenon_H141 zenon_Ha9 zenon_Hcc zenon_H1d8 zenon_H1fb zenon_H48 zenon_H2a zenon_H77 zenon_H234 zenon_H55 zenon_H189 zenon_H6d zenon_H7d zenon_H3f zenon_H1cd. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.79 apply (zenon_L53_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.79 apply (zenon_L605_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.79 apply (zenon_L289_); trivial. % 21.54/21.79 apply (zenon_L588_); trivial. % 21.54/21.79 (* end of lemma zenon_L606_ *) % 21.54/21.79 assert (zenon_L607_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((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) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 21.54/21.79 do 0 intro. intros zenon_Hfa zenon_Hf5 zenon_H4e zenon_H3f zenon_H234 zenon_Hf3 zenon_H13c zenon_H179 zenon_H18d zenon_H111 zenon_H1b4 zenon_H153 zenon_Ha4 zenon_H13a zenon_H1cb zenon_H1c3 zenon_H77 zenon_H68 zenon_H1bb zenon_H120 zenon_H186 zenon_H23d zenon_H1f zenon_H4c zenon_H1d5 zenon_H1cf zenon_H7d zenon_H9d zenon_H6d zenon_H141 zenon_H48 zenon_H131 zenon_H196 zenon_H9e zenon_Hf0 zenon_H54 zenon_Hb6 zenon_H140 zenon_H237 zenon_Ha0 zenon_H109 zenon_H117 zenon_Hbc zenon_H34 zenon_H2a zenon_H1c6 zenon_Ha9. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.79 apply (zenon_L123_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.79 apply (zenon_L359_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.79 apply (zenon_L54_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.79 apply (zenon_L581_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.79 apply (zenon_L94_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.79 apply (zenon_L83_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.79 apply (zenon_L582_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.79 apply (zenon_L73_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.79 apply (zenon_L74_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.54/21.79 apply (zenon_L596_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.54/21.79 apply (zenon_L484_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.54/21.79 apply (zenon_L604_); trivial. % 21.54/21.79 exact (zenon_H120 zenon_H11f). % 21.54/21.79 apply (zenon_L77_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.79 apply (zenon_L162_); trivial. % 21.54/21.79 apply (zenon_L600_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.79 apply (zenon_L61_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.79 apply (zenon_L62_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.79 apply (zenon_L123_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.79 apply (zenon_L605_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.79 apply (zenon_L594_); trivial. % 21.54/21.79 apply (zenon_L299_); trivial. % 21.54/21.79 (* end of lemma zenon_L607_ *) % 21.54/21.79 assert (zenon_L608_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (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 (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 21.54/21.79 do 0 intro. intros zenon_H140 zenon_H237 zenon_H18d zenon_H111 zenon_H136 zenon_H48 zenon_H1b4 zenon_H153 zenon_Hb6 zenon_H2a zenon_Ha4 zenon_H13a zenon_H1cb zenon_H1c3 zenon_H9e zenon_H10c zenon_H77 zenon_H68 zenon_H1bb zenon_H120 zenon_Hf0 zenon_H54 zenon_H1cf zenon_H115 zenon_Ha0 zenon_H6d zenon_Ha9 zenon_H9d zenon_H109 zenon_H117 zenon_Hbc zenon_H34. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.79 exact (zenon_H237 zenon_H31). % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.79 apply (zenon_L94_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.79 apply (zenon_L62_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.79 apply (zenon_L582_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.79 apply (zenon_L73_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.79 apply (zenon_L74_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.54/21.79 apply (zenon_L596_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.54/21.79 apply (zenon_L157_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.54/21.79 apply (zenon_L604_); trivial. % 21.54/21.79 exact (zenon_H120 zenon_H11f). % 21.54/21.79 apply (zenon_L77_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.79 apply (zenon_L592_); trivial. % 21.54/21.79 apply (zenon_L328_); trivial. % 21.54/21.79 (* end of lemma zenon_L608_ *) % 21.54/21.79 assert (zenon_L609_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (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 (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 21.54/21.79 do 0 intro. intros zenon_H141 zenon_H196 zenon_H140 zenon_H237 zenon_H18d zenon_H111 zenon_H136 zenon_H48 zenon_H1b4 zenon_H153 zenon_Hb6 zenon_H2a zenon_Ha4 zenon_H13a zenon_H1cb zenon_H1c3 zenon_H9e zenon_H10c zenon_H77 zenon_H68 zenon_H1bb zenon_H120 zenon_Hf0 zenon_H54 zenon_H1cf zenon_Ha0 zenon_H6d zenon_Ha9 zenon_H9d zenon_H109 zenon_H117 zenon_Hbc zenon_H34. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.79 apply (zenon_L359_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.79 apply (zenon_L54_); trivial. % 21.54/21.79 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.79 apply (zenon_L581_); trivial. % 21.54/21.79 apply (zenon_L608_); trivial. % 21.54/21.79 (* end of lemma zenon_L609_ *) % 21.54/21.79 assert (zenon_L610_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (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 (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (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 (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H23b zenon_H23d zenon_H1bb zenon_H1b4 zenon_H1cb zenon_Hb2 zenon_H1ef zenon_H173 zenon_H183 zenon_H111 zenon_H13b zenon_H4e zenon_H1f zenon_Hfa zenon_H179 zenon_H82 zenon_H1c6 zenon_H1d8 zenon_H1fb zenon_H55 zenon_H189 zenon_Hcc zenon_H131 zenon_H109 zenon_Ha0 zenon_H141 zenon_H9d zenon_H11a zenon_H18d zenon_Ha9 zenon_H1cf zenon_H77 zenon_H120 zenon_H12e zenon_H186 zenon_H1d5 zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H2a zenon_H192 zenon_H1c3 zenon_H234 zenon_Hb6 zenon_H196 zenon_H9e zenon_H117 zenon_H48 zenon_Hf5 zenon_H13c zenon_H6d zenon_Hf0 zenon_H68 zenon_H236 zenon_H237 zenon_H13a zenon_H33 zenon_H15d zenon_H139 zenon_H3f zenon_H23c zenon_H4c zenon_H140 zenon_Hbc zenon_H6f zenon_H1fe. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.80 exact (zenon_H1f zenon_H1e). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.80 exact (zenon_H4c zenon_H47). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.80 apply (zenon_L492_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.80 apply (zenon_L171_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.80 apply (zenon_L61_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.80 apply (zenon_L116_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.80 apply (zenon_L217_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.80 apply (zenon_L54_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.80 apply (zenon_L581_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.80 apply (zenon_L134_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.80 apply (zenon_L552_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.54/21.80 apply (zenon_L115_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.54/21.80 apply (zenon_L484_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.54/21.80 apply (zenon_L92_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.54/21.80 apply (zenon_L584_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.54/21.80 apply (zenon_L218_); trivial. % 21.54/21.80 apply (zenon_L585_); trivial. % 21.54/21.80 exact (zenon_H120 zenon_H11f). % 21.54/21.80 exact (zenon_H120 zenon_H11f). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.80 apply (zenon_L436_); trivial. % 21.54/21.80 apply (zenon_L262_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.80 apply (zenon_L123_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.80 apply (zenon_L586_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.80 apply (zenon_L54_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.80 apply (zenon_L581_); trivial. % 21.54/21.80 apply (zenon_L584_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.80 apply (zenon_L53_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.80 apply (zenon_L217_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.80 apply (zenon_L587_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.80 apply (zenon_L581_); trivial. % 21.54/21.80 apply (zenon_L584_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.80 apply (zenon_L289_); trivial. % 21.54/21.80 apply (zenon_L588_); trivial. % 21.54/21.80 apply (zenon_L299_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.80 apply (zenon_L147_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.80 apply (zenon_L590_); trivial. % 21.54/21.80 apply (zenon_L92_); trivial. % 21.54/21.80 apply (zenon_L134_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.80 apply (zenon_L586_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.80 exact (zenon_H4c zenon_H47). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.80 apply (zenon_L492_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.80 apply (zenon_L123_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.80 apply (zenon_L593_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.80 apply (zenon_L594_); trivial. % 21.54/21.80 apply (zenon_L262_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.80 apply (zenon_L21_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.80 apply (zenon_L590_); trivial. % 21.54/21.80 apply (zenon_L92_); trivial. % 21.54/21.80 apply (zenon_L456_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.80 exact (zenon_H1f zenon_H1e). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.80 exact (zenon_H4c zenon_H47). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.80 apply (zenon_L65_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.80 exact (zenon_H4c zenon_H47). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.80 apply (zenon_L492_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.80 apply (zenon_L171_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.80 apply (zenon_L61_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.80 apply (zenon_L123_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.80 apply (zenon_L151_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.80 apply (zenon_L289_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.80 apply (zenon_L595_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.80 apply (zenon_L552_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.54/21.80 apply (zenon_L596_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.54/21.80 apply (zenon_L484_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.54/21.80 apply (zenon_L597_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.54/21.80 apply (zenon_L599_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.54/21.80 apply (zenon_L367_); trivial. % 21.54/21.80 apply (zenon_L585_); trivial. % 21.54/21.80 exact (zenon_H120 zenon_H11f). % 21.54/21.80 exact (zenon_H120 zenon_H11f). % 21.54/21.80 apply (zenon_L154_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.80 apply (zenon_L436_); trivial. % 21.54/21.80 apply (zenon_L600_); trivial. % 21.54/21.80 apply (zenon_L606_); trivial. % 21.54/21.80 apply (zenon_L134_); trivial. % 21.54/21.80 apply (zenon_L115_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.80 apply (zenon_L586_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.80 exact (zenon_H4c zenon_H47). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.80 apply (zenon_L65_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.80 exact (zenon_H4c zenon_H47). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.80 apply (zenon_L492_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.80 apply (zenon_L297_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.80 apply (zenon_L272_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.80 apply (zenon_L607_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.80 apply (zenon_L123_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.80 apply (zenon_L609_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.80 apply (zenon_L594_); trivial. % 21.54/21.80 apply (zenon_L90_); trivial. % 21.54/21.80 apply (zenon_L134_); trivial. % 21.54/21.80 apply (zenon_L115_); trivial. % 21.54/21.80 (* end of lemma zenon_L610_ *) % 21.54/21.80 assert (zenon_L611_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H23d zenon_H1f zenon_H4c zenon_H6c zenon_H9d zenon_H33. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1e | zenon_intro zenon_H23e ]. % 21.54/21.80 exact (zenon_H1f zenon_H1e). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H47 | zenon_intro zenon_H23f ]. % 21.54/21.80 exact (zenon_H4c zenon_H47). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H67 | zenon_intro zenon_H9f ]. % 21.54/21.80 exact (zenon_H6c zenon_H67). % 21.54/21.80 apply (zenon_L245_); trivial. % 21.54/21.80 (* end of lemma zenon_L611_ *) % 21.54/21.80 assert (zenon_L612_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (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 (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((op (e0) (e1)) = (e0)) -> False). % 21.54/21.80 do 0 intro. intros zenon_H204 zenon_H23b zenon_H23d zenon_H1bb zenon_H1b4 zenon_H1cb zenon_Hb2 zenon_H1ef zenon_H173 zenon_H183 zenon_H111 zenon_H13b zenon_H4e zenon_H1f zenon_Hfa zenon_H179 zenon_H82 zenon_H1c6 zenon_H1d8 zenon_H1fb zenon_H55 zenon_H189 zenon_Hcc zenon_H131 zenon_H109 zenon_Ha0 zenon_H141 zenon_H9d zenon_H11a zenon_H18d zenon_Ha9 zenon_H1cf zenon_H77 zenon_H120 zenon_H12e zenon_H186 zenon_H1d5 zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H192 zenon_H1c3 zenon_H234 zenon_Hb6 zenon_H196 zenon_H9e zenon_H117 zenon_H48 zenon_Hf5 zenon_H13c zenon_H6d zenon_Hf0 zenon_H68 zenon_H236 zenon_H13a zenon_H33 zenon_H15d zenon_H139 zenon_H3f zenon_H23c zenon_H140 zenon_Hbc zenon_H6f zenon_H1fe zenon_H240 zenon_H2a. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 21.54/21.80 exact (zenon_H205 zenon_H2a). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 21.54/21.80 apply (zenon_L610_); trivial. % 21.54/21.80 apply (zenon_L611_); trivial. % 21.54/21.80 (* end of lemma zenon_L612_ *) % 21.54/21.80 assert (zenon_L613_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((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 (e1) (e0)) = (op (e3) (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 (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (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) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H9b zenon_H2a zenon_H1fe zenon_H6f zenon_Hbc zenon_H140 zenon_H23c zenon_H3f zenon_H139 zenon_H15d zenon_H33 zenon_H13a zenon_H236 zenon_H68 zenon_Hf0 zenon_H6d zenon_H13c zenon_Hf5 zenon_H48 zenon_H117 zenon_H196 zenon_Hb6 zenon_H234 zenon_H1c3 zenon_H192 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H1d5 zenon_H186 zenon_H12e zenon_H120 zenon_H77 zenon_H1cf zenon_Ha9 zenon_H18d zenon_H11a zenon_H141 zenon_Ha0 zenon_H109 zenon_H131 zenon_Hcc zenon_H189 zenon_H55 zenon_H1fb zenon_H1d8 zenon_H1c6 zenon_H82 zenon_H179 zenon_Hfa zenon_H4e zenon_H13b zenon_H111 zenon_H183 zenon_H173 zenon_H1ef zenon_Hb2 zenon_H1cb zenon_H1b4 zenon_H1bb zenon_H23d. % 21.54/21.80 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.54/21.80 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 21.54/21.80 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.54/21.80 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.54/21.80 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 21.54/21.80 apply (zenon_L612_); trivial. % 21.54/21.80 apply (zenon_L612_); trivial. % 21.54/21.80 (* end of lemma zenon_L613_ *) % 21.54/21.80 assert (zenon_L614_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 21.54/21.80 do 0 intro. intros zenon_H1c3 zenon_H10c zenon_H167 zenon_H77 zenon_H7f zenon_H189 zenon_H72 zenon_H156 zenon_H2a zenon_H68 zenon_H1a8 zenon_H155 zenon_H9f. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.54/21.80 apply (zenon_L98_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.54/21.80 apply (zenon_L294_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.54/21.80 apply (zenon_L440_); trivial. % 21.54/21.80 apply (zenon_L444_); trivial. % 21.54/21.80 (* end of lemma zenon_L614_ *) % 21.54/21.80 assert (zenon_L615_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H18d zenon_H9f zenon_H1a8 zenon_H68 zenon_H2a zenon_H156 zenon_H72 zenon_H189 zenon_H7f zenon_H77 zenon_H167 zenon_H10c zenon_H1c3 zenon_H234 zenon_H3f zenon_Hb9 zenon_Hb6 zenon_H120. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.54/21.80 apply (zenon_L614_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.54/21.80 apply (zenon_L484_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.54/21.80 apply (zenon_L182_); trivial. % 21.54/21.80 exact (zenon_H120 zenon_H11f). % 21.54/21.80 (* end of lemma zenon_L615_ *) % 21.54/21.80 assert (zenon_L616_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H12e zenon_H67 zenon_Hb9 zenon_H3f zenon_H234 zenon_H1c3 zenon_H10c zenon_H167 zenon_H77 zenon_H189 zenon_H72 zenon_H156 zenon_H2a zenon_H68 zenon_H1a8 zenon_H9f zenon_H18d zenon_Hbb zenon_Hb6 zenon_H120. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.80 apply (zenon_L547_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.80 apply (zenon_L615_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.80 apply (zenon_L363_); trivial. % 21.54/21.80 exact (zenon_H120 zenon_H11f). % 21.54/21.80 (* end of lemma zenon_L616_ *) % 21.54/21.80 assert (zenon_L617_ : ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_Hbb zenon_H133 zenon_H163. % 21.54/21.80 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 21.54/21.80 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e1) (e2)) = (op (e3) (e2)))). % 21.54/21.80 intro zenon_D_pnotp. % 21.54/21.80 apply zenon_H163. % 21.54/21.80 rewrite <- zenon_D_pnotp. % 21.54/21.80 exact zenon_Hbd. % 21.54/21.80 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.54/21.80 cut (((op (e3) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H251]. % 21.54/21.80 congruence. % 21.54/21.80 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e1) (e2)))). % 21.54/21.80 intro zenon_D_pnotp. % 21.54/21.80 apply zenon_H251. % 21.54/21.80 rewrite <- zenon_D_pnotp. % 21.54/21.80 exact zenon_Hbb. % 21.54/21.80 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 21.54/21.80 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 21.54/21.80 congruence. % 21.54/21.80 apply zenon_Hbe. apply refl_equal. % 21.54/21.80 apply zenon_H134. apply sym_equal. exact zenon_H133. % 21.54/21.80 apply zenon_Hbe. apply refl_equal. % 21.54/21.80 apply zenon_Hbe. apply refl_equal. % 21.54/21.80 (* end of lemma zenon_L617_ *) % 21.54/21.80 assert (zenon_L618_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (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) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (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 (e0) (e0)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H13c zenon_H25 zenon_Ha0 zenon_H164 zenon_H1cd zenon_H6d zenon_Ha9 zenon_H1bb zenon_H20f zenon_Hc0 zenon_H129 zenon_H1c6 zenon_H48 zenon_H183 zenon_Hf0 zenon_H1cb zenon_H8b zenon_H4e zenon_H153 zenon_H1cf zenon_Hfa zenon_H173 zenon_H179 zenon_H13b zenon_H192 zenon_H104 zenon_H12e zenon_H67 zenon_H3f zenon_H234 zenon_H1c3 zenon_H77 zenon_H189 zenon_H72 zenon_H156 zenon_H2a zenon_H68 zenon_H1a8 zenon_H9f zenon_H18d zenon_Hb6 zenon_H120 zenon_H54 zenon_H141 zenon_H163 zenon_Hbb zenon_Hb9 zenon_H195. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.80 apply (zenon_L116_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.80 apply (zenon_L217_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.80 apply (zenon_L54_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.80 apply (zenon_L579_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.80 apply (zenon_L292_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.80 apply (zenon_L257_); trivial. % 21.54/21.80 apply (zenon_L616_); trivial. % 21.54/21.80 apply (zenon_L77_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.80 apply (zenon_L617_); trivial. % 21.54/21.80 apply (zenon_L172_); trivial. % 21.54/21.80 (* end of lemma zenon_L618_ *) % 21.54/21.80 assert (zenon_L619_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H25 zenon_Hf0 zenon_H73 zenon_H66 zenon_H1c6 zenon_Ha0 zenon_H2a zenon_H129 zenon_Hc0 zenon_H20f zenon_H120 zenon_H1bb zenon_Ha9 zenon_H6d zenon_Hbb zenon_H1cd. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.80 apply (zenon_L171_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.80 apply (zenon_L61_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.80 apply (zenon_L22_); trivial. % 21.54/21.80 apply (zenon_L576_); trivial. % 21.54/21.80 (* end of lemma zenon_L619_ *) % 21.54/21.80 assert (zenon_L620_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H16a zenon_H2c zenon_H67 zenon_Hf0 zenon_Hef zenon_H8b zenon_H16b. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.80 apply (zenon_L180_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.80 apply (zenon_L61_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.80 exact (zenon_H8b zenon_H8a). % 21.54/21.80 exact (zenon_H16b zenon_H93). % 21.54/21.80 (* end of lemma zenon_L620_ *) % 21.54/21.80 assert (zenon_L621_ : (((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) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_Hf6 zenon_H196. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.80 exact (zenon_H7b zenon_H65). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.80 apply (zenon_L61_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.80 exact (zenon_H8b zenon_H8a). % 21.54/21.80 apply (zenon_L167_); trivial. % 21.54/21.80 (* end of lemma zenon_L621_ *) % 21.54/21.80 assert (zenon_L622_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_Hc3 zenon_Hbb zenon_H1cb. % 21.54/21.80 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.54/21.80 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 21.54/21.80 intro zenon_D_pnotp. % 21.54/21.80 apply zenon_H1cb. % 21.54/21.80 rewrite <- zenon_D_pnotp. % 21.54/21.80 exact zenon_H12a. % 21.54/21.80 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.80 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1cc]. % 21.54/21.80 congruence. % 21.54/21.80 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 21.54/21.80 intro zenon_D_pnotp. % 21.54/21.80 apply zenon_H1cc. % 21.54/21.80 rewrite <- zenon_D_pnotp. % 21.54/21.80 exact zenon_Hc3. % 21.54/21.80 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H252]. % 21.54/21.80 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.54/21.80 congruence. % 21.54/21.80 apply zenon_H12b. apply refl_equal. % 21.54/21.80 apply zenon_H252. apply sym_equal. exact zenon_Hbb. % 21.54/21.80 apply zenon_H12b. apply refl_equal. % 21.54/21.80 apply zenon_H12b. apply refl_equal. % 21.54/21.80 (* end of lemma zenon_L622_ *) % 21.54/21.80 assert (zenon_L623_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H1bb zenon_H7e zenon_H67 zenon_H120 zenon_H1b4 zenon_Hf6 zenon_Hbb zenon_H1cb. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.54/21.80 apply (zenon_L547_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.54/21.80 exact (zenon_H120 zenon_H11f). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.54/21.80 apply (zenon_L347_); trivial. % 21.54/21.80 apply (zenon_L622_); trivial. % 21.54/21.80 (* end of lemma zenon_L623_ *) % 21.54/21.80 assert (zenon_L624_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H12e zenon_H1cb zenon_H67 zenon_H1bb zenon_H1b4 zenon_Hf6 zenon_H163 zenon_H72 zenon_H77 zenon_H34 zenon_H68 zenon_H183 zenon_Hbb zenon_Hb6 zenon_H120. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.80 apply (zenon_L623_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.80 apply (zenon_L348_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.80 apply (zenon_L363_); trivial. % 21.54/21.80 exact (zenon_H120 zenon_H11f). % 21.54/21.80 (* end of lemma zenon_L624_ *) % 21.54/21.80 assert (zenon_L625_ : (((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 (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (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))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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 (e0) (e1)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_Hfa zenon_H1cf zenon_H153 zenon_H4e zenon_H18d zenon_H189 zenon_H1c3 zenon_H234 zenon_H3f zenon_Hb9 zenon_H196 zenon_H8b zenon_Hf0 zenon_H7b zenon_H16a zenon_Hb6 zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H163 zenon_Hf6 zenon_H1b4 zenon_H67 zenon_H1cb zenon_H12e zenon_H1c6 zenon_Ha0 zenon_H2a zenon_H129 zenon_Hc0 zenon_H20f zenon_H120 zenon_H1bb zenon_Ha9 zenon_H6d zenon_Hbb zenon_H1cd. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.80 apply (zenon_L574_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.80 apply (zenon_L621_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.80 apply (zenon_L624_); trivial. % 21.54/21.80 apply (zenon_L576_); trivial. % 21.54/21.80 (* end of lemma zenon_L625_ *) % 21.54/21.80 assert (zenon_L626_ : (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((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)) = (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)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H16b zenon_H2c zenon_H195 zenon_Hb9 zenon_H164 zenon_H1cb zenon_H1b4 zenon_Hf6 zenon_H163 zenon_H183 zenon_H16a zenon_H7b zenon_Hf0 zenon_H8b zenon_H196 zenon_H4e zenon_H153 zenon_H1cf zenon_Hfa zenon_H192 zenon_H12e zenon_H67 zenon_H3f zenon_H234 zenon_H1c3 zenon_H77 zenon_H189 zenon_H156 zenon_H68 zenon_H1a8 zenon_H9f zenon_H18d zenon_Hb6 zenon_H25 zenon_H13c zenon_H1c6 zenon_Ha0 zenon_H2a zenon_H129 zenon_Hc0 zenon_H20f zenon_H120 zenon_H1bb zenon_Ha9 zenon_H6d zenon_Hbb zenon_H1cd. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.80 apply (zenon_L171_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.80 apply (zenon_L620_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.80 apply (zenon_L116_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.80 apply (zenon_L625_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.80 apply (zenon_L292_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.80 apply (zenon_L80_); trivial. % 21.54/21.80 apply (zenon_L616_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.80 apply (zenon_L436_); trivial. % 21.54/21.80 apply (zenon_L172_); trivial. % 21.54/21.80 apply (zenon_L576_); trivial. % 21.54/21.80 (* end of lemma zenon_L626_ *) % 21.54/21.80 assert (zenon_L627_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 21.54/21.80 do 0 intro. intros zenon_H13f zenon_H48 zenon_H16b zenon_H8b zenon_H77 zenon_H2d zenon_H68 zenon_H16a zenon_H1bf zenon_Hb6 zenon_Hb9. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.54/21.80 apply (zenon_L217_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.54/21.80 apply (zenon_L327_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.54/21.80 exact (zenon_H1bf zenon_H105). % 21.54/21.80 apply (zenon_L182_); trivial. % 21.54/21.80 (* end of lemma zenon_L627_ *) % 21.54/21.80 assert (zenon_L628_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hdd zenon_H68 zenon_H8b zenon_Hf6 zenon_H196. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.80 exact (zenon_H7b zenon_H65). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.80 apply (zenon_L54_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.80 exact (zenon_H8b zenon_H8a). % 21.54/21.80 apply (zenon_L167_); trivial. % 21.54/21.80 (* end of lemma zenon_L628_ *) % 21.54/21.80 assert (zenon_L629_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (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) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (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 (e2) (e3)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H164 zenon_H1cd zenon_H6d zenon_Ha9 zenon_H1bb zenon_H20f zenon_Hc0 zenon_H129 zenon_Ha0 zenon_H1c6 zenon_H48 zenon_H183 zenon_H163 zenon_Hf0 zenon_H1cb zenon_H8b zenon_H4e zenon_H153 zenon_H1cf zenon_Hfa zenon_H173 zenon_H179 zenon_H13b zenon_H192 zenon_H14c zenon_H104 zenon_H12e zenon_H102 zenon_Hb9 zenon_H3f zenon_H234 zenon_H1c3 zenon_H10c zenon_H77 zenon_H189 zenon_H72 zenon_H156 zenon_H2a zenon_H68 zenon_H1a8 zenon_H9f zenon_H18d zenon_Hbb zenon_Hb6 zenon_H120. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.80 apply (zenon_L579_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.80 apply (zenon_L292_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.80 apply (zenon_L257_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.80 apply (zenon_L71_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.80 apply (zenon_L615_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.80 apply (zenon_L363_); trivial. % 21.54/21.80 exact (zenon_H120 zenon_H11f). % 21.54/21.80 (* end of lemma zenon_L629_ *) % 21.54/21.80 assert (zenon_L630_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((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 (e2) (e3)) = (e3)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (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) (e0)) = (op (e3) (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 (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.54/21.80 do 0 intro. intros zenon_H164 zenon_H1cd zenon_Hbb zenon_H6d zenon_Ha9 zenon_H1bb zenon_H120 zenon_H20f zenon_Hc0 zenon_H129 zenon_Ha0 zenon_H1c6 zenon_H12e zenon_Hb9 zenon_H48 zenon_H183 zenon_H68 zenon_H77 zenon_H163 zenon_H9f zenon_H18d zenon_Hb6 zenon_Hf0 zenon_H3f zenon_H234 zenon_H1c3 zenon_H189 zenon_H1cb zenon_H8b zenon_H4e zenon_H153 zenon_H1cf zenon_Hfa zenon_H173 zenon_H179 zenon_H13b zenon_H2a zenon_H192 zenon_H14c zenon_H104 zenon_H67 zenon_H7e. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.80 apply (zenon_L579_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.80 apply (zenon_L292_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.80 apply (zenon_L257_); trivial. % 21.54/21.80 apply (zenon_L547_); trivial. % 21.54/21.80 (* end of lemma zenon_L630_ *) % 21.54/21.80 assert (zenon_L631_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((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 (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 21.54/21.80 do 0 intro. intros zenon_H141 zenon_H1bf zenon_H16a zenon_H16b zenon_H13f zenon_H7e zenon_H67 zenon_H104 zenon_H192 zenon_H2a zenon_H13b zenon_H179 zenon_H173 zenon_Hfa zenon_H1cf zenon_H153 zenon_H4e zenon_H8b zenon_H1cb zenon_H189 zenon_H1c3 zenon_H234 zenon_H3f zenon_Hf0 zenon_Hb6 zenon_H18d zenon_H9f zenon_H163 zenon_H77 zenon_H68 zenon_H183 zenon_H48 zenon_H12e zenon_H1c6 zenon_H129 zenon_Hc0 zenon_H20f zenon_H120 zenon_H1bb zenon_Ha9 zenon_H6d zenon_Hbb zenon_H1cd zenon_H164 zenon_Ha0 zenon_Hb9. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.80 apply (zenon_L627_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.80 apply (zenon_L54_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.80 apply (zenon_L630_); trivial. % 21.54/21.80 apply (zenon_L77_); trivial. % 21.54/21.80 (* end of lemma zenon_L631_ *) % 21.54/21.80 assert (zenon_L632_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H125 zenon_H1cb zenon_Hbb zenon_Hf6 zenon_H1b4 zenon_H120 zenon_H1bb zenon_H68 zenon_H25 zenon_H7b zenon_H7e zenon_H77. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.80 apply (zenon_L623_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.80 apply (zenon_L171_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.80 exact (zenon_H7b zenon_H65). % 21.54/21.80 apply (zenon_L71_); trivial. % 21.54/21.80 (* end of lemma zenon_L632_ *) % 21.54/21.80 assert (zenon_L633_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (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) (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 (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (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) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (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 (e1) (e2)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H13c zenon_H25 zenon_Hbb zenon_Hb6 zenon_H1bf zenon_H77 zenon_H164 zenon_H1cd zenon_H6d zenon_H1bb zenon_H20f zenon_Hc0 zenon_H129 zenon_H1c6 zenon_H48 zenon_H183 zenon_H163 zenon_H18d zenon_Hf0 zenon_H3f zenon_H234 zenon_H1cb zenon_H8b zenon_H4e zenon_H1cf zenon_Hfa zenon_H173 zenon_H179 zenon_H13b zenon_H192 zenon_Ha0 zenon_H12e zenon_H67 zenon_H9f zenon_H155 zenon_H1a8 zenon_H68 zenon_H2a zenon_H156 zenon_H189 zenon_H1c3 zenon_H120 zenon_H201 zenon_Ha9 zenon_H72 zenon_Hb9 zenon_H195. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.80 apply (zenon_L116_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.80 apply (zenon_L579_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.80 apply (zenon_L292_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.80 apply (zenon_L80_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.80 apply (zenon_L547_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.80 apply (zenon_L614_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.80 apply (zenon_L363_); trivial. % 21.54/21.80 exact (zenon_H120 zenon_H11f). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.80 apply (zenon_L59_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.80 exact (zenon_H1bf zenon_H105). % 21.54/21.80 apply (zenon_L363_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.80 apply (zenon_L436_); trivial. % 21.54/21.80 apply (zenon_L172_); trivial. % 21.54/21.80 (* end of lemma zenon_L633_ *) % 21.54/21.80 assert (zenon_L634_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((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 (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (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 (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H139 zenon_Hb6 zenon_H177 zenon_H195 zenon_Hb9 zenon_H201 zenon_H1c3 zenon_H189 zenon_H156 zenon_H1a8 zenon_H12e zenon_H192 zenon_H13b zenon_H179 zenon_H173 zenon_H1cf zenon_H4e zenon_H8b zenon_H1cb zenon_H234 zenon_H3f zenon_H18d zenon_H163 zenon_H183 zenon_H48 zenon_H164 zenon_H1bf zenon_H13c zenon_H13a zenon_H1cd zenon_Hbb zenon_H6d zenon_Ha9 zenon_H1bb zenon_H120 zenon_H20f zenon_Hc0 zenon_H129 zenon_H2a zenon_Ha0 zenon_H1c6 zenon_H73 zenon_Hf0 zenon_H25 zenon_H68 zenon_Hfa zenon_H155 zenon_H77. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.80 apply (zenon_L171_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.80 apply (zenon_L61_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.80 apply (zenon_L633_); trivial. % 21.54/21.80 apply (zenon_L576_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.80 apply (zenon_L53_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.80 apply (zenon_L178_); trivial. % 21.54/21.80 apply (zenon_L115_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.80 apply (zenon_L147_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.80 apply (zenon_L619_); trivial. % 21.54/21.80 apply (zenon_L98_); trivial. % 21.54/21.80 (* end of lemma zenon_L634_ *) % 21.54/21.80 assert (zenon_L635_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.54/21.80 do 0 intro. intros zenon_H13a zenon_H47 zenon_Ha0 zenon_H2a zenon_H177 zenon_Hbb zenon_Hb6 zenon_H155. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.80 apply (zenon_L253_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.80 apply (zenon_L53_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.80 apply (zenon_L178_); trivial. % 21.54/21.80 apply (zenon_L115_); trivial. % 21.54/21.80 (* end of lemma zenon_L635_ *) % 21.54/21.80 assert (zenon_L636_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 21.54/21.80 do 0 intro. intros zenon_He4 zenon_H48 zenon_H2a zenon_H156 zenon_H4d zenon_H55 zenon_H54 zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H66 zenon_H177 zenon_H155 zenon_H9f. % 21.54/21.80 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.80 apply (zenon_L65_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.80 apply (zenon_L486_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.80 apply (zenon_L15_); trivial. % 21.54/21.80 apply (zenon_L496_); trivial. % 21.54/21.80 (* end of lemma zenon_L636_ *) % 21.54/21.80 assert (zenon_L637_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (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))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H201 zenon_H177 zenon_H54 zenon_H55 zenon_H156 zenon_H48 zenon_He4 zenon_H1bf zenon_H183 zenon_H68 zenon_H34 zenon_H129 zenon_Hb6 zenon_H9f zenon_H33 zenon_H121 zenon_H77 zenon_H13a zenon_H155 zenon_Ha0 zenon_H2a zenon_Ha9 zenon_H66 zenon_Hb9 zenon_H196. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.80 apply (zenon_L94_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.80 apply (zenon_L636_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.80 exact (zenon_H1bf zenon_H105). % 21.54/21.80 apply (zenon_L495_); trivial. % 21.54/21.80 (* end of lemma zenon_L637_ *) % 21.54/21.80 assert (zenon_L638_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 21.54/21.80 do 0 intro. intros zenon_H1c3 zenon_H1cb zenon_Hbb zenon_H1b4 zenon_H120 zenon_H67 zenon_H7e zenon_H1bb zenon_H72 zenon_H186 zenon_H189 zenon_H6d zenon_H155 zenon_H9f. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.54/21.80 apply (zenon_L623_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.54/21.80 apply (zenon_L438_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.54/21.80 apply (zenon_L439_); trivial. % 21.54/21.80 apply (zenon_L444_); trivial. % 21.54/21.80 (* end of lemma zenon_L638_ *) % 21.54/21.80 assert (zenon_L639_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H12e zenon_H6d zenon_H189 zenon_H186 zenon_H1bb zenon_H67 zenon_H1b4 zenon_H1cb zenon_H1c3 zenon_H9f zenon_H155 zenon_H163 zenon_H72 zenon_H77 zenon_H34 zenon_H68 zenon_H183 zenon_Hbb zenon_Hb6 zenon_H120. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.80 apply (zenon_L638_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.80 apply (zenon_L449_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.80 apply (zenon_L363_); trivial. % 21.54/21.80 exact (zenon_H120 zenon_H11f). % 21.54/21.80 (* end of lemma zenon_L639_ *) % 21.54/21.80 assert (zenon_L640_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (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 (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e1)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H1cf zenon_H196 zenon_Hb9 zenon_Ha9 zenon_H2a zenon_Ha0 zenon_H13a zenon_H121 zenon_H33 zenon_H1bf zenon_He4 zenon_H48 zenon_H156 zenon_H55 zenon_H54 zenon_H177 zenon_H201 zenon_Hb6 zenon_Hbb zenon_H183 zenon_H68 zenon_H34 zenon_H163 zenon_H9f zenon_H1b4 zenon_H67 zenon_H186 zenon_H12e zenon_H8b zenon_H1c3 zenon_H77 zenon_H155 zenon_H129 zenon_Hc0 zenon_H20f zenon_H120 zenon_H10c zenon_H1bb zenon_H189 zenon_H6d zenon_H1cb. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.80 apply (zenon_L637_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.80 apply (zenon_L639_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.80 exact (zenon_H8b zenon_H8a). % 21.54/21.80 apply (zenon_L572_); trivial. % 21.54/21.80 (* end of lemma zenon_L640_ *) % 21.54/21.80 assert (zenon_L641_ : (((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)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H1c6 zenon_H1cb zenon_H1bb zenon_H120 zenon_H20f zenon_Hc0 zenon_H129 zenon_H155 zenon_H1c3 zenon_H8b zenon_H12e zenon_H186 zenon_H67 zenon_H1b4 zenon_H9f zenon_H163 zenon_H34 zenon_H68 zenon_H183 zenon_Hbb zenon_Hb6 zenon_H201 zenon_H177 zenon_H54 zenon_H156 zenon_He4 zenon_H1bf zenon_H33 zenon_H121 zenon_H13a zenon_Ha0 zenon_Hb9 zenon_H196 zenon_H1cf zenon_Ha9 zenon_Hcc zenon_H1d8 zenon_H1fb zenon_H48 zenon_H2a zenon_H77 zenon_H234 zenon_H55 zenon_H189 zenon_H6d zenon_H7d zenon_H3f zenon_H1cd. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.54/21.80 apply (zenon_L53_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.54/21.80 apply (zenon_L640_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.54/21.80 apply (zenon_L289_); trivial. % 21.54/21.80 apply (zenon_L588_); trivial. % 21.54/21.80 (* end of lemma zenon_L641_ *) % 21.54/21.80 assert (zenon_L642_ : ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H66 zenon_Ha9 zenon_H155 zenon_H13a zenon_H77 zenon_H121 zenon_H33 zenon_Hb6 zenon_H129 zenon_H34 zenon_H68 zenon_H183 zenon_H1bf zenon_He4 zenon_H48 zenon_H156 zenon_H55 zenon_H54 zenon_H201 zenon_Ha0 zenon_H2a zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.80 apply (zenon_L637_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.80 apply (zenon_L53_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.80 apply (zenon_L178_); trivial. % 21.54/21.80 apply (zenon_L154_); trivial. % 21.54/21.80 (* end of lemma zenon_L642_ *) % 21.54/21.80 assert (zenon_L643_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e0) (e1)) = (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) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (~((e2) = (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((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) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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 (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H15d zenon_H13b zenon_H179 zenon_H173 zenon_Hfa zenon_H4e zenon_Hf0 zenon_H18d zenon_H82 zenon_H23c zenon_H77 zenon_Ha9 zenon_H13a zenon_H121 zenon_H33 zenon_Hb6 zenon_H129 zenon_H68 zenon_H183 zenon_H1bf zenon_He4 zenon_H156 zenon_H55 zenon_H201 zenon_Ha0 zenon_H2a zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196 zenon_H6d zenon_H6f zenon_H1cd zenon_H3f zenon_H7d zenon_H189 zenon_H234 zenon_H1fb zenon_H1d8 zenon_Hcc zenon_H1cf zenon_H163 zenon_H1b4 zenon_H186 zenon_H12e zenon_H8b zenon_H1c3 zenon_Hc0 zenon_H20f zenon_H120 zenon_H1bb zenon_H1cb zenon_H1c6 zenon_H139 zenon_H34 zenon_H48. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.80 apply (zenon_L376_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.80 apply (zenon_L65_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.80 apply (zenon_L579_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.80 apply (zenon_L53_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.80 apply (zenon_L95_); trivial. % 21.54/21.80 apply (zenon_L154_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.80 apply (zenon_L635_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.80 apply (zenon_L492_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.80 apply (zenon_L641_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.80 apply (zenon_L53_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.80 apply (zenon_L178_); trivial. % 21.54/21.80 apply (zenon_L115_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.80 apply (zenon_L21_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.80 apply (zenon_L642_); trivial. % 21.54/21.80 apply (zenon_L98_); trivial. % 21.54/21.80 apply (zenon_L456_); trivial. % 21.54/21.80 (* end of lemma zenon_L643_ *) % 21.54/21.80 assert (zenon_L644_ : (((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 (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H13e zenon_H2d zenon_H1ef zenon_H1bf zenon_H8b zenon_H191. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H14c | zenon_intro zenon_H151 ]. % 21.54/21.80 apply (zenon_L405_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H105 | zenon_intro zenon_H152 ]. % 21.54/21.80 exact (zenon_H1bf zenon_H105). % 21.54/21.80 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H8a | zenon_intro zenon_H110 ]. % 21.54/21.80 exact (zenon_H8b zenon_H8a). % 21.54/21.80 exact (zenon_H191 zenon_H110). % 21.54/21.80 (* end of lemma zenon_L644_ *) % 21.54/21.80 assert (zenon_L645_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H89 zenon_H1ef zenon_H2d zenon_H1bf zenon_H191 zenon_H13e. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.54/21.80 apply (zenon_L644_); trivial. % 21.54/21.80 apply (zenon_L644_); trivial. % 21.54/21.80 (* end of lemma zenon_L645_ *) % 21.54/21.80 assert (zenon_L646_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (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) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((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 (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 21.54/21.80 do 0 intro. intros zenon_H141 zenon_H191 zenon_H1bf zenon_H1ef zenon_H13e zenon_H7e zenon_H67 zenon_H104 zenon_H192 zenon_H2a zenon_H13b zenon_H179 zenon_H173 zenon_Hfa zenon_H1cf zenon_H153 zenon_H4e zenon_H8b zenon_H1cb zenon_H189 zenon_H1c3 zenon_H234 zenon_H3f zenon_Hf0 zenon_Hb6 zenon_H18d zenon_H9f zenon_H163 zenon_H77 zenon_H68 zenon_H183 zenon_H48 zenon_H12e zenon_H1c6 zenon_H129 zenon_Hc0 zenon_H20f zenon_H120 zenon_H1bb zenon_Ha9 zenon_H6d zenon_Hbb zenon_H1cd zenon_H164 zenon_Ha0 zenon_Hb9. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.80 apply (zenon_L644_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.80 apply (zenon_L54_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.80 apply (zenon_L630_); trivial. % 21.54/21.80 apply (zenon_L77_); trivial. % 21.54/21.80 (* end of lemma zenon_L646_ *) % 21.54/21.80 assert (zenon_L647_ : (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (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) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (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)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.80 do 0 intro. intros zenon_Ha0 zenon_H164 zenon_H1cd zenon_H6d zenon_Ha9 zenon_H1bb zenon_H20f zenon_Hc0 zenon_H129 zenon_H1c6 zenon_H12e zenon_H48 zenon_H183 zenon_H163 zenon_Hf0 zenon_H1cb zenon_H8b zenon_H4e zenon_H153 zenon_H1cf zenon_Hfa zenon_H173 zenon_H179 zenon_H13b zenon_H192 zenon_H104 zenon_H67 zenon_H13e zenon_H1ef zenon_H1bf zenon_H191 zenon_H141 zenon_Hb9 zenon_H3f zenon_H234 zenon_H1c3 zenon_H10c zenon_H167 zenon_H77 zenon_H189 zenon_H72 zenon_H156 zenon_H2a zenon_H68 zenon_H1a8 zenon_H9f zenon_H18d zenon_Hbb zenon_Hb6 zenon_H120. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.80 apply (zenon_L646_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.80 apply (zenon_L615_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.80 apply (zenon_L363_); trivial. % 21.54/21.80 exact (zenon_H120 zenon_H11f). % 21.54/21.80 (* end of lemma zenon_L647_ *) % 21.54/21.80 assert (zenon_L648_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> False). % 21.54/21.80 do 0 intro. intros zenon_H117 zenon_Hb6 zenon_H54 zenon_H10c zenon_Hf0 zenon_H191 zenon_Ha0 zenon_H115. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.54/21.80 apply (zenon_L151_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.54/21.80 apply (zenon_L74_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.54/21.80 exact (zenon_H191 zenon_H110). % 21.54/21.80 apply (zenon_L77_); trivial. % 21.54/21.80 (* end of lemma zenon_L648_ *) % 21.54/21.80 assert (zenon_L649_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((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 (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((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)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (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) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (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)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H13c zenon_H25 zenon_Ha0 zenon_H191 zenon_Hf0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H164 zenon_H1cd zenon_H6d zenon_H1bb zenon_H20f zenon_Hc0 zenon_H129 zenon_H1c6 zenon_H12e zenon_H48 zenon_H183 zenon_H163 zenon_H1cb zenon_H8b zenon_H4e zenon_H153 zenon_H1cf zenon_Hfa zenon_H173 zenon_H179 zenon_H13b zenon_H192 zenon_H104 zenon_H67 zenon_H13e zenon_H1ef zenon_H1bf zenon_H141 zenon_H3f zenon_H234 zenon_H1c3 zenon_H77 zenon_H189 zenon_H156 zenon_H2a zenon_H68 zenon_H1a8 zenon_H9f zenon_H18d zenon_Hbb zenon_H120 zenon_H89 zenon_Ha9 zenon_H72 zenon_Hb9 zenon_H195. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.80 apply (zenon_L116_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.80 apply (zenon_L645_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.80 apply (zenon_L54_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.80 apply (zenon_L579_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.80 apply (zenon_L292_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.80 apply (zenon_L257_); trivial. % 21.54/21.80 apply (zenon_L647_); trivial. % 21.54/21.80 apply (zenon_L648_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.80 apply (zenon_L436_); trivial. % 21.54/21.80 apply (zenon_L172_); trivial. % 21.54/21.80 (* end of lemma zenon_L649_ *) % 21.54/21.80 assert (zenon_L650_ : (((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) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((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 (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (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) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (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)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.80 do 0 intro. intros zenon_H13a zenon_H164 zenon_H1cd zenon_Hbb zenon_H6d zenon_Ha9 zenon_H1bb zenon_H120 zenon_H20f zenon_Hc0 zenon_H129 zenon_H1c6 zenon_H12e zenon_H48 zenon_H183 zenon_H68 zenon_H77 zenon_H163 zenon_H18d zenon_Hf0 zenon_H3f zenon_H234 zenon_H1c3 zenon_H189 zenon_H1cb zenon_H8b zenon_H4e zenon_H1cf zenon_Hfa zenon_H173 zenon_H179 zenon_H13b zenon_H192 zenon_H104 zenon_H67 zenon_H7e zenon_H13e zenon_H1ef zenon_H1bf zenon_H191 zenon_H141 zenon_Ha0 zenon_H2a zenon_Hb6 zenon_H153 zenon_Hb9 zenon_H196. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.80 apply (zenon_L646_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.80 apply (zenon_L53_); trivial. % 21.54/21.80 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.80 apply (zenon_L95_); trivial. % 21.54/21.81 apply (zenon_L154_); trivial. % 21.54/21.81 (* end of lemma zenon_L650_ *) % 21.54/21.81 assert (zenon_L651_ : (((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)) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.54/21.81 do 0 intro. intros zenon_H125 zenon_H1d5 zenon_H66 zenon_H68 zenon_H25 zenon_H7b zenon_H7e zenon_H77. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.81 apply (zenon_L252_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.81 apply (zenon_L171_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.81 exact (zenon_H7b zenon_H65). % 21.54/21.81 apply (zenon_L71_); trivial. % 21.54/21.81 (* end of lemma zenon_L651_ *) % 21.54/21.81 assert (zenon_L652_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (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) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (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 (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 (e1) (e2)) = (op (e3) (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) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (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) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (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) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 21.54/21.81 do 0 intro. intros zenon_H92 zenon_H117 zenon_H13e zenon_H1ef zenon_H89 zenon_H1d5 zenon_H19d zenon_H2a zenon_H15d zenon_H201 zenon_H139 zenon_H16a zenon_H2c zenon_H1b4 zenon_H7b zenon_H13f zenon_H1bf zenon_Hf5 zenon_H125 zenon_H73 zenon_H141 zenon_H13b zenon_H12e zenon_H183 zenon_H163 zenon_Hfa zenon_H173 zenon_H179 zenon_H192 zenon_H104 zenon_H156 zenon_H1a8 zenon_H164 zenon_H68 zenon_H195 zenon_H13c zenon_Hf0 zenon_H1cf zenon_H1c3 zenon_H1cb zenon_H6d zenon_H189 zenon_H120 zenon_H20f zenon_Hc0 zenon_H129 zenon_H1bb zenon_H234 zenon_H3f zenon_H18d zenon_H8b zenon_H4e zenon_H77 zenon_Ha9 zenon_H1cd zenon_H1c6 zenon_H6f zenon_H82 zenon_H48 zenon_Hb6 zenon_Ha0 zenon_H177 zenon_Hbb zenon_H196 zenon_Hb9 zenon_H13a zenon_H23c zenon_H1d8 zenon_H1fb zenon_H7d zenon_Hcc zenon_H121 zenon_H33 zenon_H55 zenon_He4 zenon_H186 zenon_H1fe. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.81 apply (zenon_L161_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.81 apply (zenon_L376_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.81 apply (zenon_L65_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.81 apply (zenon_L376_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.81 apply (zenon_L25_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.81 apply (zenon_L574_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.81 apply (zenon_L61_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.81 apply (zenon_L618_); trivial. % 21.54/21.81 apply (zenon_L576_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.81 apply (zenon_L53_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.81 apply (zenon_L178_); trivial. % 21.54/21.81 apply (zenon_L154_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.81 apply (zenon_L147_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.81 apply (zenon_L619_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.81 apply (zenon_L626_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.81 apply (zenon_L53_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.81 apply (zenon_L95_); trivial. % 21.54/21.81 apply (zenon_L154_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.81 apply (zenon_L574_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.81 exact (zenon_H7b zenon_H65). % 21.54/21.81 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.81 apply (zenon_L574_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.81 apply (zenon_L621_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.81 apply (zenon_L116_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.81 apply (zenon_L627_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.81 apply (zenon_L628_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.81 apply (zenon_L629_); trivial. % 21.54/21.81 apply (zenon_L77_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.81 apply (zenon_L617_); trivial. % 21.54/21.81 apply (zenon_L172_); trivial. % 21.54/21.81 apply (zenon_L63_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.81 apply (zenon_L53_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.81 apply (zenon_L178_); trivial. % 21.54/21.81 apply (zenon_L92_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.81 apply (zenon_L631_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.81 apply (zenon_L53_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.81 apply (zenon_L95_); trivial. % 21.54/21.81 apply (zenon_L154_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.81 apply (zenon_L21_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.81 apply (zenon_L94_); trivial. % 21.54/21.81 apply (zenon_L632_); trivial. % 21.54/21.81 apply (zenon_L634_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.81 apply (zenon_L627_); trivial. % 21.54/21.81 apply (zenon_L643_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.54/21.81 apply (zenon_L161_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.54/21.81 apply (zenon_L376_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.54/21.81 apply (zenon_L65_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.54/21.81 apply (zenon_L376_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.54/21.81 apply (zenon_L25_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.81 apply (zenon_L574_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.81 apply (zenon_L61_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.81 apply (zenon_L649_); trivial. % 21.54/21.81 apply (zenon_L576_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.81 apply (zenon_L53_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.81 apply (zenon_L178_); trivial. % 21.54/21.81 apply (zenon_L154_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.81 apply (zenon_L147_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.81 apply (zenon_L619_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.81 apply (zenon_L171_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.81 apply (zenon_L61_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.81 apply (zenon_L116_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.81 apply (zenon_L217_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.81 apply (zenon_L54_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.81 apply (zenon_L624_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.81 apply (zenon_L292_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.81 apply (zenon_L257_); trivial. % 21.54/21.81 apply (zenon_L647_); trivial. % 21.54/21.81 apply (zenon_L77_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.81 apply (zenon_L617_); trivial. % 21.54/21.81 apply (zenon_L172_); trivial. % 21.54/21.81 apply (zenon_L576_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.81 apply (zenon_L53_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.81 apply (zenon_L95_); trivial. % 21.54/21.81 apply (zenon_L154_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.54/21.81 apply (zenon_L574_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.54/21.81 exact (zenon_H7b zenon_H65). % 21.54/21.81 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.81 apply (zenon_L574_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.81 apply (zenon_L621_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.81 apply (zenon_L116_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.54/21.81 apply (zenon_L645_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.54/21.81 apply (zenon_L628_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.54/21.81 apply (zenon_L629_); trivial. % 21.54/21.81 apply (zenon_L648_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.81 apply (zenon_L436_); trivial. % 21.54/21.81 apply (zenon_L172_); trivial. % 21.54/21.81 apply (zenon_L63_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.81 apply (zenon_L53_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.81 apply (zenon_L178_); trivial. % 21.54/21.81 apply (zenon_L92_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.54/21.81 apply (zenon_L650_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.54/21.81 apply (zenon_L21_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.54/21.81 apply (zenon_L651_); trivial. % 21.54/21.81 apply (zenon_L632_); trivial. % 21.54/21.81 apply (zenon_L634_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.54/21.81 apply (zenon_L645_); trivial. % 21.54/21.81 apply (zenon_L643_); trivial. % 21.54/21.81 (* end of lemma zenon_L652_ *) % 21.54/21.81 assert (zenon_L653_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((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) (e2)) = (e0))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((op (e2) (e1)) = (e2)) -> False). % 21.54/21.81 do 0 intro. intros zenon_H91 zenon_H13e zenon_Hbb zenon_H104 zenon_H13d zenon_H89 zenon_H6d. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.54/21.81 exact (zenon_H1ba zenon_H6d). % 21.54/21.81 apply (zenon_L197_); trivial. % 21.54/21.81 (* end of lemma zenon_L653_ *) % 21.54/21.81 assert (zenon_L654_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (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) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> False). % 21.54/21.81 do 0 intro. intros zenon_H230 zenon_H3f zenon_H2a zenon_H1d8 zenon_H1fb zenon_H48 zenon_H6d zenon_H77 zenon_H234 zenon_H55 zenon_H189 zenon_H23d zenon_H1bb zenon_H1b4 zenon_H1cb zenon_Hb2 zenon_H1ef zenon_H173 zenon_H183 zenon_H111 zenon_H13b zenon_H4e zenon_Hfa zenon_H179 zenon_H82 zenon_H1c6 zenon_Hcc zenon_H131 zenon_H109 zenon_Ha0 zenon_H141 zenon_H11a zenon_H18d zenon_Ha9 zenon_H1cf zenon_H12e zenon_H186 zenon_H1d5 zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H192 zenon_H1c3 zenon_Hb6 zenon_H196 zenon_H117 zenon_Hf5 zenon_H13c zenon_Hf0 zenon_H68 zenon_H236 zenon_H13a zenon_H33 zenon_H15d zenon_H139 zenon_H23c zenon_H140 zenon_Hbc zenon_H6f zenon_H1fe zenon_H13e zenon_H19d zenon_H201 zenon_H16a zenon_H2c zenon_H13f zenon_H125 zenon_H73 zenon_H163 zenon_H104 zenon_H156 zenon_H1a8 zenon_H164 zenon_H195 zenon_H20f zenon_H129 zenon_H177 zenon_H121 zenon_He4. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.54/21.81 apply (zenon_L2_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.54/21.81 apply (zenon_L482_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.54/21.81 apply (zenon_L315_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.54/21.81 apply (zenon_L317_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.54/21.81 apply (zenon_L318_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.54/21.81 apply (zenon_L11_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.54/21.81 apply (zenon_L319_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.54/21.81 apply (zenon_L485_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.54/21.81 apply (zenon_L435_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.54/21.81 apply (zenon_L522_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.54/21.81 apply (zenon_L37_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.54/21.81 apply (zenon_L458_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.54/21.81 apply (zenon_L613_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.54/21.81 apply (zenon_L531_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.54/21.81 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.54/21.81 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.54/21.81 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.54/21.81 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.54/21.81 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.54/21.81 exact (zenon_H1ba zenon_H6d). % 21.54/21.81 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.54/21.81 apply (zenon_L652_); trivial. % 21.54/21.81 apply (zenon_L652_); trivial. % 21.54/21.81 apply (zenon_L653_); trivial. % 21.54/21.81 apply (zenon_L51_); trivial. % 21.54/21.81 apply (zenon_L588_); trivial. % 21.54/21.81 (* end of lemma zenon_L654_ *) % 21.54/21.81 assert (zenon_L655_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (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)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (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 (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> ((~((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) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (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)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.81 do 0 intro. intros zenon_He4 zenon_H177 zenon_H20f zenon_H195 zenon_H164 zenon_H1a8 zenon_H104 zenon_H73 zenon_H125 zenon_H13f zenon_H2c zenon_H16a zenon_H19d zenon_H13e zenon_H1fe zenon_H6f zenon_Hbc zenon_H140 zenon_H23c zenon_H139 zenon_H15d zenon_H13a zenon_H236 zenon_Hf0 zenon_H13c zenon_Hf5 zenon_H117 zenon_H196 zenon_H1c3 zenon_H192 zenon_H1b7 zenon_H7d zenon_H24e zenon_H1d5 zenon_H186 zenon_H11a zenon_H141 zenon_Ha0 zenon_H109 zenon_H131 zenon_Hcc zenon_H1c6 zenon_H82 zenon_H179 zenon_Hfa zenon_H4e zenon_H13b zenon_H111 zenon_H173 zenon_H1ef zenon_Hb2 zenon_H1cb zenon_H1b4 zenon_H1bb zenon_H23d zenon_H189 zenon_H55 zenon_H234 zenon_H1fb zenon_H1d8 zenon_H2a zenon_H230 zenon_H201 zenon_H1cd zenon_H8b zenon_H12e zenon_H48 zenon_H136 zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H163 zenon_H18d zenon_Hbb zenon_H120 zenon_H1cf zenon_H156 zenon_H3f zenon_H1bf zenon_H121 zenon_H33 zenon_H9f zenon_Ha9 zenon_Hb6 zenon_Hb9 zenon_H129. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.54/21.81 apply (zenon_L147_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.54/21.81 apply (zenon_L569_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.54/21.81 apply (zenon_L654_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.81 apply (zenon_L94_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.81 apply (zenon_L578_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.81 exact (zenon_H8b zenon_H8a). % 21.54/21.81 apply (zenon_L240_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.81 apply (zenon_L486_); trivial. % 21.54/21.81 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.81 exact (zenon_H1bf zenon_H105). % 21.54/21.81 apply (zenon_L493_); trivial. % 21.54/21.81 (* end of lemma zenon_L655_ *) % 21.54/21.81 assert (zenon_L656_ : ((op (e0) (e2)) = (e1)) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (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)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (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 (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> ((~((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) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (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)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.82 do 0 intro. intros zenon_H153 zenon_Hc0 zenon_H7b zenon_He4 zenon_H177 zenon_H20f zenon_H195 zenon_H164 zenon_H1a8 zenon_H104 zenon_H73 zenon_H125 zenon_H13f zenon_H2c zenon_H16a zenon_H19d zenon_H13e zenon_H1fe zenon_H6f zenon_Hbc zenon_H140 zenon_H23c zenon_H139 zenon_H15d zenon_H13a zenon_H236 zenon_Hf0 zenon_H13c zenon_Hf5 zenon_H117 zenon_H196 zenon_H1c3 zenon_H192 zenon_H1b7 zenon_H7d zenon_H24e zenon_H1d5 zenon_H186 zenon_H11a zenon_H141 zenon_Ha0 zenon_H109 zenon_H131 zenon_Hcc zenon_H1c6 zenon_H82 zenon_H179 zenon_Hfa zenon_H4e zenon_H13b zenon_H111 zenon_H173 zenon_H1ef zenon_Hb2 zenon_H1cb zenon_H1b4 zenon_H1bb zenon_H23d zenon_H189 zenon_H55 zenon_H234 zenon_H1fb zenon_H1d8 zenon_H2a zenon_H230 zenon_H201 zenon_H1cd zenon_H8b zenon_H12e zenon_H48 zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H163 zenon_H18d zenon_Hbb zenon_H120 zenon_H1cf zenon_H156 zenon_H3f zenon_H1bf zenon_H121 zenon_H33 zenon_H9f zenon_Ha9 zenon_Hb6 zenon_Hb9 zenon_H129. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.54/21.82 apply (zenon_L297_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.54/21.82 apply (zenon_L272_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.54/21.82 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.54/21.82 apply (zenon_L147_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.54/21.82 apply (zenon_L569_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.54/21.82 apply (zenon_L574_); trivial. % 21.54/21.82 apply (zenon_L575_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.54/21.82 apply (zenon_L568_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.54/21.82 apply (zenon_L62_); trivial. % 21.54/21.82 apply (zenon_L580_); trivial. % 21.54/21.82 apply (zenon_L655_); trivial. % 21.54/21.82 (* end of lemma zenon_L656_ *) % 21.54/21.82 assert (zenon_L657_ : (~((op (e2) (e3)) = (op (e3) (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)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (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)) = (op (e3) (e3)))) -> (~((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)) = (e2))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (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)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.54/21.82 do 0 intro. intros zenon_H129 zenon_Ha9 zenon_H33 zenon_H121 zenon_H1bf zenon_H1cf zenon_H163 zenon_H183 zenon_H48 zenon_H8b zenon_H1cd zenon_H201 zenon_H230 zenon_H1d8 zenon_H1fb zenon_H55 zenon_H23d zenon_H1bb zenon_H1b4 zenon_H1cb zenon_Hb2 zenon_H1ef zenon_H173 zenon_H111 zenon_H13b zenon_H4e zenon_Hfa zenon_H179 zenon_H82 zenon_H1c6 zenon_Hcc zenon_H131 zenon_H109 zenon_Ha0 zenon_H141 zenon_H11a zenon_H186 zenon_H1d5 zenon_H24e zenon_H7d zenon_H1b7 zenon_H196 zenon_H117 zenon_Hf5 zenon_H13c zenon_Hf0 zenon_H236 zenon_H13a zenon_H15d zenon_H139 zenon_H23c zenon_H140 zenon_Hbc zenon_H6f zenon_H1fe zenon_H13e zenon_H19d zenon_H16a zenon_H2c zenon_H13f zenon_H125 zenon_H73 zenon_H164 zenon_H195 zenon_H20f zenon_H177 zenon_He4 zenon_H7b zenon_Hc0 zenon_H153 zenon_H192 zenon_H14c zenon_H104 zenon_H12e zenon_H67 zenon_Hb9 zenon_H3f zenon_H234 zenon_H1c3 zenon_H10c zenon_H77 zenon_H189 zenon_H72 zenon_H156 zenon_H2a zenon_H68 zenon_H1a8 zenon_H9f zenon_H18d zenon_Hbb zenon_Hb6 zenon_H120. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.82 apply (zenon_L656_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.82 apply (zenon_L292_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.82 apply (zenon_L257_); trivial. % 21.54/21.82 apply (zenon_L616_); trivial. % 21.54/21.82 (* end of lemma zenon_L657_ *) % 21.54/21.82 assert (zenon_L658_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.54/21.82 do 0 intro. intros zenon_H212 zenon_H25 zenon_H179 zenon_H7f zenon_H7d zenon_H160 zenon_Hbb zenon_Hbc. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H34 | zenon_intro zenon_H213 ]. % 21.54/21.82 apply (zenon_L297_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H7e | zenon_intro zenon_H214 ]. % 21.54/21.82 apply (zenon_L31_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H102 | zenon_intro zenon_H9d ]. % 21.54/21.82 apply (zenon_L104_); trivial. % 21.54/21.82 apply (zenon_L48_); trivial. % 21.54/21.82 (* end of lemma zenon_L658_ *) % 21.54/21.82 assert (zenon_L659_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))) -> ((op (e3) (e3)) = (e1)) -> False). % 21.54/21.82 do 0 intro. intros zenon_H253 zenon_H11f. % 21.54/21.82 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 21.54/21.82 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 21.54/21.82 congruence. % 21.54/21.82 exact (zenon_H120 zenon_H11f). % 21.54/21.82 exact (zenon_H120 zenon_H11f). % 21.54/21.82 (* end of lemma zenon_L659_ *) % 21.54/21.82 assert (zenon_L660_ : (~((op (e3) (op (e3) (e3))) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> False). % 21.54/21.82 do 0 intro. intros zenon_H254 zenon_H11f. % 21.54/21.82 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 21.54/21.82 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.54/21.82 congruence. % 21.54/21.82 apply zenon_Ha2. apply refl_equal. % 21.54/21.82 exact (zenon_H120 zenon_H11f). % 21.54/21.82 (* end of lemma zenon_L660_ *) % 21.54/21.82 assert (zenon_L661_ : ((op (e3) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (op (e3) (op (e3) (e3))))) -> False). % 21.54/21.82 do 0 intro. intros zenon_He0 zenon_H11f zenon_H255. % 21.54/21.82 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H244 | zenon_intro zenon_H245 ]. % 21.54/21.82 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((e0) = (op (e3) (op (e3) (e3))))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_H255. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_H244. % 21.54/21.82 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 21.54/21.82 cut (((op (e3) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H256]. % 21.54/21.82 congruence. % 21.54/21.82 cut (((op (e3) (e1)) = (e0)) = ((op (e3) (op (e3) (e3))) = (e0))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_H256. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_He0. % 21.54/21.82 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.54/21.82 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 21.54/21.82 congruence. % 21.54/21.82 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H244 | zenon_intro zenon_H245 ]. % 21.54/21.82 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e1)) = (op (e3) (op (e3) (e3))))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_H257. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_H244. % 21.54/21.82 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 21.54/21.82 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H254]. % 21.54/21.82 congruence. % 21.54/21.82 apply (zenon_L660_); trivial. % 21.54/21.82 apply zenon_H245. apply refl_equal. % 21.54/21.82 apply zenon_H245. apply refl_equal. % 21.54/21.82 apply zenon_H46. apply refl_equal. % 21.54/21.82 apply zenon_H245. apply refl_equal. % 21.54/21.82 apply zenon_H245. apply refl_equal. % 21.54/21.82 (* end of lemma zenon_L661_ *) % 21.54/21.82 assert (zenon_L662_ : ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> False). % 21.54/21.82 do 0 intro. intros zenon_Hef zenon_He0 zenon_H11f. % 21.54/21.82 apply (zenon_notand_s _ _ ax21); [ zenon_intro zenon_H249 | zenon_intro zenon_H258 ]. % 21.54/21.82 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H24b ]. % 21.54/21.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e2) = (op (op (e3) (e3)) (op (e3) (e3))))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_H249. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_H24a. % 21.54/21.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 21.54/21.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H24c]. % 21.54/21.82 congruence. % 21.54/21.82 cut (((op (e1) (e1)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_H24c. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_Hef. % 21.54/21.82 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.54/21.82 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 21.54/21.82 congruence. % 21.54/21.82 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H24b ]. % 21.54/21.82 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))))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_H259. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_H24a. % 21.54/21.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 21.54/21.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 21.54/21.82 congruence. % 21.54/21.82 apply (zenon_L659_); trivial. % 21.54/21.82 apply zenon_H24b. apply refl_equal. % 21.54/21.82 apply zenon_H24b. apply refl_equal. % 21.54/21.82 apply zenon_H6a. apply refl_equal. % 21.54/21.82 apply zenon_H24b. apply refl_equal. % 21.54/21.82 apply zenon_H24b. apply refl_equal. % 21.54/21.82 apply (zenon_notand_s _ _ zenon_H258); [ zenon_intro zenon_H25a | zenon_intro zenon_H255 ]. % 21.54/21.82 apply zenon_H25a. apply sym_equal. exact zenon_H11f. % 21.54/21.82 apply (zenon_L661_); trivial. % 21.54/21.82 (* end of lemma zenon_L662_ *) % 21.54/21.82 assert (zenon_L663_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 21.54/21.82 do 0 intro. intros zenon_Hf5 zenon_H38 zenon_H136. % 21.54/21.82 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_Hf5. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_H38. % 21.54/21.82 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 21.54/21.82 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 21.54/21.82 congruence. % 21.54/21.82 apply zenon_Hf9. apply refl_equal. % 21.54/21.82 apply zenon_H215. apply sym_equal. exact zenon_H136. % 21.54/21.82 (* end of lemma zenon_L663_ *) % 21.54/21.82 assert (zenon_L664_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.82 do 0 intro. intros zenon_H25b zenon_H38 zenon_Hf5 zenon_H186 zenon_H4d zenon_H20f zenon_H17c zenon_Hb9 zenon_H195. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H136 | zenon_intro zenon_H25c ]. % 21.54/21.82 apply (zenon_L663_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H5c | zenon_intro zenon_H25d ]. % 21.54/21.82 apply (zenon_L138_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Ha5 ]. % 21.54/21.82 apply (zenon_L570_); trivial. % 21.54/21.82 apply (zenon_L172_); trivial. % 21.54/21.82 (* end of lemma zenon_L664_ *) % 21.54/21.82 assert (zenon_L665_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.82 do 0 intro. intros zenon_H25e zenon_H136 zenon_Hf5 zenon_H9f zenon_H1b4 zenon_H17c zenon_Hb9 zenon_H196. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H38 | zenon_intro zenon_H25f ]. % 21.54/21.82 apply (zenon_L663_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H155 | zenon_intro zenon_H260 ]. % 21.54/21.82 apply (zenon_L444_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H9e ]. % 21.54/21.82 apply (zenon_L347_); trivial. % 21.54/21.82 apply (zenon_L154_); trivial. % 21.54/21.82 (* end of lemma zenon_L665_ *) % 21.54/21.82 assert (zenon_L666_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 21.54/21.82 do 0 intro. intros zenon_H19a zenon_H195 zenon_H20f zenon_H4d zenon_H186 zenon_H25b zenon_H196 zenon_H1b4 zenon_H9f zenon_Hf5 zenon_H25e zenon_Hb9 zenon_Ha0 zenon_H68 zenon_H17c. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.54/21.82 apply (zenon_L664_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.54/21.82 apply (zenon_L665_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.54/21.82 apply (zenon_L77_); trivial. % 21.54/21.82 apply (zenon_L295_); trivial. % 21.54/21.82 (* end of lemma zenon_L666_ *) % 21.54/21.82 assert (zenon_L667_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 21.54/21.82 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_Hdb zenon_H156 zenon_H4d zenon_H129 zenon_H17c zenon_H8b zenon_H77 zenon_H7b zenon_H16a zenon_H7d zenon_H7e. % 21.54/21.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.54/21.82 apply (zenon_L55_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.54/21.82 apply (zenon_L486_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.54/21.82 apply (zenon_L127_); trivial. % 21.54/21.82 apply (zenon_L31_); trivial. % 21.54/21.82 (* end of lemma zenon_L667_ *) % 21.54/21.82 assert (zenon_L668_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.82 do 0 intro. intros zenon_H13a zenon_H68 zenon_Ha0 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H25b zenon_H186 zenon_H20f zenon_H195 zenon_H19a zenon_H7e zenon_H7d zenon_H16a zenon_H7b zenon_H77 zenon_H8b zenon_H17c zenon_H129 zenon_H4d zenon_H156 zenon_Hb6 zenon_He4 zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.54/21.82 apply (zenon_L666_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.54/21.82 apply (zenon_L667_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.54/21.82 apply (zenon_L178_); trivial. % 21.54/21.82 apply (zenon_L154_); trivial. % 21.54/21.82 (* end of lemma zenon_L668_ *) % 21.54/21.82 assert (zenon_L669_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.54/21.82 do 0 intro. intros zenon_H1bb zenon_H67 zenon_He0 zenon_Hef zenon_H196 zenon_Hb9 zenon_Hbb zenon_H177 zenon_He4 zenon_Hb6 zenon_H156 zenon_H4d zenon_H8b zenon_H77 zenon_H7b zenon_H16a zenon_H7d zenon_H7e zenon_H19a zenon_H195 zenon_H20f zenon_H186 zenon_H25b zenon_H1b4 zenon_Hf5 zenon_H25e zenon_Ha0 zenon_H68 zenon_H13a zenon_Hc0 zenon_H129. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.54/21.82 apply (zenon_L547_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.54/21.82 apply (zenon_L662_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.54/21.82 apply (zenon_L668_); trivial. % 21.54/21.82 apply (zenon_L190_); trivial. % 21.54/21.82 (* end of lemma zenon_L669_ *) % 21.54/21.82 assert (zenon_L670_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.54/21.82 do 0 intro. intros zenon_H164 zenon_H48 zenon_H129 zenon_Hc0 zenon_H13a zenon_H68 zenon_Ha0 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H25b zenon_H186 zenon_H20f zenon_H195 zenon_H19a zenon_H7d zenon_H16a zenon_H7b zenon_H77 zenon_H8b zenon_H4d zenon_H156 zenon_Hb6 zenon_He4 zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196 zenon_Hef zenon_H1bb zenon_H14c zenon_H104 zenon_H67 zenon_H7e. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.82 apply (zenon_L456_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.82 apply (zenon_L669_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.82 apply (zenon_L257_); trivial. % 21.54/21.82 apply (zenon_L547_); trivial. % 21.54/21.82 (* end of lemma zenon_L670_ *) % 21.54/21.82 assert (zenon_L671_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.82 do 0 intro. intros zenon_H25b zenon_H38 zenon_Hf5 zenon_H20f zenon_H11f zenon_H93 zenon_Hb9 zenon_H195. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H136 | zenon_intro zenon_H25c ]. % 21.54/21.82 apply (zenon_L663_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H5c | zenon_intro zenon_H25d ]. % 21.54/21.82 apply (zenon_L412_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Ha5 ]. % 21.54/21.82 apply (zenon_L228_); trivial. % 21.54/21.82 apply (zenon_L172_); trivial. % 21.54/21.82 (* end of lemma zenon_L671_ *) % 21.54/21.82 assert (zenon_L672_ : ((op (e0) (e3)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (op (e0) (op (e0) (e0))))) -> False). % 21.54/21.82 do 0 intro. intros zenon_Hf6 zenon_H9f zenon_H261. % 21.54/21.82 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H21a | zenon_intro zenon_H21b ]. % 21.54/21.82 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((e2) = (op (e0) (op (e0) (e0))))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_H261. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_H21a. % 21.54/21.82 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 21.54/21.82 cut (((op (e0) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H262]. % 21.54/21.82 congruence. % 21.54/21.82 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (op (e0) (e0))) = (e2))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_H262. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_Hf6. % 21.54/21.82 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.54/21.82 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 21.54/21.82 congruence. % 21.54/21.82 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H21a | zenon_intro zenon_H21b ]. % 21.54/21.82 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e3)) = (op (e0) (op (e0) (e0))))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_H21d. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_H21a. % 21.54/21.82 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 21.54/21.82 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 21.54/21.82 congruence. % 21.54/21.82 apply (zenon_L442_); trivial. % 21.54/21.82 apply zenon_H21b. apply refl_equal. % 21.54/21.82 apply zenon_H21b. apply refl_equal. % 21.54/21.82 apply zenon_H6a. apply refl_equal. % 21.54/21.82 apply zenon_H21b. apply refl_equal. % 21.54/21.82 apply zenon_H21b. apply refl_equal. % 21.54/21.82 (* end of lemma zenon_L672_ *) % 21.54/21.82 assert (zenon_L673_ : ((op (e3) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 21.54/21.82 do 0 intro. intros zenon_H11f zenon_Hf6 zenon_H9f. % 21.54/21.82 apply (zenon_notand_s _ _ ax16); [ zenon_intro zenon_H229 | zenon_intro zenon_H263 ]. % 21.54/21.82 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H220 | zenon_intro zenon_H221 ]. % 21.54/21.82 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (e0) (e0))))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_H229. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_H220. % 21.54/21.82 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 21.54/21.82 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H22a]. % 21.54/21.82 congruence. % 21.54/21.82 cut (((op (e3) (e3)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_H22a. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_H11f. % 21.54/21.82 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.54/21.82 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 21.54/21.82 congruence. % 21.54/21.82 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H220 | zenon_intro zenon_H221 ]. % 21.54/21.82 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))))). % 21.54/21.82 intro zenon_D_pnotp. % 21.54/21.82 apply zenon_H223. % 21.54/21.82 rewrite <- zenon_D_pnotp. % 21.54/21.82 exact zenon_H220. % 21.54/21.82 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 21.54/21.82 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H217]. % 21.54/21.82 congruence. % 21.54/21.82 apply (zenon_L441_); trivial. % 21.54/21.82 apply zenon_H221. apply refl_equal. % 21.54/21.82 apply zenon_H221. apply refl_equal. % 21.54/21.82 apply zenon_H4a. apply refl_equal. % 21.54/21.82 apply zenon_H221. apply refl_equal. % 21.54/21.82 apply zenon_H221. apply refl_equal. % 21.54/21.82 apply (zenon_notand_s _ _ zenon_H263); [ zenon_intro zenon_H1d3 | zenon_intro zenon_H261 ]. % 21.54/21.82 apply zenon_H1d3. apply sym_equal. exact zenon_H9f. % 21.54/21.82 apply (zenon_L672_); trivial. % 21.54/21.82 (* end of lemma zenon_L673_ *) % 21.54/21.82 assert (zenon_L674_ : (((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)) = (e2)) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.82 do 0 intro. intros zenon_H25e zenon_H195 zenon_H93 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H9f zenon_H11f zenon_Hb9 zenon_H196. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H38 | zenon_intro zenon_H25f ]. % 21.54/21.82 apply (zenon_L671_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H155 | zenon_intro zenon_H260 ]. % 21.54/21.82 apply (zenon_L187_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H9e ]. % 21.54/21.82 apply (zenon_L673_); trivial. % 21.54/21.82 apply (zenon_L154_); trivial. % 21.54/21.82 (* end of lemma zenon_L674_ *) % 21.54/21.82 assert (zenon_L675_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((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 (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((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) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.82 do 0 intro. intros zenon_Hf0 zenon_H1cf zenon_H1d5 zenon_H12e zenon_H67 zenon_H104 zenon_H14c zenon_H1bb zenon_Hef zenon_H177 zenon_He4 zenon_Hb6 zenon_H156 zenon_H4d zenon_H8b zenon_H7b zenon_H16a zenon_H19a zenon_H186 zenon_Ha0 zenon_H68 zenon_H13a zenon_Hc0 zenon_H129 zenon_H48 zenon_H164 zenon_Hbc zenon_Hbb zenon_H7d zenon_H179 zenon_H25 zenon_H212 zenon_H77 zenon_H25e zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H9f zenon_Hb9 zenon_H196. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.54/21.82 exact (zenon_H7b zenon_H65). % 21.54/21.82 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.54/21.82 apply (zenon_L61_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.54/21.82 exact (zenon_H8b zenon_H8a). % 21.54/21.82 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.82 apply (zenon_L252_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.82 apply (zenon_L100_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.82 exact (zenon_H8b zenon_H8a). % 21.54/21.82 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.82 apply (zenon_L670_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.82 apply (zenon_L658_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.82 apply (zenon_L367_); trivial. % 21.54/21.82 apply (zenon_L674_); trivial. % 21.54/21.82 (* end of lemma zenon_L675_ *) % 21.54/21.82 assert (zenon_L676_ : (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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 (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (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)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e0) (e0)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (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) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 21.54/21.82 do 0 intro. intros zenon_H120 zenon_H192 zenon_H2a zenon_H3f zenon_H11a zenon_Ha9 zenon_H33 zenon_H121 zenon_H163 zenon_H183 zenon_H1cd zenon_H201 zenon_H230 zenon_H1d8 zenon_H1fb zenon_H55 zenon_H23d zenon_H1cb zenon_Hb2 zenon_H1ef zenon_H173 zenon_H111 zenon_H13b zenon_H4e zenon_Hfa zenon_H82 zenon_H1c6 zenon_Hcc zenon_H131 zenon_H109 zenon_H141 zenon_H24e zenon_H1b7 zenon_H117 zenon_H13c zenon_H236 zenon_H15d zenon_H139 zenon_H23c zenon_H140 zenon_H6f zenon_H1fe zenon_H13e zenon_H19d zenon_H2c zenon_H13f zenon_H125 zenon_H73 zenon_H234 zenon_H1c3 zenon_H10c zenon_H189 zenon_H1a8 zenon_H18d zenon_H196 zenon_Hb9 zenon_H9f zenon_H1b4 zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H25e zenon_H77 zenon_H212 zenon_H25 zenon_H179 zenon_H7d zenon_Hbc zenon_H164 zenon_H48 zenon_H129 zenon_Hc0 zenon_H13a zenon_H68 zenon_Ha0 zenon_H186 zenon_H19a zenon_H16a zenon_H7b zenon_H8b zenon_H156 zenon_He4 zenon_H177 zenon_Hef zenon_H1bb zenon_H14c zenon_H104 zenon_H67 zenon_H12e zenon_H1d5 zenon_H1cf zenon_Hf0 zenon_H1bf zenon_Hb6 zenon_Hbb. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.54/21.82 apply (zenon_L94_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.54/21.82 apply (zenon_L657_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.54/21.82 exact (zenon_H8b zenon_H8a). % 21.54/21.82 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.54/21.82 apply (zenon_L553_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.54/21.82 apply (zenon_L292_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.54/21.82 apply (zenon_L257_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.54/21.82 apply (zenon_L547_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.54/21.82 apply (zenon_L658_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.54/21.82 apply (zenon_L367_); trivial. % 21.54/21.82 exact (zenon_H120 zenon_H11f). % 21.54/21.82 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.54/21.82 apply (zenon_L675_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.54/21.82 exact (zenon_H1bf zenon_H105). % 21.54/21.82 apply (zenon_L363_); trivial. % 21.54/21.82 (* end of lemma zenon_L676_ *) % 21.54/21.82 assert (zenon_L677_ : (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (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)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (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) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.54/21.82 do 0 intro. intros zenon_Ha0 zenon_H120 zenon_H192 zenon_H2a zenon_H3f zenon_H11a zenon_Ha9 zenon_H33 zenon_H121 zenon_H183 zenon_H1cd zenon_H201 zenon_H230 zenon_H1d8 zenon_H1fb zenon_H55 zenon_H23d zenon_H1cb zenon_Hb2 zenon_H1ef zenon_H173 zenon_H111 zenon_H13b zenon_H4e zenon_Hfa zenon_H82 zenon_H1c6 zenon_Hcc zenon_H131 zenon_H109 zenon_H141 zenon_H24e zenon_H1b7 zenon_H117 zenon_H13c zenon_H236 zenon_H15d zenon_H139 zenon_H23c zenon_H140 zenon_H6f zenon_H1fe zenon_H13e zenon_H19d zenon_H2c zenon_H13f zenon_H125 zenon_H73 zenon_H234 zenon_H1c3 zenon_H189 zenon_H1a8 zenon_H18d zenon_H196 zenon_H9f zenon_H1b4 zenon_H25b zenon_Hf5 zenon_H20f zenon_H25e zenon_H77 zenon_H212 zenon_H25 zenon_H179 zenon_H7d zenon_Hbc zenon_H164 zenon_H48 zenon_H129 zenon_Hc0 zenon_H13a zenon_H68 zenon_H186 zenon_H19a zenon_H16a zenon_H7b zenon_H8b zenon_H156 zenon_He4 zenon_H177 zenon_Hef zenon_H1bb zenon_H104 zenon_H67 zenon_H12e zenon_H1d5 zenon_H1cf zenon_Hf0 zenon_H1bf zenon_Hb6 zenon_H163 zenon_Hbb zenon_Hb9 zenon_H195. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.54/21.82 apply (zenon_L116_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.54/21.82 apply (zenon_L254_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.54/21.82 apply (zenon_L274_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.54/21.82 apply (zenon_L676_); trivial. % 21.54/21.82 apply (zenon_L80_); trivial. % 21.54/21.82 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.54/21.82 apply (zenon_L617_); trivial. % 21.54/21.82 apply (zenon_L172_); trivial. % 21.54/21.82 (* end of lemma zenon_L677_ *) % 21.54/21.82 assert (zenon_L678_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 21.68/21.83 do 0 intro. intros zenon_H201 zenon_H48 zenon_H31 zenon_H77 zenon_H72 zenon_H1bf zenon_Hb6 zenon_Hbb. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.68/21.83 apply (zenon_L239_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.68/21.83 apply (zenon_L59_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.68/21.83 exact (zenon_H1bf zenon_H105). % 21.68/21.83 apply (zenon_L363_); trivial. % 21.68/21.83 (* end of lemma zenon_L678_ *) % 21.68/21.83 assert (zenon_L679_ : (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (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 (e0) (e2)) = (op (e1) (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)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e0) (e3)) = (op (e2) (e3)))) -> (~((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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (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 (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((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) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (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) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (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 (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.68/21.83 do 0 intro. intros zenon_H120 zenon_Hbb zenon_H18d zenon_H1a8 zenon_H68 zenon_H2a zenon_H156 zenon_H189 zenon_H10c zenon_H1c3 zenon_H234 zenon_H3f zenon_H67 zenon_H12e zenon_H104 zenon_H14c zenon_H192 zenon_Hc0 zenon_H7b zenon_He4 zenon_H177 zenon_H20f zenon_H195 zenon_H164 zenon_H73 zenon_H125 zenon_H13f zenon_H2c zenon_H16a zenon_H19d zenon_H13e zenon_H1fe zenon_H6f zenon_Hbc zenon_H140 zenon_H23c zenon_H139 zenon_H15d zenon_H13a zenon_H236 zenon_Hf0 zenon_H13c zenon_Hf5 zenon_H117 zenon_H196 zenon_H1b7 zenon_H7d zenon_H24e zenon_H1d5 zenon_H186 zenon_H11a zenon_H141 zenon_Ha0 zenon_H109 zenon_H131 zenon_Hcc zenon_H1c6 zenon_H82 zenon_H179 zenon_Hfa zenon_H4e zenon_H13b zenon_H111 zenon_H173 zenon_H1ef zenon_Hb2 zenon_H1cb zenon_H1b4 zenon_H1bb zenon_H23d zenon_H55 zenon_H1fb zenon_H1d8 zenon_H230 zenon_H201 zenon_H1cd zenon_H8b zenon_H48 zenon_H183 zenon_H163 zenon_H1cf zenon_H77 zenon_H72 zenon_H1bf zenon_H121 zenon_H33 zenon_H9f zenon_H171 zenon_Ha9 zenon_Hb6 zenon_Hb9 zenon_H129. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.68/21.83 apply (zenon_L657_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.68/21.83 apply (zenon_L59_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.68/21.83 exact (zenon_H1bf zenon_H105). % 21.68/21.83 apply (zenon_L493_); trivial. % 21.68/21.83 (* end of lemma zenon_L679_ *) % 21.68/21.83 assert (zenon_L680_ : ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (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))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((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) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (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))))) -> (~((op (e0) (e2)) = (op (e1) (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)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e0) (e3)) = (op (e2) (e3)))) -> (~((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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (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 (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((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) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (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))))) -> (~((e1) = (e2))) -> ((op (e1) (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 (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.83 do 0 intro. intros zenon_H25 zenon_Ha0 zenon_H120 zenon_H18d zenon_H1a8 zenon_H68 zenon_H2a zenon_H156 zenon_H189 zenon_H1c3 zenon_H234 zenon_H3f zenon_H67 zenon_H12e zenon_H104 zenon_H192 zenon_Hc0 zenon_H7b zenon_He4 zenon_H177 zenon_H20f zenon_H164 zenon_H73 zenon_H125 zenon_H13f zenon_H2c zenon_H16a zenon_H19d zenon_H13e zenon_H1fe zenon_H6f zenon_Hbc zenon_H140 zenon_H23c zenon_H139 zenon_H15d zenon_H13a zenon_H236 zenon_Hf0 zenon_H13c zenon_Hf5 zenon_H117 zenon_H196 zenon_H1b7 zenon_H7d zenon_H24e zenon_H1d5 zenon_H186 zenon_H11a zenon_H141 zenon_H109 zenon_H131 zenon_Hcc zenon_H1c6 zenon_H82 zenon_H179 zenon_Hfa zenon_H4e zenon_H13b zenon_H111 zenon_H173 zenon_H1ef zenon_Hb2 zenon_H1cb zenon_H1b4 zenon_H1bb zenon_H23d zenon_H55 zenon_H1fb zenon_H1d8 zenon_H230 zenon_H201 zenon_H1cd zenon_H8b zenon_H48 zenon_H183 zenon_H1cf zenon_H77 zenon_H72 zenon_H1bf zenon_H121 zenon_H33 zenon_H9f zenon_H171 zenon_Ha9 zenon_Hb6 zenon_H129 zenon_H163 zenon_Hbb zenon_Hb9 zenon_H195. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.83 apply (zenon_L116_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.68/21.83 apply (zenon_L678_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.68/21.83 apply (zenon_L62_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.68/21.83 apply (zenon_L679_); trivial. % 21.68/21.83 apply (zenon_L80_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.83 apply (zenon_L617_); trivial. % 21.68/21.83 apply (zenon_L172_); trivial. % 21.68/21.83 (* end of lemma zenon_L680_ *) % 21.68/21.83 assert (zenon_L681_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 21.68/21.83 do 0 intro. intros zenon_H13c zenon_Ha0 zenon_H25 zenon_H129 zenon_Hc0 zenon_H20f zenon_H120 zenon_H1bb zenon_H163 zenon_Hbb zenon_Ha9 zenon_Hf7. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.83 apply (zenon_L116_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.83 apply (zenon_L571_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.83 apply (zenon_L617_); trivial. % 21.68/21.83 apply (zenon_L299_); trivial. % 21.68/21.83 (* end of lemma zenon_L681_ *) % 21.68/21.83 assert (zenon_L682_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 21.68/21.83 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hdd zenon_H68 zenon_H8b zenon_H16b. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.83 exact (zenon_H7b zenon_H65). % 21.68/21.83 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.83 apply (zenon_L54_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.83 exact (zenon_H8b zenon_H8a). % 21.68/21.83 exact (zenon_H16b zenon_H93). % 21.68/21.83 (* end of lemma zenon_L682_ *) % 21.68/21.83 assert (zenon_L683_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((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 (e0) (e1)) = (op (e1) (e1)))) -> (((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 (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((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) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.83 do 0 intro. intros zenon_H16a zenon_H7b zenon_H120 zenon_Hb6 zenon_Hbb zenon_H18d zenon_H9f zenon_H1a8 zenon_H68 zenon_H2a zenon_H156 zenon_H72 zenon_H189 zenon_H77 zenon_H10c zenon_H1c3 zenon_H234 zenon_H3f zenon_Hb9 zenon_H102 zenon_H12e zenon_H104 zenon_H14c zenon_H192 zenon_H13b zenon_H179 zenon_H173 zenon_Hfa zenon_H1cf zenon_H153 zenon_H4e zenon_H1cb zenon_Hf0 zenon_H163 zenon_H183 zenon_H48 zenon_H1c6 zenon_Ha0 zenon_H129 zenon_Hc0 zenon_H20f zenon_H1bb zenon_Ha9 zenon_H1cd zenon_H164 zenon_H8b zenon_Hf6 zenon_H196. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.83 exact (zenon_H7b zenon_H65). % 21.68/21.83 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.83 apply (zenon_L629_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.83 exact (zenon_H8b zenon_H8a). % 21.68/21.83 apply (zenon_L167_); trivial. % 21.68/21.83 (* end of lemma zenon_L683_ *) % 21.68/21.83 assert (zenon_L684_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.83 do 0 intro. intros zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_H167 zenon_Hb9 zenon_H195. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H136 | zenon_intro zenon_H25c ]. % 21.68/21.83 apply (zenon_L421_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H5c | zenon_intro zenon_H25d ]. % 21.68/21.83 apply (zenon_L138_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Ha5 ]. % 21.68/21.83 apply (zenon_L294_); trivial. % 21.68/21.83 apply (zenon_L172_); trivial. % 21.68/21.83 (* end of lemma zenon_L684_ *) % 21.68/21.83 assert (zenon_L685_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((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) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.83 do 0 intro. intros zenon_H164 zenon_H9f zenon_H155 zenon_H177 zenon_H66 zenon_H77 zenon_H68 zenon_H183 zenon_H7f zenon_H48 zenon_H14c zenon_H104 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_Hb9 zenon_H195. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.83 apply (zenon_L496_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.83 apply (zenon_L57_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.83 apply (zenon_L257_); trivial. % 21.68/21.83 apply (zenon_L684_); trivial. % 21.68/21.83 (* end of lemma zenon_L685_ *) % 21.68/21.83 assert (zenon_L686_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (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) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((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 (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.83 do 0 intro. intros zenon_He4 zenon_H2a zenon_H156 zenon_H55 zenon_H54 zenon_H13c zenon_Ha0 zenon_H164 zenon_H9f zenon_H155 zenon_H177 zenon_H66 zenon_H77 zenon_H68 zenon_H183 zenon_H48 zenon_H104 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H4e zenon_H25 zenon_H140 zenon_H163 zenon_Hbb zenon_Hb9 zenon_H195. % 21.68/21.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.68/21.83 apply (zenon_L65_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.68/21.83 apply (zenon_L486_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.68/21.83 apply (zenon_L15_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.83 apply (zenon_L116_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.68/21.83 apply (zenon_L264_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.68/21.83 apply (zenon_L274_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.68/21.83 apply (zenon_L685_); trivial. % 21.68/21.83 apply (zenon_L80_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.83 apply (zenon_L617_); trivial. % 21.68/21.83 apply (zenon_L172_); trivial. % 21.68/21.83 (* end of lemma zenon_L686_ *) % 21.68/21.83 assert (zenon_L687_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> False). % 21.68/21.83 do 0 intro. intros zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hef zenon_H14c zenon_Ha0 zenon_Hb6 zenon_H106. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.68/21.83 apply (zenon_L193_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.68/21.83 apply (zenon_L265_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.68/21.83 apply (zenon_L278_); trivial. % 21.68/21.83 apply (zenon_L363_); trivial. % 21.68/21.83 (* end of lemma zenon_L687_ *) % 21.68/21.83 assert (zenon_L688_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (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)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 21.68/21.83 do 0 intro. intros zenon_H201 zenon_H195 zenon_Hb9 zenon_Hbb zenon_H163 zenon_H140 zenon_H25 zenon_H4e zenon_H186 zenon_H20f zenon_H25b zenon_H104 zenon_H48 zenon_H183 zenon_H68 zenon_H77 zenon_H177 zenon_H155 zenon_H9f zenon_H164 zenon_H13c zenon_H54 zenon_H55 zenon_H156 zenon_H2a zenon_He4 zenon_H1bf zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hef zenon_H14c zenon_Ha0 zenon_Hb6. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.68/21.83 apply (zenon_L94_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.68/21.83 apply (zenon_L686_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.68/21.83 exact (zenon_H1bf zenon_H105). % 21.68/21.83 apply (zenon_L687_); trivial. % 21.68/21.83 (* end of lemma zenon_L688_ *) % 21.68/21.83 assert (zenon_L689_ : (~((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))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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)) = (op (e0) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (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) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((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 (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 21.68/21.83 do 0 intro. intros zenon_H192 zenon_H2a zenon_H12e zenon_H3f zenon_H11a zenon_H120 zenon_Ha9 zenon_H33 zenon_H121 zenon_H1cf zenon_H163 zenon_H183 zenon_H1cd zenon_H201 zenon_H230 zenon_H1d8 zenon_H1fb zenon_H55 zenon_H23d zenon_H1cb zenon_Hb2 zenon_H1ef zenon_H173 zenon_H111 zenon_H13b zenon_H4e zenon_Hfa zenon_H179 zenon_H82 zenon_H1c6 zenon_Hcc zenon_H131 zenon_H109 zenon_H141 zenon_H1d5 zenon_H24e zenon_H1b7 zenon_H117 zenon_H13c zenon_Hf0 zenon_H236 zenon_H15d zenon_H139 zenon_H23c zenon_H140 zenon_Hbc zenon_H6f zenon_H1fe zenon_H13e zenon_H19d zenon_H2c zenon_H13f zenon_H125 zenon_H73 zenon_H234 zenon_H1c3 zenon_H10c zenon_H189 zenon_H1a8 zenon_H9f zenon_H18d zenon_H7e zenon_H67 zenon_H104 zenon_H14c zenon_H1bb zenon_Hef zenon_H196 zenon_Hb9 zenon_H177 zenon_He4 zenon_H156 zenon_H8b zenon_H77 zenon_H7b zenon_H16a zenon_H7d zenon_H19a zenon_H195 zenon_H20f zenon_H186 zenon_H25b zenon_H1b4 zenon_Hf5 zenon_H25e zenon_Ha0 zenon_H68 zenon_H13a zenon_Hc0 zenon_H129 zenon_H48 zenon_H164 zenon_H1bf zenon_Hb6 zenon_Hbb. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.68/21.83 apply (zenon_L94_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.68/21.83 apply (zenon_L657_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.68/21.83 exact (zenon_H8b zenon_H8a). % 21.68/21.83 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.83 apply (zenon_L553_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.83 apply (zenon_L292_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.83 apply (zenon_L80_); trivial. % 21.68/21.83 apply (zenon_L547_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.68/21.83 apply (zenon_L670_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.68/21.83 exact (zenon_H1bf zenon_H105). % 21.68/21.83 apply (zenon_L363_); trivial. % 21.68/21.83 (* end of lemma zenon_L689_ *) % 21.68/21.83 assert (zenon_L690_ : (~((e0) = (e3))) -> (~((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))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (((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) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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)) = (op (e0) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((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 (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.83 do 0 intro. intros zenon_Ha0 zenon_H192 zenon_H2a zenon_H12e zenon_H3f zenon_H11a zenon_H120 zenon_Ha9 zenon_H33 zenon_H121 zenon_H1cf zenon_H183 zenon_H1cd zenon_H201 zenon_H230 zenon_H1d8 zenon_H1fb zenon_H55 zenon_H23d zenon_H1cb zenon_Hb2 zenon_H1ef zenon_H173 zenon_H111 zenon_H13b zenon_H4e zenon_Hfa zenon_H179 zenon_H82 zenon_H1c6 zenon_Hcc zenon_H131 zenon_H109 zenon_H141 zenon_H1d5 zenon_H24e zenon_H1b7 zenon_H117 zenon_H13c zenon_Hf0 zenon_H236 zenon_H15d zenon_H139 zenon_H23c zenon_H140 zenon_Hbc zenon_H6f zenon_H1fe zenon_H13e zenon_H19d zenon_H2c zenon_H13f zenon_H125 zenon_H73 zenon_H234 zenon_H1c3 zenon_H189 zenon_H1a8 zenon_H9f zenon_H18d zenon_H7e zenon_H67 zenon_H104 zenon_H1bb zenon_Hef zenon_H196 zenon_H177 zenon_He4 zenon_H156 zenon_H8b zenon_H77 zenon_H7b zenon_H16a zenon_H7d zenon_H19a zenon_H20f zenon_H186 zenon_H25b zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H68 zenon_H13a zenon_Hc0 zenon_H129 zenon_H48 zenon_H164 zenon_H1bf zenon_Hb6 zenon_H25 zenon_H163 zenon_Hbb zenon_Hb9 zenon_H195. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.83 apply (zenon_L116_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.68/21.83 apply (zenon_L254_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.68/21.83 apply (zenon_L274_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.68/21.83 apply (zenon_L689_); trivial. % 21.68/21.83 apply (zenon_L80_); trivial. % 21.68/21.83 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.83 apply (zenon_L617_); trivial. % 21.68/21.83 apply (zenon_L172_); trivial. % 21.68/21.83 (* end of lemma zenon_L690_ *) % 21.68/21.83 assert (zenon_L691_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.68/21.84 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H25 zenon_Hf0 zenon_H9f zenon_H155 zenon_H189 zenon_H186 zenon_H7e zenon_H67 zenon_H1b4 zenon_H1cb zenon_H1c3 zenon_H1c6 zenon_Ha0 zenon_H2a zenon_H129 zenon_Hc0 zenon_H20f zenon_H120 zenon_H1bb zenon_Ha9 zenon_H6d zenon_Hbb zenon_H1cd. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.84 apply (zenon_L61_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.84 apply (zenon_L638_); trivial. % 21.68/21.84 apply (zenon_L576_); trivial. % 21.68/21.84 (* end of lemma zenon_L691_ *) % 21.68/21.84 assert (zenon_L692_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (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)) = (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))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (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)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H1a2 zenon_H212 zenon_H155 zenon_Hb6 zenon_H177 zenon_Ha0 zenon_H25e zenon_H25b zenon_H19a zenon_H195 zenon_Hb9 zenon_H33 zenon_H121 zenon_H1bf zenon_H1cf zenon_H183 zenon_H48 zenon_H8b zenon_H1cd zenon_H201 zenon_H230 zenon_H1d8 zenon_H1fb zenon_H55 zenon_H23d zenon_Hb2 zenon_H1ef zenon_H173 zenon_H111 zenon_H13b zenon_H4e zenon_Hfa zenon_H179 zenon_H82 zenon_H1c6 zenon_Hcc zenon_H131 zenon_H109 zenon_H141 zenon_H11a zenon_H186 zenon_H24e zenon_H7d zenon_H1b7 zenon_H196 zenon_H117 zenon_Hf5 zenon_Hf0 zenon_H236 zenon_H13a zenon_H15d zenon_H139 zenon_H23c zenon_H140 zenon_Hbc zenon_H6f zenon_H1fe zenon_H13e zenon_H19d zenon_H16a zenon_H2c zenon_H13f zenon_H73 zenon_H164 zenon_He4 zenon_H192 zenon_H104 zenon_H12e zenon_H3f zenon_H234 zenon_H1c3 zenon_H189 zenon_H156 zenon_H1a8 zenon_H18d zenon_H13c zenon_H129 zenon_Hc0 zenon_H20f zenon_H163 zenon_Ha9 zenon_H2a zenon_H1d5 zenon_H125 zenon_H1cb zenon_Hbb zenon_H1b4 zenon_H120 zenon_H1bb zenon_H68 zenon_H25 zenon_H7b zenon_H77. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.84 apply (zenon_L635_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.84 apply (zenon_L25_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.84 apply (zenon_L677_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.84 apply (zenon_L100_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.84 apply (zenon_L633_); trivial. % 21.68/21.84 apply (zenon_L680_); trivial. % 21.68/21.84 apply (zenon_L681_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L53_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L178_); trivial. % 21.68/21.84 apply (zenon_L115_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.68/21.84 apply (zenon_L264_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.68/21.84 apply (zenon_L274_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.68/21.84 apply (zenon_L688_); trivial. % 21.68/21.84 apply (zenon_L80_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.84 apply (zenon_L22_); trivial. % 21.68/21.84 apply (zenon_L681_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L53_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L193_); trivial. % 21.68/21.84 apply (zenon_L154_); trivial. % 21.68/21.84 apply (zenon_L98_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.84 apply (zenon_L690_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.84 apply (zenon_L100_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.84 apply (zenon_L691_); trivial. % 21.68/21.84 apply (zenon_L680_); trivial. % 21.68/21.84 apply (zenon_L681_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L53_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L178_); trivial. % 21.68/21.84 apply (zenon_L115_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.84 apply (zenon_L651_); trivial. % 21.68/21.84 apply (zenon_L632_); trivial. % 21.68/21.84 (* end of lemma zenon_L692_ *) % 21.68/21.84 assert (zenon_L693_ : (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((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) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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 (e0) (e3)) = (op (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H7b zenon_H77 zenon_Ha9 zenon_H13a zenon_H121 zenon_H33 zenon_Hb6 zenon_H129 zenon_H68 zenon_H183 zenon_H1bf zenon_He4 zenon_H156 zenon_H55 zenon_H201 zenon_Ha0 zenon_H2a zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196 zenon_H3f zenon_H1cf zenon_H120 zenon_H18d zenon_H163 zenon_H12e zenon_H8b zenon_H1cd zenon_H230 zenon_H1d8 zenon_H1fb zenon_H234 zenon_H189 zenon_H23d zenon_H1bb zenon_H1b4 zenon_H1cb zenon_Hb2 zenon_H1ef zenon_H173 zenon_H111 zenon_H13b zenon_H4e zenon_Hfa zenon_H179 zenon_H82 zenon_H1c6 zenon_Hcc zenon_H131 zenon_H109 zenon_H141 zenon_H11a zenon_H186 zenon_H1d5 zenon_H24e zenon_H7d zenon_H1b7 zenon_H192 zenon_H1c3 zenon_H117 zenon_Hf5 zenon_H13c zenon_Hf0 zenon_H236 zenon_H15d zenon_H139 zenon_H23c zenon_H140 zenon_Hbc zenon_H6f zenon_H1fe zenon_H13e zenon_H19d zenon_H16a zenon_H2c zenon_H13f zenon_H125 zenon_H73 zenon_H104 zenon_H1a8 zenon_H164 zenon_H195 zenon_H20f zenon_Hc0 zenon_H34 zenon_H48. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.84 apply (zenon_L376_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.84 apply (zenon_L65_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_L656_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L53_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L95_); trivial. % 21.68/21.84 apply (zenon_L154_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.84 apply (zenon_L635_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.84 apply (zenon_L492_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.68/21.84 apply (zenon_L297_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.68/21.84 apply (zenon_L272_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.84 apply (zenon_L569_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.84 apply (zenon_L641_); trivial. % 21.68/21.84 apply (zenon_L575_); trivial. % 21.68/21.84 apply (zenon_L655_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L53_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L178_); trivial. % 21.68/21.84 apply (zenon_L154_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.84 apply (zenon_L642_); trivial. % 21.68/21.84 apply (zenon_L98_); trivial. % 21.68/21.84 apply (zenon_L456_); trivial. % 21.68/21.84 (* end of lemma zenon_L693_ *) % 21.68/21.84 assert (zenon_L694_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((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) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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 (e0) (e3)) = (op (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((e0) = (e1))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H19a zenon_H25b zenon_H25e zenon_H212 zenon_H1a2 zenon_H16b zenon_H7b zenon_H77 zenon_Ha9 zenon_H13a zenon_H121 zenon_H33 zenon_Hb6 zenon_H129 zenon_H68 zenon_H183 zenon_H1bf zenon_He4 zenon_H156 zenon_H55 zenon_H201 zenon_Ha0 zenon_H2a zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196 zenon_H3f zenon_H1cf zenon_H120 zenon_H18d zenon_H163 zenon_H12e zenon_H8b zenon_H1cd zenon_H230 zenon_H1d8 zenon_H1fb zenon_H234 zenon_H189 zenon_H23d zenon_H1bb zenon_H1b4 zenon_H1cb zenon_Hb2 zenon_H1ef zenon_H173 zenon_H111 zenon_H13b zenon_H4e zenon_Hfa zenon_H179 zenon_H82 zenon_H1c6 zenon_Hcc zenon_H131 zenon_H109 zenon_H141 zenon_H11a zenon_H186 zenon_H1d5 zenon_H24e zenon_H7d zenon_H1b7 zenon_H192 zenon_H1c3 zenon_H117 zenon_Hf5 zenon_H13c zenon_Hf0 zenon_H236 zenon_H15d zenon_H139 zenon_H23c zenon_H140 zenon_Hbc zenon_H6f zenon_H1fe zenon_H13e zenon_H19d zenon_H16a zenon_H2c zenon_H13f zenon_H125 zenon_H73 zenon_H104 zenon_H1a8 zenon_H164 zenon_H195 zenon_H20f zenon_Hc0 zenon_H48. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.68/21.84 apply (zenon_L161_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.84 apply (zenon_L376_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.84 apply (zenon_L65_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.84 apply (zenon_L376_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.84 apply (zenon_L25_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.84 apply (zenon_L677_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.84 apply (zenon_L100_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.84 apply (zenon_L618_); trivial. % 21.68/21.84 apply (zenon_L680_); trivial. % 21.68/21.84 apply (zenon_L681_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L53_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L95_); trivial. % 21.68/21.84 apply (zenon_L154_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.84 apply (zenon_L94_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.84 apply (zenon_L677_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.84 apply (zenon_L100_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.84 apply (zenon_L626_); trivial. % 21.68/21.84 apply (zenon_L680_); trivial. % 21.68/21.84 apply (zenon_L681_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L53_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L178_); trivial. % 21.68/21.84 apply (zenon_L154_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.68/21.84 exact (zenon_H7b zenon_H65). % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.84 apply (zenon_L621_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.84 apply (zenon_L116_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.84 apply (zenon_L217_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.84 apply (zenon_L682_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.84 apply (zenon_L683_); trivial. % 21.68/21.84 apply (zenon_L77_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.84 apply (zenon_L617_); trivial. % 21.68/21.84 apply (zenon_L172_); trivial. % 21.68/21.84 apply (zenon_L63_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L53_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L95_); trivial. % 21.68/21.84 apply (zenon_L92_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.84 apply (zenon_L677_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.84 apply (zenon_L100_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.84 apply (zenon_L631_); trivial. % 21.68/21.84 apply (zenon_L680_); trivial. % 21.68/21.84 apply (zenon_L681_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L53_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L178_); trivial. % 21.68/21.84 apply (zenon_L154_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.84 apply (zenon_L651_); trivial. % 21.68/21.84 apply (zenon_L632_); trivial. % 21.68/21.84 apply (zenon_L692_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.68/21.84 apply (zenon_L627_); trivial. % 21.68/21.84 apply (zenon_L693_); trivial. % 21.68/21.84 (* end of lemma zenon_L694_ *) % 21.68/21.84 assert (zenon_L695_ : (~((e2) = (e3))) -> ((op (e3) (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)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((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 (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (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)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (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 (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((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) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (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))))) -> (~((e1) = (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 (e1) (e3)) = (op (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)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.84 do 0 intro. intros zenon_Ha9 zenon_Hbb zenon_H163 zenon_H1bb zenon_H120 zenon_H20f zenon_Hc0 zenon_H129 zenon_H25 zenon_H13c zenon_H89 zenon_H54 zenon_H191 zenon_H18d zenon_H1a8 zenon_H68 zenon_H156 zenon_H189 zenon_H1c3 zenon_H234 zenon_H3f zenon_H67 zenon_H12e zenon_H104 zenon_H192 zenon_H7b zenon_He4 zenon_H177 zenon_H164 zenon_H73 zenon_H125 zenon_H13f zenon_H2c zenon_H16a zenon_H19d zenon_H13e zenon_H1fe zenon_H6f zenon_Hbc zenon_H140 zenon_H23c zenon_H139 zenon_H15d zenon_H13a zenon_H236 zenon_Hf0 zenon_Hf5 zenon_H117 zenon_H1b7 zenon_H7d zenon_H24e zenon_H1d5 zenon_H186 zenon_H11a zenon_H141 zenon_H109 zenon_H131 zenon_Hcc zenon_H1c6 zenon_H82 zenon_H179 zenon_Hfa zenon_H4e zenon_H13b zenon_H111 zenon_H173 zenon_H1ef zenon_Hb2 zenon_H1cb zenon_H1b4 zenon_H23d zenon_H55 zenon_H1fb zenon_H1d8 zenon_H230 zenon_H201 zenon_H1cd zenon_H8b zenon_H48 zenon_H183 zenon_H1cf zenon_H77 zenon_H1bf zenon_H121 zenon_H33 zenon_H195 zenon_H25b zenon_H25e zenon_H212 zenon_H19a zenon_Ha0 zenon_H2a zenon_Hb6 zenon_H153 zenon_Hb9 zenon_H196. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.84 apply (zenon_L677_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.84 apply (zenon_L100_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.84 apply (zenon_L649_); trivial. % 21.68/21.84 apply (zenon_L680_); trivial. % 21.68/21.84 apply (zenon_L681_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L53_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L95_); trivial. % 21.68/21.84 apply (zenon_L154_); trivial. % 21.68/21.84 (* end of lemma zenon_L695_ *) % 21.68/21.84 assert (zenon_L696_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((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) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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 (e0) (e3)) = (op (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((e0) = (e1))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H19a zenon_H25b zenon_H25e zenon_H212 zenon_H1a2 zenon_H191 zenon_H89 zenon_H7b zenon_H77 zenon_Ha9 zenon_H13a zenon_H121 zenon_H33 zenon_Hb6 zenon_H129 zenon_H68 zenon_H183 zenon_H1bf zenon_He4 zenon_H156 zenon_H55 zenon_H201 zenon_Ha0 zenon_H2a zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196 zenon_H3f zenon_H1cf zenon_H120 zenon_H18d zenon_H163 zenon_H12e zenon_H8b zenon_H1cd zenon_H230 zenon_H1d8 zenon_H1fb zenon_H234 zenon_H189 zenon_H23d zenon_H1bb zenon_H1b4 zenon_H1cb zenon_Hb2 zenon_H1ef zenon_H173 zenon_H111 zenon_H13b zenon_H4e zenon_Hfa zenon_H179 zenon_H82 zenon_H1c6 zenon_Hcc zenon_H131 zenon_H109 zenon_H141 zenon_H11a zenon_H186 zenon_H1d5 zenon_H24e zenon_H7d zenon_H1b7 zenon_H192 zenon_H1c3 zenon_H117 zenon_Hf5 zenon_H13c zenon_Hf0 zenon_H236 zenon_H15d zenon_H139 zenon_H23c zenon_H140 zenon_Hbc zenon_H6f zenon_H1fe zenon_H13e zenon_H19d zenon_H16a zenon_H2c zenon_H13f zenon_H125 zenon_H73 zenon_H104 zenon_H1a8 zenon_H164 zenon_H195 zenon_H20f zenon_Hc0 zenon_H48. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.68/21.84 apply (zenon_L161_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.84 apply (zenon_L376_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.84 apply (zenon_L65_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.84 apply (zenon_L376_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.84 apply (zenon_L492_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.84 apply (zenon_L695_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.84 apply (zenon_L94_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.68/21.84 apply (zenon_L695_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.68/21.84 exact (zenon_H7b zenon_H65). % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.84 apply (zenon_L621_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.84 apply (zenon_L116_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.84 apply (zenon_L217_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.84 apply (zenon_L628_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.84 apply (zenon_L683_); trivial. % 21.68/21.84 apply (zenon_L648_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.84 apply (zenon_L436_); trivial. % 21.68/21.84 apply (zenon_L172_); trivial. % 21.68/21.84 apply (zenon_L63_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L53_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L178_); trivial. % 21.68/21.84 apply (zenon_L92_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.84 apply (zenon_L171_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.84 apply (zenon_L690_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.84 apply (zenon_L100_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.84 apply (zenon_L650_); trivial. % 21.68/21.84 apply (zenon_L680_); trivial. % 21.68/21.84 apply (zenon_L681_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L53_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L95_); trivial. % 21.68/21.84 apply (zenon_L154_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.84 apply (zenon_L147_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.84 apply (zenon_L94_); trivial. % 21.68/21.84 apply (zenon_L632_); trivial. % 21.68/21.84 apply (zenon_L692_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.68/21.84 apply (zenon_L645_); trivial. % 21.68/21.84 apply (zenon_L693_); trivial. % 21.68/21.84 (* end of lemma zenon_L696_ *) % 21.68/21.84 assert (zenon_L697_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (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) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (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))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((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)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (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) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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 (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (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) (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) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H92 zenon_H89 zenon_H19d zenon_H2a zenon_H1a2 zenon_H212 zenon_H230 zenon_H1fb zenon_H55 zenon_H23d zenon_H1b4 zenon_Hb2 zenon_H1ef zenon_H111 zenon_H82 zenon_Hcc zenon_H131 zenon_H109 zenon_H141 zenon_H186 zenon_H1d5 zenon_H24e zenon_H7d zenon_H1b7 zenon_H192 zenon_H117 zenon_Hf5 zenon_H13c zenon_H236 zenon_H33 zenon_H15d zenon_H139 zenon_H23c zenon_H140 zenon_Hbc zenon_H6f zenon_H1fe zenon_H13e zenon_H2c zenon_H13f zenon_H125 zenon_H73 zenon_H104 zenon_H164 zenon_H121 zenon_He4 zenon_H1a8 zenon_H1c3 zenon_H1cb zenon_H189 zenon_H20f zenon_Hc0 zenon_H129 zenon_H1bb zenon_H234 zenon_H18d zenon_Ha9 zenon_H1cd zenon_H1c6 zenon_H1cf zenon_H11a zenon_H3f zenon_H120 zenon_H12e zenon_H8b zenon_H156 zenon_H1bf zenon_H201 zenon_H16a zenon_H195 zenon_Hfa zenon_Hf0 zenon_H163 zenon_H183 zenon_H13b zenon_H7b zenon_H173 zenon_H179 zenon_H77 zenon_H19a zenon_H25e zenon_H25b zenon_H4e zenon_H1d8 zenon_H68 zenon_H48 zenon_Hb6 zenon_Ha0 zenon_H177 zenon_Hbb zenon_H196 zenon_Hb9 zenon_H13a. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.68/21.84 apply (zenon_L694_); trivial. % 21.68/21.84 apply (zenon_L696_); trivial. % 21.68/21.84 (* end of lemma zenon_L697_ *) % 21.68/21.84 assert (zenon_L698_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (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 (e3) (e3)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((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)) = (op (e3) (e2)))) -> (~((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (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)) = (op (e2) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (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) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H13a zenon_Hb9 zenon_H196 zenon_Hbb zenon_H177 zenon_Ha0 zenon_Hb6 zenon_H48 zenon_H68 zenon_H1d8 zenon_H4e zenon_H25b zenon_H25e zenon_H19a zenon_H77 zenon_H179 zenon_H173 zenon_H7b zenon_H13b zenon_H183 zenon_H163 zenon_Hf0 zenon_Hfa zenon_H195 zenon_H16a zenon_H201 zenon_H1bf zenon_H156 zenon_H12e zenon_H120 zenon_H3f zenon_H11a zenon_H1cf zenon_H1c6 zenon_H1cd zenon_Ha9 zenon_H18d zenon_H234 zenon_H1bb zenon_H129 zenon_Hc0 zenon_H20f zenon_H189 zenon_H1cb zenon_H1c3 zenon_H1a8 zenon_He4 zenon_H121 zenon_H164 zenon_H104 zenon_H73 zenon_H125 zenon_H13f zenon_H2c zenon_H13e zenon_H1fe zenon_H6f zenon_Hbc zenon_H140 zenon_H23c zenon_H139 zenon_H15d zenon_H33 zenon_H236 zenon_H13c zenon_Hf5 zenon_H117 zenon_H192 zenon_H1b7 zenon_H7d zenon_H24e zenon_H1d5 zenon_H186 zenon_H141 zenon_H109 zenon_H131 zenon_Hcc zenon_H82 zenon_H111 zenon_H1ef zenon_Hb2 zenon_H1b4 zenon_H23d zenon_H55 zenon_H1fb zenon_H230 zenon_H212 zenon_H1a2 zenon_H2a zenon_H19d zenon_H89 zenon_H92. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.68/21.84 apply (zenon_L697_); trivial. % 21.68/21.84 apply (zenon_L697_); trivial. % 21.68/21.84 (* end of lemma zenon_L698_ *) % 21.68/21.84 assert (zenon_L699_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (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) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((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 (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (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))))) -> (~((e2) = (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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (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))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> False). % 21.68/21.84 do 0 intro. intros zenon_H264 zenon_H230 zenon_H109 zenon_H1d5 zenon_Hf5 zenon_H6f zenon_H1c3 zenon_H189 zenon_H1cf zenon_H16a zenon_H13b zenon_H173 zenon_H25e zenon_H25b zenon_H94 zenon_Hb2 zenon_H19a zenon_H18d zenon_H1b4 zenon_H20f zenon_H1b7 zenon_H179 zenon_H24e zenon_H125 zenon_H1ef zenon_H186 zenon_H1a2 zenon_Hcc zenon_H1cd zenon_H1cb zenon_H19d zenon_H195 zenon_H12e zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H1bb zenon_Hfa zenon_H13c zenon_H55 zenon_H1a8 zenon_H23d zenon_H11a zenon_H1fe zenon_H1c6 zenon_H13e zenon_H111 zenon_H140 zenon_H68 zenon_H13f zenon_H156 zenon_H117 zenon_Hb6 zenon_H4e zenon_H163 zenon_H73 zenon_H131 zenon_H1ec zenon_Ha9 zenon_H201 zenon_H82 zenon_H139 zenon_H13a zenon_H2c zenon_H236 zenon_H15d zenon_H23c zenon_H183 zenon_H196 zenon_H33 zenon_H129 zenon_H121 zenon_H190 zenon_H177 zenon_He4 zenon_H192 zenon_H104 zenon_H164 zenon_H141 zenon_Ha0 zenon_H77 zenon_H234 zenon_Hf0 zenon_H48 zenon_H1fb zenon_H1d8 zenon_H2a zenon_H3f. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1bf | zenon_intro zenon_H6d ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.68/21.84 apply (zenon_L2_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.68/21.84 apply (zenon_L482_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.68/21.84 apply (zenon_L315_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.68/21.84 apply (zenon_L317_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.68/21.84 apply (zenon_L318_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.68/21.84 apply (zenon_L11_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.68/21.84 apply (zenon_L483_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.68/21.84 apply (zenon_L485_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 21.68/21.84 apply (zenon_L537_); trivial. % 21.68/21.84 apply (zenon_L537_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.68/21.84 apply (zenon_L522_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.68/21.84 apply (zenon_L37_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.68/21.84 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.68/21.84 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.68/21.84 apply (zenon_L554_); trivial. % 21.68/21.84 apply (zenon_L554_); trivial. % 21.68/21.84 apply (zenon_L565_); trivial. % 21.68/21.84 apply (zenon_L238_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 21.68/21.84 exact (zenon_H205 zenon_H2a). % 21.68/21.84 apply (zenon_L567_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.68/21.84 apply (zenon_L531_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.68/21.84 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.68/21.84 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.68/21.84 apply (zenon_L698_); trivial. % 21.68/21.84 apply (zenon_L197_); trivial. % 21.68/21.84 apply (zenon_L51_); trivial. % 21.68/21.84 apply (zenon_L532_); trivial. % 21.68/21.84 apply (zenon_L654_); trivial. % 21.68/21.84 (* end of lemma zenon_L699_ *) % 21.68/21.84 assert (zenon_L700_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H28 zenon_H31 zenon_H1d8. % 21.68/21.84 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 21.68/21.84 apply (zenon_L254_); trivial. % 21.68/21.84 (* end of lemma zenon_L700_ *) % 21.68/21.84 assert (zenon_L701_ : ((op (e0) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H67 zenon_H9f zenon_Ha9. % 21.68/21.84 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 21.68/21.84 cut (((e3) = (e3)) = ((e2) = (e3))). % 21.68/21.84 intro zenon_D_pnotp. % 21.68/21.84 apply zenon_Ha9. % 21.68/21.84 rewrite <- zenon_D_pnotp. % 21.68/21.84 exact zenon_Ha1. % 21.68/21.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.68/21.84 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 21.68/21.84 congruence. % 21.68/21.84 cut (((op (e0) (e0)) = (e2)) = ((e3) = (e2))). % 21.68/21.84 intro zenon_D_pnotp. % 21.68/21.84 apply zenon_Haa. % 21.68/21.84 rewrite <- zenon_D_pnotp. % 21.68/21.84 exact zenon_H67. % 21.68/21.84 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.68/21.84 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 21.68/21.84 congruence. % 21.68/21.84 exact (zenon_Ha4 zenon_H9f). % 21.68/21.84 apply zenon_H6a. apply refl_equal. % 21.68/21.84 apply zenon_Ha2. apply refl_equal. % 21.68/21.84 apply zenon_Ha2. apply refl_equal. % 21.68/21.84 (* end of lemma zenon_L701_ *) % 21.68/21.84 assert (zenon_L702_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 21.68/21.84 do 0 intro. intros zenon_H55 zenon_H2d zenon_Hdd. % 21.68/21.84 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 21.68/21.84 intro zenon_D_pnotp. % 21.68/21.84 apply zenon_H55. % 21.68/21.84 rewrite <- zenon_D_pnotp. % 21.68/21.84 exact zenon_H2d. % 21.68/21.84 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H265]. % 21.68/21.84 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 21.68/21.84 congruence. % 21.68/21.84 apply zenon_H86. apply refl_equal. % 21.68/21.84 apply zenon_H265. apply sym_equal. exact zenon_Hdd. % 21.68/21.84 (* end of lemma zenon_L702_ *) % 21.68/21.84 assert (zenon_L703_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> False). % 21.68/21.84 do 0 intro. intros zenon_H266 zenon_H2d zenon_H55 zenon_Hf0 zenon_H3f zenon_H1ba zenon_H6f zenon_Hdb. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_Hdd | zenon_intro zenon_H267 ]. % 21.68/21.84 apply (zenon_L702_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H53 | zenon_intro zenon_H268 ]. % 21.68/21.84 apply (zenon_L118_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H6d | zenon_intro zenon_H10d ]. % 21.68/21.84 exact (zenon_H1ba zenon_H6d). % 21.68/21.84 apply (zenon_L205_); trivial. % 21.68/21.84 (* end of lemma zenon_L703_ *) % 21.68/21.84 assert (zenon_L704_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> False). % 21.68/21.84 do 0 intro. intros zenon_H266 zenon_H2d zenon_H55 zenon_H7f zenon_H1f1 zenon_H1ba zenon_H6f zenon_Hdb. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_Hdd | zenon_intro zenon_H267 ]. % 21.68/21.84 apply (zenon_L702_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H53 | zenon_intro zenon_H268 ]. % 21.68/21.84 apply (zenon_L284_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H6d | zenon_intro zenon_H10d ]. % 21.68/21.84 exact (zenon_H1ba zenon_H6d). % 21.68/21.84 apply (zenon_L205_); trivial. % 21.68/21.84 (* end of lemma zenon_L704_ *) % 21.68/21.84 assert (zenon_L705_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (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)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> False). % 21.68/21.84 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_Hf0 zenon_H16b zenon_H8b zenon_H77 zenon_H68 zenon_H16a zenon_H266 zenon_H2d zenon_H55 zenon_H1f1 zenon_H1ba zenon_H6f zenon_Hdb. % 21.68/21.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.68/21.84 apply (zenon_L55_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.68/21.84 apply (zenon_L703_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.68/21.84 apply (zenon_L327_); trivial. % 21.68/21.84 apply (zenon_L704_); trivial. % 21.68/21.84 (* end of lemma zenon_L705_ *) % 21.68/21.84 assert (zenon_L706_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> False). % 21.68/21.84 do 0 intro. intros zenon_H24 zenon_H67 zenon_H76. % 21.68/21.84 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 21.68/21.84 intro zenon_D_pnotp. % 21.68/21.84 apply zenon_H24. % 21.68/21.84 rewrite <- zenon_D_pnotp. % 21.68/21.84 exact zenon_H67. % 21.68/21.84 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 21.68/21.84 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 21.68/21.84 congruence. % 21.68/21.84 apply zenon_H27. apply refl_equal. % 21.68/21.84 apply zenon_H124. apply sym_equal. exact zenon_H76. % 21.68/21.84 (* end of lemma zenon_L706_ *) % 21.68/21.84 assert (zenon_L707_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H117 zenon_Ha0 zenon_H2d zenon_H10c zenon_Hf0 zenon_Hb6 zenon_H105 zenon_H9e zenon_H196. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.84 apply (zenon_L67_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.84 apply (zenon_L74_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.84 apply (zenon_L400_); trivial. % 21.68/21.84 apply (zenon_L154_); trivial. % 21.68/21.84 (* end of lemma zenon_L707_ *) % 21.68/21.84 assert (zenon_L708_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.68/21.84 do 0 intro. intros zenon_H13a zenon_H33 zenon_H9d zenon_Hb6 zenon_H3d zenon_Ha0 zenon_H31 zenon_Ha9 zenon_Hf6. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.84 apply (zenon_L245_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.84 apply (zenon_L55_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.84 apply (zenon_L68_); trivial. % 21.68/21.84 apply (zenon_L92_); trivial. % 21.68/21.84 (* end of lemma zenon_L708_ *) % 21.68/21.84 assert (zenon_L709_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H1cf zenon_H68 zenon_H31 zenon_Hf7 zenon_H186 zenon_H8b zenon_H171 zenon_H1cd. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.68/21.84 apply (zenon_L264_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.68/21.84 apply (zenon_L438_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.68/21.84 exact (zenon_H8b zenon_H8a). % 21.68/21.84 apply (zenon_L240_); trivial. % 21.68/21.84 (* end of lemma zenon_L709_ *) % 21.68/21.84 assert (zenon_L710_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H1c3 zenon_Ha9 zenon_Ha0 zenon_H3d zenon_Hb6 zenon_H9d zenon_H33 zenon_H13a zenon_H1cd zenon_H171 zenon_H8b zenon_H186 zenon_H31 zenon_H68 zenon_H1cf zenon_H128 zenon_H77 zenon_H181. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.68/21.84 apply (zenon_L708_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.68/21.84 apply (zenon_L709_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.68/21.84 apply (zenon_L218_); trivial. % 21.68/21.84 exact (zenon_H181 zenon_H17c). % 21.68/21.84 (* end of lemma zenon_L710_ *) % 21.68/21.84 assert (zenon_L711_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (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)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e0)) = (e0)) -> (((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))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H13f zenon_H48 zenon_H16b zenon_H16a zenon_H196 zenon_H9e zenon_Hf0 zenon_H10c zenon_H2d zenon_H117 zenon_H1c3 zenon_Ha9 zenon_Ha0 zenon_H3d zenon_Hb6 zenon_H9d zenon_H33 zenon_H13a zenon_H1cd zenon_H171 zenon_H8b zenon_H186 zenon_H31 zenon_H68 zenon_H1cf zenon_H77 zenon_H181. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.68/21.84 apply (zenon_L217_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.68/21.84 apply (zenon_L327_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.68/21.84 apply (zenon_L707_); trivial. % 21.68/21.84 apply (zenon_L710_); trivial. % 21.68/21.84 (* end of lemma zenon_L711_ *) % 21.68/21.84 assert (zenon_L712_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H16a zenon_H68 zenon_H2f zenon_H1ba zenon_H8b zenon_Hf7 zenon_H195. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.84 apply (zenon_L28_); trivial. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.84 exact (zenon_H1ba zenon_H6d). % 21.68/21.84 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.84 exact (zenon_H8b zenon_H8a). % 21.68/21.84 apply (zenon_L228_); trivial. % 21.68/21.84 (* end of lemma zenon_L712_ *) % 21.68/21.84 assert (zenon_L713_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (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) (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 (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 (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (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 (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.84 do 0 intro. intros zenon_H6f zenon_H1f1 zenon_H55 zenon_H266 zenon_He4 zenon_Hb2 zenon_Hfa zenon_H67 zenon_H24 zenon_Hf5 zenon_Ha9 zenon_H13f zenon_H48 zenon_H16b zenon_H196 zenon_Hf0 zenon_H2d zenon_H117 zenon_H1c3 zenon_Ha0 zenon_H3d zenon_Hb6 zenon_H33 zenon_H13a zenon_H1cd zenon_H186 zenon_H31 zenon_H1cf zenon_H77 zenon_H181 zenon_H3c zenon_H13c zenon_H1b3 zenon_H1a8 zenon_H16a zenon_H68 zenon_H2f zenon_H1ba zenon_H8b zenon_H195. % 21.68/21.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.85 apply (zenon_L701_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.85 apply (zenon_L705_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.85 apply (zenon_L68_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.68/21.85 apply (zenon_L701_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.68/21.85 apply (zenon_L46_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.68/21.85 apply (zenon_L67_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.85 apply (zenon_L706_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.85 exact (zenon_H1b3 zenon_Hef). % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.85 apply (zenon_L214_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.85 exact (zenon_H1b3 zenon_Hef). % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.85 exact (zenon_H1ba zenon_H6d). % 21.68/21.85 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.85 apply (zenon_L46_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.85 apply (zenon_L711_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.85 apply (zenon_L436_); trivial. % 21.68/21.85 apply (zenon_L262_); trivial. % 21.68/21.85 apply (zenon_L712_); trivial. % 21.68/21.85 (* end of lemma zenon_L713_ *) % 21.68/21.85 assert (zenon_L714_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H16a zenon_H2c zenon_H67 zenon_H6f zenon_H6e zenon_H8b zenon_H16b. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.85 apply (zenon_L180_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.85 apply (zenon_L21_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.85 exact (zenon_H8b zenon_H8a). % 21.68/21.85 exact (zenon_H16b zenon_H93). % 21.68/21.85 (* end of lemma zenon_L714_ *) % 21.68/21.85 assert (zenon_L715_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H16a zenon_H68 zenon_H2d zenon_Ha9 zenon_H10d zenon_H8b zenon_H16b. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.85 apply (zenon_L27_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.85 apply (zenon_L289_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.85 exact (zenon_H8b zenon_H8a). % 21.68/21.85 exact (zenon_H16b zenon_H93). % 21.68/21.85 (* end of lemma zenon_L715_ *) % 21.68/21.85 assert (zenon_L716_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H1a8 zenon_H67 zenon_H2c zenon_H1b3 zenon_H1c6 zenon_H6f zenon_H1ba zenon_Hf0 zenon_H55 zenon_H266 zenon_Hb6 zenon_H3f zenon_H16b zenon_H8b zenon_H2d zenon_H68 zenon_H16a zenon_Ha9. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.85 apply (zenon_L714_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.85 exact (zenon_H1b3 zenon_Hef). % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.85 exact (zenon_H1ba zenon_H6d). % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.68/21.85 apply (zenon_L703_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.68/21.85 apply (zenon_L216_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.68/21.85 apply (zenon_L715_); trivial. % 21.68/21.85 apply (zenon_L371_); trivial. % 21.68/21.85 (* end of lemma zenon_L716_ *) % 21.68/21.85 assert (zenon_L717_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H16a zenon_H68 zenon_H2d zenon_Hf0 zenon_Hef zenon_H8b zenon_H16b. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.85 apply (zenon_L27_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.85 apply (zenon_L61_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.85 exact (zenon_H8b zenon_H8a). % 21.68/21.85 exact (zenon_H16b zenon_H93). % 21.68/21.85 (* end of lemma zenon_L717_ *) % 21.68/21.85 assert (zenon_L718_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.68/21.85 do 0 intro. intros zenon_H164 zenon_H48 zenon_Hac zenon_Ha0 zenon_H31 zenon_H177 zenon_H67 zenon_H7e. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.85 apply (zenon_L456_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.85 apply (zenon_L107_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.85 apply (zenon_L406_); trivial. % 21.68/21.85 apply (zenon_L547_); trivial. % 21.68/21.85 (* end of lemma zenon_L718_ *) % 21.68/21.85 assert (zenon_L719_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (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 (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H117 zenon_H2d zenon_Ha9 zenon_H6d zenon_H1b4 zenon_H104 zenon_H164 zenon_H48 zenon_Ha0 zenon_H31 zenon_H177 zenon_H67 zenon_H7e zenon_Ha6 zenon_H179 zenon_H121 zenon_H9e zenon_H196. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.85 apply (zenon_L67_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.85 apply (zenon_L289_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.68/21.85 apply (zenon_L123_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.68/21.85 apply (zenon_L718_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.68/21.85 apply (zenon_L129_); trivial. % 21.68/21.85 apply (zenon_L602_); trivial. % 21.68/21.85 apply (zenon_L154_); trivial. % 21.68/21.85 (* end of lemma zenon_L719_ *) % 21.68/21.85 assert (zenon_L720_ : (((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 (e2) (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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (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 (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (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 (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H1a8 zenon_H6f zenon_H2c zenon_H16b zenon_Hf0 zenon_H16a zenon_H196 zenon_H9e zenon_H121 zenon_H179 zenon_Ha6 zenon_H7e zenon_H67 zenon_H177 zenon_Ha0 zenon_H48 zenon_H164 zenon_H104 zenon_H1b4 zenon_Ha9 zenon_H2d zenon_H117 zenon_H1cf zenon_H68 zenon_H31 zenon_Hf7 zenon_H186 zenon_H8b zenon_H1cd. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.85 apply (zenon_L714_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.85 apply (zenon_L717_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.85 apply (zenon_L719_); trivial. % 21.68/21.85 apply (zenon_L709_); trivial. % 21.68/21.85 (* end of lemma zenon_L720_ *) % 21.68/21.85 assert (zenon_L721_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((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 (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (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 (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (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 (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.68/21.85 do 0 intro. intros zenon_Hfa zenon_H24 zenon_H77 zenon_H4d zenon_H1a8 zenon_H6f zenon_H2c zenon_H16b zenon_Hf0 zenon_H16a zenon_H196 zenon_H9e zenon_H121 zenon_H179 zenon_Ha6 zenon_H7e zenon_H67 zenon_H177 zenon_Ha0 zenon_H48 zenon_H164 zenon_H104 zenon_H1b4 zenon_Ha9 zenon_H2d zenon_H117 zenon_H1cf zenon_H68 zenon_H31 zenon_H186 zenon_H8b zenon_H1cd. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.85 apply (zenon_L706_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.85 apply (zenon_L717_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.85 apply (zenon_L59_); trivial. % 21.68/21.85 apply (zenon_L720_); trivial. % 21.68/21.85 (* end of lemma zenon_L721_ *) % 21.68/21.85 assert (zenon_L722_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (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) (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)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (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) (e2)) = (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))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 21.68/21.85 do 0 intro. intros zenon_Hb2 zenon_H1cd zenon_H8b zenon_H186 zenon_H31 zenon_H68 zenon_H1cf zenon_H117 zenon_Ha9 zenon_H1b4 zenon_H104 zenon_H164 zenon_H48 zenon_H177 zenon_H67 zenon_H179 zenon_H121 zenon_H9e zenon_H196 zenon_H16a zenon_Hf0 zenon_H16b zenon_H2c zenon_H6f zenon_H1a8 zenon_H4d zenon_H77 zenon_H24 zenon_Hfa zenon_Ha0 zenon_H2d zenon_Hb6 zenon_H7e. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.68/21.85 apply (zenon_L701_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.68/21.85 apply (zenon_L721_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.68/21.85 apply (zenon_L67_); trivial. % 21.68/21.85 apply (zenon_L134_); trivial. % 21.68/21.85 (* end of lemma zenon_L722_ *) % 21.68/21.85 assert (zenon_L723_ : (((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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (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) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (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) (e2)) = (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))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H82 zenon_H4e zenon_H13a zenon_H3d zenon_Hb2 zenon_H1cd zenon_H8b zenon_H186 zenon_H31 zenon_H68 zenon_H1cf zenon_H117 zenon_Ha9 zenon_H1b4 zenon_H104 zenon_H164 zenon_H48 zenon_H177 zenon_H67 zenon_H179 zenon_H121 zenon_H196 zenon_H16a zenon_Hf0 zenon_H16b zenon_H2c zenon_H6f zenon_H1a8 zenon_H4d zenon_H77 zenon_H24 zenon_Hfa zenon_Ha0 zenon_H2d zenon_Hb6. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.85 apply (zenon_L251_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.85 apply (zenon_L14_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.85 apply (zenon_L217_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.85 apply (zenon_L701_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.85 apply (zenon_L55_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.85 apply (zenon_L68_); trivial. % 21.68/21.85 apply (zenon_L722_); trivial. % 21.68/21.85 (* end of lemma zenon_L723_ *) % 21.68/21.85 assert (zenon_L724_ : (((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)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H19a zenon_Ha0 zenon_H9e zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_He0 zenon_H1b7. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.68/21.85 apply (zenon_L156_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.68/21.85 apply (zenon_L157_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.68/21.85 apply (zenon_L158_); trivial. % 21.68/21.85 apply (zenon_L556_); trivial. % 21.68/21.85 (* end of lemma zenon_L724_ *) % 21.68/21.85 assert (zenon_L725_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H18d zenon_Hb6 zenon_H1b7 zenon_He0 zenon_H68 zenon_H48 zenon_H9e zenon_Ha0 zenon_H19a zenon_H93 zenon_H77 zenon_H7e zenon_H18a. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.68/21.85 apply (zenon_L115_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.68/21.85 apply (zenon_L724_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.68/21.85 apply (zenon_L218_); trivial. % 21.68/21.85 apply (zenon_L140_); trivial. % 21.68/21.85 (* end of lemma zenon_L725_ *) % 21.68/21.85 assert (zenon_L726_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> False). % 21.68/21.85 do 0 intro. intros zenon_H1a2 zenon_H67 zenon_Ha9 zenon_H72 zenon_Hb6 zenon_H105 zenon_Ha0 zenon_H11d. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.68/21.85 apply (zenon_L446_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.68/21.85 apply (zenon_L436_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.68/21.85 apply (zenon_L400_); trivial. % 21.68/21.85 apply (zenon_L80_); trivial. % 21.68/21.85 (* end of lemma zenon_L726_ *) % 21.68/21.85 assert (zenon_L727_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.68/21.85 do 0 intro. intros zenon_H16a zenon_H7b zenon_H1ba zenon_H8b zenon_H164 zenon_H18a zenon_H77 zenon_H19a zenon_H9e zenon_H48 zenon_H68 zenon_H1b7 zenon_H18d zenon_Ha0 zenon_H105 zenon_Hb6 zenon_H72 zenon_Ha9 zenon_H1a2 zenon_H67 zenon_H7e. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.85 exact (zenon_H7b zenon_H65). % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.85 exact (zenon_H1ba zenon_H6d). % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.85 exact (zenon_H8b zenon_H8a). % 21.68/21.85 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.85 apply (zenon_L456_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.85 apply (zenon_L725_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.85 apply (zenon_L726_); trivial. % 21.68/21.85 apply (zenon_L547_); trivial. % 21.68/21.85 (* end of lemma zenon_L727_ *) % 21.68/21.85 assert (zenon_L728_ : (((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 (e2) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (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))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.68/21.85 do 0 intro. intros zenon_H13a zenon_Ha9 zenon_H67 zenon_H6f zenon_H1ba zenon_H1f1 zenon_H55 zenon_H2d zenon_H266 zenon_H16a zenon_H68 zenon_H77 zenon_H8b zenon_H16b zenon_Hf0 zenon_He4 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H155. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.85 apply (zenon_L701_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.85 apply (zenon_L705_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.85 apply (zenon_L68_); trivial. % 21.68/21.85 apply (zenon_L115_); trivial. % 21.68/21.85 (* end of lemma zenon_L728_ *) % 21.68/21.85 assert (zenon_L729_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> False). % 21.68/21.85 do 0 intro. intros zenon_H266 zenon_H2d zenon_H55 zenon_H105 zenon_H190 zenon_H1ba zenon_H6f zenon_Hdb. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_Hdd | zenon_intro zenon_H267 ]. % 21.68/21.85 apply (zenon_L702_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H53 | zenon_intro zenon_H268 ]. % 21.68/21.85 apply (zenon_L143_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H6d | zenon_intro zenon_H10d ]. % 21.68/21.85 exact (zenon_H1ba zenon_H6d). % 21.68/21.85 apply (zenon_L205_); trivial. % 21.68/21.85 (* end of lemma zenon_L729_ *) % 21.68/21.85 assert (zenon_L730_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H13e zenon_H1ef zenon_Hdb zenon_H6f zenon_H1ba zenon_H190 zenon_H55 zenon_H2d zenon_H266 zenon_H8b zenon_H191. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H14c | zenon_intro zenon_H151 ]. % 21.68/21.85 apply (zenon_L405_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H105 | zenon_intro zenon_H152 ]. % 21.68/21.85 apply (zenon_L729_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H8a | zenon_intro zenon_H110 ]. % 21.68/21.85 exact (zenon_H8b zenon_H8a). % 21.68/21.85 exact (zenon_H191 zenon_H110). % 21.68/21.85 (* end of lemma zenon_L730_ *) % 21.68/21.85 assert (zenon_L731_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H117 zenon_Ha0 zenon_H2d zenon_H10c zenon_Hf0 zenon_H191 zenon_H9e zenon_H196. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.85 apply (zenon_L67_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.85 apply (zenon_L74_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.85 exact (zenon_H191 zenon_H110). % 21.68/21.85 apply (zenon_L154_); trivial. % 21.68/21.85 (* end of lemma zenon_L731_ *) % 21.68/21.85 assert (zenon_L732_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H13a zenon_Ha9 zenon_H67 zenon_Hb6 zenon_H3d zenon_Ha0 zenon_H31 zenon_Ha5 zenon_Hf5. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.85 apply (zenon_L701_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.85 apply (zenon_L55_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.85 apply (zenon_L68_); trivial. % 21.68/21.85 apply (zenon_L262_); trivial. % 21.68/21.85 (* end of lemma zenon_L732_ *) % 21.68/21.85 assert (zenon_L733_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (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 (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((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))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.85 do 0 intro. intros zenon_Hfa zenon_H77 zenon_H1b3 zenon_Hf5 zenon_H31 zenon_Ha0 zenon_H3d zenon_Hb6 zenon_H67 zenon_Ha9 zenon_H13a zenon_H117 zenon_H2d zenon_Hf0 zenon_H191 zenon_H9e zenon_H196 zenon_H3c zenon_H13c zenon_H16a zenon_H68 zenon_H2f zenon_H1ba zenon_H8b zenon_H195. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.85 apply (zenon_L24_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.85 exact (zenon_H1b3 zenon_Hef). % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.85 apply (zenon_L46_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.85 apply (zenon_L731_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.85 apply (zenon_L436_); trivial. % 21.68/21.85 apply (zenon_L732_); trivial. % 21.68/21.85 apply (zenon_L712_); trivial. % 21.68/21.85 (* end of lemma zenon_L733_ *) % 21.68/21.85 assert (zenon_L734_ : (((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)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> False). % 21.68/21.85 do 0 intro. intros zenon_H16a zenon_H68 zenon_H2d zenon_H1ba zenon_H8b zenon_H77 zenon_H128. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.85 apply (zenon_L27_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.85 exact (zenon_H1ba zenon_H6d). % 21.68/21.85 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.85 exact (zenon_H8b zenon_H8a). % 21.68/21.85 apply (zenon_L218_); trivial. % 21.68/21.85 (* end of lemma zenon_L734_ *) % 21.68/21.85 assert (zenon_L735_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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)) = (e2))) -> (((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)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H13f zenon_H10d zenon_H7e zenon_H67 zenon_H1a2 zenon_Ha9 zenon_H72 zenon_Hb6 zenon_Ha0 zenon_H18d zenon_H1b7 zenon_H48 zenon_H9e zenon_H19a zenon_H18a zenon_H164 zenon_H7b zenon_H16a zenon_H68 zenon_H2d zenon_H1ba zenon_H8b zenon_H77. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.68/21.85 apply (zenon_L217_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.68/21.85 apply (zenon_L113_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.68/21.85 apply (zenon_L727_); trivial. % 21.68/21.85 apply (zenon_L734_); trivial. % 21.68/21.85 (* end of lemma zenon_L735_ *) % 21.68/21.85 assert (zenon_L736_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((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) (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) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H13a zenon_H31 zenon_Hfa zenon_H24 zenon_Ha9 zenon_H13f zenon_H7e zenon_H67 zenon_H1a2 zenon_Hb6 zenon_Ha0 zenon_H18d zenon_H1b7 zenon_H48 zenon_H19a zenon_H18a zenon_H164 zenon_H7b zenon_H2d zenon_H77 zenon_H117 zenon_Hf0 zenon_H191 zenon_H196 zenon_H13e zenon_H1ef zenon_H6f zenon_H190 zenon_H55 zenon_H266 zenon_H1c6 zenon_H1b3 zenon_H3d zenon_H1a8 zenon_H16a zenon_H68 zenon_H2f zenon_H1ba zenon_H8b zenon_H195. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.85 apply (zenon_L701_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.85 apply (zenon_L730_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.85 apply (zenon_L68_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.85 apply (zenon_L706_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.85 exact (zenon_H1b3 zenon_Hef). % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.85 apply (zenon_L214_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.85 exact (zenon_H1b3 zenon_Hef). % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.85 exact (zenon_H1ba zenon_H6d). % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.68/21.85 apply (zenon_L730_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.68/21.85 apply (zenon_L731_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.68/21.85 apply (zenon_L735_); trivial. % 21.68/21.85 apply (zenon_L371_); trivial. % 21.68/21.85 apply (zenon_L712_); trivial. % 21.68/21.85 (* end of lemma zenon_L736_ *) % 21.68/21.85 assert (zenon_L737_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.68/21.85 do 0 intro. intros zenon_H13a zenon_Ha9 zenon_H67 zenon_H191 zenon_H8b zenon_H266 zenon_H2d zenon_H55 zenon_H190 zenon_H1ba zenon_H6f zenon_H1ef zenon_H13e zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H155. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.85 apply (zenon_L701_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.85 apply (zenon_L730_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.85 apply (zenon_L68_); trivial. % 21.68/21.85 apply (zenon_L115_); trivial. % 21.68/21.85 (* end of lemma zenon_L737_ *) % 21.68/21.85 assert (zenon_L738_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H153 zenon_H3d zenon_H1d8. % 21.68/21.85 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H135 ]. % 21.68/21.85 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e1)) = (op (e0) (e2)))). % 21.68/21.85 intro zenon_D_pnotp. % 21.68/21.85 apply zenon_H1d8. % 21.68/21.85 rewrite <- zenon_D_pnotp. % 21.68/21.85 exact zenon_H1d6. % 21.68/21.85 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 21.68/21.85 cut (((op (e0) (e2)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1d9]. % 21.68/21.85 congruence. % 21.68/21.85 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e0) (e1)))). % 21.68/21.85 intro zenon_D_pnotp. % 21.68/21.85 apply zenon_H1d9. % 21.68/21.85 rewrite <- zenon_D_pnotp. % 21.68/21.85 exact zenon_H153. % 21.68/21.85 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H269]. % 21.68/21.85 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 21.68/21.85 congruence. % 21.68/21.85 apply zenon_H135. apply refl_equal. % 21.68/21.85 apply zenon_H269. apply sym_equal. exact zenon_H3d. % 21.68/21.85 apply zenon_H135. apply refl_equal. % 21.68/21.85 apply zenon_H135. apply refl_equal. % 21.68/21.85 (* end of lemma zenon_L738_ *) % 21.68/21.85 assert (zenon_L739_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> (((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 (e2) (e3)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H201 zenon_H1d8 zenon_H4e zenon_H3c zenon_H196 zenon_H9e zenon_H6d zenon_H2d zenon_H117 zenon_H183 zenon_H128 zenon_H1cf zenon_H68 zenon_H31 zenon_H186 zenon_H8b zenon_H1cd zenon_H13a zenon_H33 zenon_H9d zenon_Hb6 zenon_H3d zenon_Ha0 zenon_Ha9 zenon_H1c3 zenon_H77 zenon_H181. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.68/21.85 apply (zenon_L738_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.68/21.85 apply (zenon_L14_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.68/21.85 apply (zenon_L404_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.68/21.85 apply (zenon_L91_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.68/21.85 apply (zenon_L710_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.68/21.85 apply (zenon_L367_); trivial. % 21.68/21.85 exact (zenon_H181 zenon_H17c). % 21.68/21.85 (* end of lemma zenon_L739_ *) % 21.68/21.85 assert (zenon_L740_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H201 zenon_H1d8 zenon_H3d zenon_H156 zenon_H3f zenon_H1bf zenon_H1cf zenon_H68 zenon_H31 zenon_H4e zenon_H76 zenon_H8b zenon_H77. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.68/21.85 apply (zenon_L738_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.68/21.85 apply (zenon_L486_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.68/21.85 exact (zenon_H1bf zenon_H105). % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.68/21.85 apply (zenon_L264_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.68/21.85 apply (zenon_L83_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.68/21.85 exact (zenon_H8b zenon_H8a). % 21.68/21.85 apply (zenon_L367_); trivial. % 21.68/21.85 (* end of lemma zenon_L740_ *) % 21.68/21.85 assert (zenon_L741_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H125 zenon_H177 zenon_Ha0 zenon_Hac zenon_H48 zenon_H164 zenon_H8b zenon_H4e zenon_H31 zenon_H1cf zenon_H1bf zenon_H3f zenon_H156 zenon_H3d zenon_H1d8 zenon_H201 zenon_H68 zenon_H2f zenon_H7e zenon_H77. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.68/21.85 apply (zenon_L718_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.68/21.85 apply (zenon_L740_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.68/21.85 apply (zenon_L28_); trivial. % 21.68/21.85 apply (zenon_L71_); trivial. % 21.68/21.85 (* end of lemma zenon_L741_ *) % 21.68/21.85 assert (zenon_L742_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (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 (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H1c6 zenon_Hb6 zenon_H16b zenon_Ha9 zenon_H2d zenon_H16a zenon_H125 zenon_H177 zenon_Ha0 zenon_H48 zenon_H164 zenon_H8b zenon_H4e zenon_H31 zenon_H1cf zenon_H1bf zenon_H3f zenon_H156 zenon_H3d zenon_H1d8 zenon_H201 zenon_H68 zenon_H2f zenon_H7e zenon_H77. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.68/21.85 apply (zenon_L55_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.68/21.85 apply (zenon_L216_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.68/21.85 apply (zenon_L715_); trivial. % 21.68/21.85 apply (zenon_L741_); trivial. % 21.68/21.85 (* end of lemma zenon_L742_ *) % 21.68/21.85 assert (zenon_L743_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.68/21.85 do 0 intro. intros zenon_H13a zenon_H47 zenon_Ha9 zenon_H6e zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H155. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.85 apply (zenon_L253_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.85 apply (zenon_L110_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.85 apply (zenon_L68_); trivial. % 21.68/21.85 apply (zenon_L115_); trivial. % 21.68/21.85 (* end of lemma zenon_L743_ *) % 21.68/21.85 assert (zenon_L744_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H139 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H47 zenon_H13a zenon_H68 zenon_H31 zenon_H155 zenon_H77. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.85 apply (zenon_L251_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.85 apply (zenon_L743_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.85 apply (zenon_L264_); trivial. % 21.68/21.85 apply (zenon_L98_); trivial. % 21.68/21.85 (* end of lemma zenon_L744_ *) % 21.68/21.85 assert (zenon_L745_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (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 (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H139 zenon_H16b zenon_H8b zenon_Hf0 zenon_H2c zenon_H16a zenon_Hef zenon_H173 zenon_H68 zenon_H31 zenon_H155 zenon_H77. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.85 apply (zenon_L620_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.85 apply (zenon_L226_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.85 apply (zenon_L264_); trivial. % 21.68/21.85 apply (zenon_L98_); trivial. % 21.68/21.85 (* end of lemma zenon_L745_ *) % 21.68/21.85 assert (zenon_L746_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 21.68/21.85 do 0 intro. intros zenon_H201 zenon_H48 zenon_H31 zenon_H77 zenon_H72 zenon_H1bf zenon_H1cd zenon_H7f. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.68/21.85 apply (zenon_L239_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.68/21.85 apply (zenon_L59_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.68/21.85 exact (zenon_H1bf zenon_H105). % 21.68/21.85 apply (zenon_L331_); trivial. % 21.68/21.85 (* end of lemma zenon_L746_ *) % 21.68/21.85 assert (zenon_L747_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.68/21.85 do 0 intro. intros zenon_Hc3 zenon_H9d zenon_H18a. % 21.68/21.85 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.68/21.85 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 21.68/21.85 intro zenon_D_pnotp. % 21.68/21.85 apply zenon_H18a. % 21.68/21.85 rewrite <- zenon_D_pnotp. % 21.68/21.85 exact zenon_H12a. % 21.68/21.85 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.68/21.85 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 21.68/21.85 congruence. % 21.68/21.85 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 21.68/21.85 intro zenon_D_pnotp. % 21.68/21.85 apply zenon_H18b. % 21.68/21.85 rewrite <- zenon_D_pnotp. % 21.68/21.85 exact zenon_Hc3. % 21.68/21.85 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 21.68/21.85 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.68/21.85 congruence. % 21.68/21.85 apply zenon_H12b. apply refl_equal. % 21.68/21.85 apply zenon_Hb0. apply sym_equal. exact zenon_H9d. % 21.68/21.85 apply zenon_H12b. apply refl_equal. % 21.68/21.85 apply zenon_H12b. apply refl_equal. % 21.68/21.85 (* end of lemma zenon_L747_ *) % 21.68/21.85 assert (zenon_L748_ : (((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) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H13f zenon_H3c zenon_H100 zenon_H7f zenon_H1f1 zenon_H1bf zenon_H26a zenon_H155 zenon_Hf7 zenon_Ha9 zenon_Hb6 zenon_H9d zenon_H18a. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.68/21.85 apply (zenon_L69_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.68/21.85 apply (zenon_L284_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.68/21.85 exact (zenon_H1bf zenon_H105). % 21.68/21.85 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H9e | zenon_intro zenon_H26b ]. % 21.68/21.85 apply (zenon_L115_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H26c ]. % 21.68/21.85 apply (zenon_L299_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc3 ]. % 21.68/21.85 apply (zenon_L182_); trivial. % 21.68/21.85 apply (zenon_L747_); trivial. % 21.68/21.85 (* end of lemma zenon_L748_ *) % 21.68/21.85 assert (zenon_L749_ : (((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)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.68/21.85 do 0 intro. intros zenon_H13a zenon_H33 zenon_H18a zenon_H9d zenon_Ha9 zenon_H26a zenon_H1bf zenon_H1f1 zenon_H100 zenon_H3c zenon_H13f zenon_H201 zenon_H48 zenon_H77 zenon_H1cd zenon_H139 zenon_H16b zenon_H8b zenon_Hf0 zenon_H2c zenon_H16a zenon_H173 zenon_H68 zenon_Hfa zenon_H2d zenon_H23c zenon_He4 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H155. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.85 apply (zenon_L245_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.68/21.85 apply (zenon_L55_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.68/21.85 apply (zenon_L492_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.68/21.85 apply (zenon_L327_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.85 apply (zenon_L24_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.85 apply (zenon_L745_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.85 apply (zenon_L746_); trivial. % 21.68/21.85 apply (zenon_L748_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.85 apply (zenon_L68_); trivial. % 21.68/21.85 apply (zenon_L115_); trivial. % 21.68/21.85 (* end of lemma zenon_L749_ *) % 21.68/21.85 assert (zenon_L750_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> False). % 21.68/21.85 do 0 intro. intros zenon_H1cf zenon_H68 zenon_H31 zenon_Hf7 zenon_H186 zenon_H8b zenon_H77 zenon_H106. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.68/21.85 apply (zenon_L264_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.68/21.85 apply (zenon_L438_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.68/21.85 exact (zenon_H8b zenon_H8a). % 21.68/21.85 apply (zenon_L367_); trivial. % 21.68/21.85 (* end of lemma zenon_L750_ *) % 21.68/21.85 assert (zenon_L751_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> False). % 21.68/21.85 do 0 intro. intros zenon_H201 zenon_H48 zenon_H156 zenon_H3f zenon_H1bf zenon_H1cf zenon_H68 zenon_H31 zenon_Hf7 zenon_H186 zenon_H8b zenon_H77. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.68/21.85 apply (zenon_L239_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.68/21.85 apply (zenon_L486_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.68/21.85 exact (zenon_H1bf zenon_H105). % 21.68/21.85 apply (zenon_L750_); trivial. % 21.68/21.85 (* end of lemma zenon_L751_ *) % 21.68/21.85 assert (zenon_L752_ : (((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 (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> False). % 21.68/21.85 do 0 intro. intros zenon_Hfa zenon_H67 zenon_H24 zenon_H1b3 zenon_H181 zenon_H16b zenon_H155 zenon_H1c3 zenon_H201 zenon_H48 zenon_H156 zenon_H3f zenon_H1bf zenon_H1cf zenon_H68 zenon_H31 zenon_H186 zenon_H8b zenon_H77. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.85 apply (zenon_L706_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.85 exact (zenon_H1b3 zenon_Hef). % 21.68/21.85 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.68/21.85 apply (zenon_L239_); trivial. % 21.68/21.85 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.68/21.86 apply (zenon_L59_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.68/21.86 exact (zenon_H1bf zenon_H105). % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.68/21.86 apply (zenon_L98_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.68/21.86 apply (zenon_L750_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.68/21.86 exact (zenon_H16b zenon_H93). % 21.68/21.86 exact (zenon_H181 zenon_H17c). % 21.68/21.86 apply (zenon_L751_); trivial. % 21.68/21.86 (* end of lemma zenon_L752_ *) % 21.68/21.86 assert (zenon_L753_ : (((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)) = (e1)) -> (~((op (e3) (e0)) = (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)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.68/21.86 do 0 intro. intros zenon_H13a zenon_Ha9 zenon_H67 zenon_H7e zenon_H7d zenon_H16a zenon_H68 zenon_H2d zenon_H77 zenon_H8b zenon_H16b zenon_H4d zenon_H156 zenon_He4 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H155. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.86 apply (zenon_L701_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.86 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.68/21.86 apply (zenon_L55_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.68/21.86 apply (zenon_L486_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.68/21.86 apply (zenon_L327_); trivial. % 21.68/21.86 apply (zenon_L31_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.86 apply (zenon_L68_); trivial. % 21.68/21.86 apply (zenon_L115_); trivial. % 21.68/21.86 (* end of lemma zenon_L753_ *) % 21.68/21.86 assert (zenon_L754_ : (((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 (e0) (e0)) = (op (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 (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((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)) = (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)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H15d zenon_Hfa zenon_H24 zenon_H1a8 zenon_H6f zenon_H2c zenon_Hf0 zenon_H196 zenon_H121 zenon_H179 zenon_H177 zenon_H164 zenon_H104 zenon_H1b4 zenon_H117 zenon_H1cf zenon_H186 zenon_H1cd zenon_Hb2 zenon_H82 zenon_H139 zenon_H4e zenon_H48 zenon_H13a zenon_Ha9 zenon_H67 zenon_H7d zenon_H16a zenon_H68 zenon_H2d zenon_H77 zenon_H8b zenon_H16b zenon_H4d zenon_H156 zenon_He4 zenon_Ha0 zenon_H31 zenon_Hb6. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.86 apply (zenon_L251_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.86 apply (zenon_L723_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.86 apply (zenon_L239_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.86 apply (zenon_L744_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.86 apply (zenon_L14_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.86 apply (zenon_L217_); trivial. % 21.68/21.86 apply (zenon_L753_); trivial. % 21.68/21.86 (* end of lemma zenon_L754_ *) % 21.68/21.86 assert (zenon_L755_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H13e zenon_H2d zenon_H1ef zenon_H4d zenon_H131 zenon_H8b zenon_H191. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H14c | zenon_intro zenon_H151 ]. % 21.68/21.86 apply (zenon_L405_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H105 | zenon_intro zenon_H152 ]. % 21.68/21.86 apply (zenon_L128_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H8a | zenon_intro zenon_H110 ]. % 21.68/21.86 exact (zenon_H8b zenon_H8a). % 21.68/21.86 exact (zenon_H191 zenon_H110). % 21.68/21.86 (* end of lemma zenon_L755_ *) % 21.68/21.86 assert (zenon_L756_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H38 zenon_H31 zenon_H26d. % 21.68/21.86 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H1fc | zenon_intro zenon_Hf9 ]. % 21.68/21.86 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e2)) = (op (e0) (e3)))). % 21.68/21.86 intro zenon_D_pnotp. % 21.68/21.86 apply zenon_H26d. % 21.68/21.86 rewrite <- zenon_D_pnotp. % 21.68/21.86 exact zenon_H1fc. % 21.68/21.86 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 21.68/21.86 cut (((op (e0) (e3)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H26e]. % 21.68/21.86 congruence. % 21.68/21.86 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e2)))). % 21.68/21.86 intro zenon_D_pnotp. % 21.68/21.86 apply zenon_H26e. % 21.68/21.86 rewrite <- zenon_D_pnotp. % 21.68/21.86 exact zenon_H38. % 21.68/21.86 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 21.68/21.86 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 21.68/21.86 congruence. % 21.68/21.86 apply zenon_Hf9. apply refl_equal. % 21.68/21.86 apply zenon_H26f. apply sym_equal. exact zenon_H31. % 21.68/21.86 apply zenon_Hf9. apply refl_equal. % 21.68/21.86 apply zenon_Hf9. apply refl_equal. % 21.68/21.86 (* end of lemma zenon_L756_ *) % 21.68/21.86 assert (zenon_L757_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H36 zenon_H31 zenon_H26d. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 21.68/21.86 apply (zenon_L756_); trivial. % 21.68/21.86 (* end of lemma zenon_L757_ *) % 21.68/21.86 assert (zenon_L758_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H3a zenon_H4d zenon_H4e. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 21.68/21.86 apply (zenon_L14_); trivial. % 21.68/21.86 (* end of lemma zenon_L758_ *) % 21.68/21.86 assert (zenon_L759_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 21.68/21.86 do 0 intro. intros zenon_H18d zenon_Hb6 zenon_H1b7 zenon_H68 zenon_H93 zenon_H48 zenon_H9e zenon_Ha0 zenon_H19a zenon_H53 zenon_H189 zenon_Hef zenon_He0. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.68/21.86 apply (zenon_L115_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.68/21.86 apply (zenon_L724_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.68/21.86 apply (zenon_L139_); trivial. % 21.68/21.86 apply (zenon_L662_); trivial. % 21.68/21.86 (* end of lemma zenon_L759_ *) % 21.68/21.86 assert (zenon_L760_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (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 (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.68/21.86 do 0 intro. intros zenon_H13f zenon_Ha8 zenon_He0 zenon_Hef zenon_H189 zenon_H19a zenon_Ha0 zenon_H9e zenon_H48 zenon_H68 zenon_H1b7 zenon_Hb6 zenon_H18d zenon_H4d zenon_H131 zenon_H77 zenon_H93. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.68/21.86 apply (zenon_L151_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.68/21.86 apply (zenon_L759_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.68/21.86 apply (zenon_L128_); trivial. % 21.68/21.86 apply (zenon_L218_); trivial. % 21.68/21.86 (* end of lemma zenon_L760_ *) % 21.68/21.86 assert (zenon_L761_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_Hfa zenon_H25 zenon_H77 zenon_H131 zenon_H4d zenon_H18d zenon_Hb6 zenon_H1b7 zenon_H68 zenon_H48 zenon_H9e zenon_Ha0 zenon_H19a zenon_H189 zenon_He0 zenon_Ha8 zenon_H13f zenon_H160 zenon_H163 zenon_H93 zenon_H195. % 21.68/21.86 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.86 apply (zenon_L171_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.86 apply (zenon_L760_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.86 apply (zenon_L227_); trivial. % 21.68/21.86 apply (zenon_L228_); trivial. % 21.68/21.86 (* end of lemma zenon_L761_ *) % 21.68/21.86 assert (zenon_L762_ : (((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)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H191 zenon_Hc3 zenon_H1cb. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.68/21.86 apply (zenon_L68_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.68/21.86 apply (zenon_L124_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.68/21.86 exact (zenon_H191 zenon_H110). % 21.68/21.86 apply (zenon_L622_); trivial. % 21.68/21.86 (* end of lemma zenon_L762_ *) % 21.68/21.86 assert (zenon_L763_ : (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (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)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H26d zenon_H1cb zenon_H191 zenon_H4d zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H1a2 zenon_Ha8 zenon_H94 zenon_Hfa zenon_H25 zenon_H77 zenon_H131 zenon_H18d zenon_H48 zenon_H19a zenon_H189 zenon_H13f zenon_H160 zenon_H163 zenon_H195 zenon_H26a zenon_H93 zenon_H68 zenon_He0 zenon_H1b7. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.68/21.86 apply (zenon_L756_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H9e | zenon_intro zenon_H26b ]. % 21.68/21.86 apply (zenon_L761_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H26c ]. % 21.68/21.86 apply (zenon_L90_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc3 ]. % 21.68/21.86 apply (zenon_L47_); trivial. % 21.68/21.86 apply (zenon_L762_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.68/21.86 apply (zenon_L158_); trivial. % 21.68/21.86 apply (zenon_L556_); trivial. % 21.68/21.86 (* end of lemma zenon_L763_ *) % 21.68/21.86 assert (zenon_L764_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H22d zenon_H14c zenon_H1ef zenon_H55 zenon_H53 zenon_H7b zenon_H26d zenon_H1cb zenon_H191 zenon_H4d zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H1a2 zenon_H94 zenon_Hfa zenon_H25 zenon_H77 zenon_H131 zenon_H18d zenon_H48 zenon_H19a zenon_H189 zenon_H13f zenon_H160 zenon_H163 zenon_H195 zenon_H26a zenon_H93 zenon_H68 zenon_He0 zenon_H1b7. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H2d | zenon_intro zenon_H22e ]. % 21.68/21.86 apply (zenon_L405_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H54 | zenon_intro zenon_H22f ]. % 21.68/21.86 apply (zenon_L15_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H65 | zenon_intro zenon_Ha8 ]. % 21.68/21.86 exact (zenon_H7b zenon_H65). % 21.68/21.86 apply (zenon_L763_); trivial. % 21.68/21.86 (* end of lemma zenon_L764_ *) % 21.68/21.86 assert (zenon_L765_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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 (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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 (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (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) (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.68/21.86 do 0 intro. intros zenon_H1cf zenon_H1d5 zenon_H125 zenon_H8b zenon_H164 zenon_H179 zenon_H1b7 zenon_H68 zenon_H93 zenon_H26a zenon_H195 zenon_H163 zenon_H13f zenon_H189 zenon_H19a zenon_H48 zenon_H18d zenon_H131 zenon_H77 zenon_H25 zenon_Hfa zenon_H94 zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H191 zenon_H1cb zenon_H26d zenon_H7b zenon_H53 zenon_H55 zenon_H1ef zenon_H22d zenon_H14c zenon_H104 zenon_H67 zenon_H7e. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.68/21.86 apply (zenon_L651_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.68/21.86 apply (zenon_L59_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.68/21.86 exact (zenon_H8b zenon_H8a). % 21.68/21.86 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.86 apply (zenon_L297_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.86 apply (zenon_L764_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.86 apply (zenon_L257_); trivial. % 21.68/21.86 apply (zenon_L547_); trivial. % 21.68/21.86 (* end of lemma zenon_L765_ *) % 21.68/21.86 assert (zenon_L766_ : (((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))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> False). % 21.68/21.86 do 0 intro. intros zenon_H16a zenon_H7b zenon_H53 zenon_H77 zenon_H8b zenon_H68 zenon_H115. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.86 exact (zenon_H7b zenon_H65). % 21.68/21.86 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.86 apply (zenon_L56_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.86 exact (zenon_H8b zenon_H8a). % 21.68/21.86 apply (zenon_L158_); trivial. % 21.68/21.86 (* end of lemma zenon_L766_ *) % 21.68/21.86 assert (zenon_L767_ : (((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 (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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 (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)) = (e2))) -> (((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))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H141 zenon_H13e zenon_H7e zenon_H67 zenon_H104 zenon_H22d zenon_H1ef zenon_H55 zenon_H26d zenon_H1cb zenon_H191 zenon_H4d zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H1a2 zenon_H94 zenon_Hfa zenon_H25 zenon_H131 zenon_H18d zenon_H48 zenon_H19a zenon_H189 zenon_H13f zenon_H163 zenon_H195 zenon_H26a zenon_H1b7 zenon_H179 zenon_H164 zenon_H125 zenon_H1d5 zenon_H1cf zenon_H1ba zenon_H16a zenon_H7b zenon_H53 zenon_H77 zenon_H8b zenon_H68. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.86 apply (zenon_L755_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.86 apply (zenon_L111_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.86 exact (zenon_H7b zenon_H65). % 21.68/21.86 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.86 exact (zenon_H1ba zenon_H6d). % 21.68/21.86 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.86 exact (zenon_H8b zenon_H8a). % 21.68/21.86 apply (zenon_L765_); trivial. % 21.68/21.86 apply (zenon_L766_); trivial. % 21.68/21.86 (* end of lemma zenon_L767_ *) % 21.68/21.86 assert (zenon_L768_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H82 zenon_H77 zenon_H67 zenon_H4e zenon_H5a zenon_H55 zenon_H53 zenon_H34 zenon_H48. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.86 apply (zenon_L251_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.86 apply (zenon_L16_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.86 apply (zenon_L15_); trivial. % 21.68/21.86 apply (zenon_L456_); trivial. % 21.68/21.86 (* end of lemma zenon_L768_ *) % 21.68/21.86 assert (zenon_L769_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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 (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 (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((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))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H141 zenon_H13e zenon_H1bf zenon_H89 zenon_H7e zenon_H67 zenon_H104 zenon_H22d zenon_H1ef zenon_H55 zenon_H26d zenon_H1cb zenon_H191 zenon_H4d zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H1a2 zenon_H94 zenon_Hfa zenon_H25 zenon_H131 zenon_H18d zenon_H48 zenon_H19a zenon_H189 zenon_H13f zenon_H163 zenon_H195 zenon_H26a zenon_H1b7 zenon_H179 zenon_H164 zenon_H125 zenon_H1d5 zenon_H1cf zenon_H5a zenon_H16a zenon_H7b zenon_H53 zenon_H77 zenon_H8b zenon_H68. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.86 apply (zenon_L645_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.86 apply (zenon_L111_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.86 exact (zenon_H7b zenon_H65). % 21.68/21.86 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.86 apply (zenon_L319_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.86 exact (zenon_H8b zenon_H8a). % 21.68/21.86 apply (zenon_L765_); trivial. % 21.68/21.86 apply (zenon_L766_); trivial. % 21.68/21.86 (* end of lemma zenon_L769_ *) % 21.68/21.86 assert (zenon_L770_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((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 (e2) (e2)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((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)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H91 zenon_H89 zenon_H16a zenon_H8b zenon_H53 zenon_H77 zenon_H7b zenon_H1fe zenon_H5a zenon_H4e zenon_H55 zenon_H141 zenon_H1cf zenon_H179 zenon_H22d zenon_H26d zenon_H31 zenon_H26a zenon_H1cb zenon_H1a2 zenon_H94 zenon_H13f zenon_H19a zenon_H1b7 zenon_Ha0 zenon_H189 zenon_H18d zenon_Hb6 zenon_H163 zenon_H195 zenon_Hfa zenon_H104 zenon_H164 zenon_H1d5 zenon_H125 zenon_H48 zenon_H1ef zenon_H131 zenon_H4d zenon_H13e zenon_H82 zenon_H67 zenon_H68 zenon_H92. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.68/21.86 apply (zenon_L378_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.68/21.86 apply (zenon_L20_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.86 apply (zenon_L251_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.86 apply (zenon_L16_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.86 apply (zenon_L15_); trivial. % 21.68/21.86 apply (zenon_L767_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.68/21.86 apply (zenon_L755_); trivial. % 21.68/21.86 apply (zenon_L768_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.68/21.86 apply (zenon_L378_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.68/21.86 apply (zenon_L20_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.86 apply (zenon_L251_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.86 apply (zenon_L16_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.86 apply (zenon_L15_); trivial. % 21.68/21.86 apply (zenon_L769_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.68/21.86 apply (zenon_L755_); trivial. % 21.68/21.86 apply (zenon_L768_); trivial. % 21.68/21.86 (* end of lemma zenon_L770_ *) % 21.68/21.86 assert (zenon_L771_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H139 zenon_H77 zenon_Hef zenon_H173 zenon_H68 zenon_H13a zenon_H47 zenon_Hb6 zenon_H3d zenon_Ha0 zenon_H31 zenon_Ha9. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.86 apply (zenon_L251_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.86 apply (zenon_L226_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.86 apply (zenon_L264_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.86 apply (zenon_L253_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.86 apply (zenon_L55_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.86 apply (zenon_L68_); trivial. % 21.68/21.86 apply (zenon_L92_); trivial. % 21.68/21.86 (* end of lemma zenon_L771_ *) % 21.68/21.86 assert (zenon_L772_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H18d zenon_H77 zenon_H31 zenon_H68 zenon_H173 zenon_Hef zenon_H16a zenon_H2c zenon_Hf0 zenon_H8b zenon_H16b zenon_H139 zenon_H186 zenon_H4d zenon_H53 zenon_H189 zenon_H7e zenon_H18a. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.68/21.86 apply (zenon_L745_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.68/21.86 apply (zenon_L138_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.68/21.86 apply (zenon_L139_); trivial. % 21.68/21.86 apply (zenon_L140_); trivial. % 21.68/21.86 (* end of lemma zenon_L772_ *) % 21.68/21.86 assert (zenon_L773_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H82 zenon_Ha9 zenon_Ha0 zenon_H3d zenon_Hb6 zenon_H13a zenon_H4e zenon_H55 zenon_H18d zenon_H77 zenon_H31 zenon_H68 zenon_H173 zenon_Hef zenon_H16a zenon_H2c zenon_Hf0 zenon_H8b zenon_H16b zenon_H139 zenon_H186 zenon_H4d zenon_H53 zenon_H189 zenon_H18a. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.86 apply (zenon_L771_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.86 apply (zenon_L14_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.86 apply (zenon_L15_); trivial. % 21.68/21.86 apply (zenon_L772_); trivial. % 21.68/21.86 (* end of lemma zenon_L773_ *) % 21.68/21.86 assert (zenon_L774_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((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) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H139 zenon_H1e zenon_H173 zenon_H68 zenon_H31 zenon_H16a zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_H196. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.86 apply (zenon_L20_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.86 apply (zenon_L226_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.86 apply (zenon_L264_); trivial. % 21.68/21.86 apply (zenon_L621_); trivial. % 21.68/21.86 (* end of lemma zenon_L774_ *) % 21.68/21.86 assert (zenon_L775_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((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) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H139 zenon_H77 zenon_H47 zenon_H173 zenon_H68 zenon_H31 zenon_H16a zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_H196. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.86 apply (zenon_L251_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.86 apply (zenon_L226_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.86 apply (zenon_L264_); trivial. % 21.68/21.86 apply (zenon_L621_); trivial. % 21.68/21.86 (* end of lemma zenon_L775_ *) % 21.68/21.86 assert (zenon_L776_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (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) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H82 zenon_H196 zenon_H8b zenon_Hef zenon_Hf0 zenon_H7b zenon_H16a zenon_H31 zenon_H68 zenon_H173 zenon_H77 zenon_H139 zenon_H4e zenon_H4d zenon_H55 zenon_H53 zenon_H34 zenon_H48. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.86 apply (zenon_L775_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.86 apply (zenon_L14_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.86 apply (zenon_L15_); trivial. % 21.68/21.86 apply (zenon_L456_); trivial. % 21.68/21.86 (* end of lemma zenon_L776_ *) % 21.68/21.86 assert (zenon_L777_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (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 (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((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 (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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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 (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (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) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H1fe zenon_H125 zenon_H1d5 zenon_H141 zenon_H104 zenon_H22d zenon_H26d zenon_H1cb zenon_Hb6 zenon_Ha0 zenon_H1a2 zenon_H94 zenon_Hfa zenon_H18d zenon_H19a zenon_H189 zenon_H13f zenon_H163 zenon_H195 zenon_H26a zenon_H1b7 zenon_H179 zenon_H164 zenon_H1cf zenon_H1ba zenon_H191 zenon_H131 zenon_H1ef zenon_H13e zenon_H82 zenon_H196 zenon_H8b zenon_Hef zenon_Hf0 zenon_H7b zenon_H16a zenon_H31 zenon_H68 zenon_H173 zenon_H77 zenon_H139 zenon_H4e zenon_H4d zenon_H55 zenon_H53 zenon_H48. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.68/21.86 apply (zenon_L774_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.86 apply (zenon_L775_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.86 apply (zenon_L25_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.86 apply (zenon_L15_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.86 apply (zenon_L767_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.86 apply (zenon_L226_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.86 apply (zenon_L651_); trivial. % 21.68/21.86 apply (zenon_L621_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.68/21.86 apply (zenon_L755_); trivial. % 21.68/21.86 apply (zenon_L776_); trivial. % 21.68/21.86 (* end of lemma zenon_L777_ *) % 21.68/21.86 assert (zenon_L778_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((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) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H92 zenon_H139 zenon_Hf0 zenon_H196 zenon_H31 zenon_Hef zenon_H173 zenon_H68 zenon_H82 zenon_H141 zenon_H1ba zenon_H1cf zenon_H179 zenon_H22d zenon_H26d zenon_H26a zenon_H1cb zenon_H1a2 zenon_H94 zenon_H13f zenon_H19a zenon_H1b7 zenon_Ha0 zenon_H189 zenon_H18d zenon_Hb6 zenon_H163 zenon_H195 zenon_Hfa zenon_H104 zenon_H164 zenon_H1d5 zenon_H125 zenon_H1ef zenon_H131 zenon_H4d zenon_H13e zenon_H55 zenon_H48 zenon_H4e zenon_H1fe zenon_H7b zenon_H77 zenon_H53 zenon_H8b zenon_H16a. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.68/21.86 apply (zenon_L378_); trivial. % 21.68/21.86 apply (zenon_L777_); trivial. % 21.68/21.86 (* end of lemma zenon_L778_ *) % 21.68/21.86 assert (zenon_L779_ : (((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) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_H16b. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.86 exact (zenon_H7b zenon_H65). % 21.68/21.86 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.86 apply (zenon_L61_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.86 exact (zenon_H8b zenon_H8a). % 21.68/21.86 exact (zenon_H16b zenon_H93). % 21.68/21.86 (* end of lemma zenon_L779_ *) % 21.68/21.86 assert (zenon_L780_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H11f zenon_H7f zenon_H1b7. % 21.68/21.86 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.68/21.86 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 21.68/21.86 intro zenon_D_pnotp. % 21.68/21.86 apply zenon_H1b7. % 21.68/21.86 rewrite <- zenon_D_pnotp. % 21.68/21.86 exact zenon_H12a. % 21.68/21.86 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.68/21.86 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 21.68/21.86 congruence. % 21.68/21.86 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 21.68/21.86 intro zenon_D_pnotp. % 21.68/21.86 apply zenon_H1b8. % 21.68/21.86 rewrite <- zenon_D_pnotp. % 21.68/21.86 exact zenon_H11f. % 21.68/21.86 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 21.68/21.86 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.68/21.86 congruence. % 21.68/21.86 apply zenon_H12b. apply refl_equal. % 21.68/21.86 apply zenon_H80. apply sym_equal. exact zenon_H7f. % 21.68/21.86 apply zenon_H12b. apply refl_equal. % 21.68/21.86 apply zenon_H12b. apply refl_equal. % 21.68/21.86 (* end of lemma zenon_L780_ *) % 21.68/21.86 assert (zenon_L781_ : (((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) (e3)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H1cf zenon_H68 zenon_H31 zenon_H77 zenon_H4d zenon_H8b zenon_H17c zenon_H1cb. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.68/21.86 apply (zenon_L264_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.68/21.86 apply (zenon_L59_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.68/21.86 exact (zenon_H8b zenon_H8a). % 21.68/21.86 apply (zenon_L236_); trivial. % 21.68/21.86 (* end of lemma zenon_L781_ *) % 21.68/21.86 assert (zenon_L782_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e2) (e2)) = (e2)) -> False). % 21.68/21.86 do 0 intro. intros zenon_H2f zenon_H8a. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.68/21.86 apply (zenon_L36_); trivial. % 21.68/21.86 (* end of lemma zenon_L782_ *) % 21.68/21.86 assert (zenon_L783_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> False). % 21.68/21.86 do 0 intro. intros zenon_Hcb zenon_H17c zenon_Hbb. % 21.68/21.86 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.68/21.86 exact (zenon_H1a3 zenon_Hbb). % 21.68/21.86 exact (zenon_H181 zenon_H17c). % 21.68/21.86 (* end of lemma zenon_L783_ *) % 21.68/21.86 assert (zenon_L784_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> False). % 21.68/21.86 do 0 intro. intros zenon_H36 zenon_H17c zenon_Hbb. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.68/21.86 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.68/21.86 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.68/21.86 apply (zenon_L783_); trivial. % 21.68/21.86 (* end of lemma zenon_L784_ *) % 21.68/21.86 assert (zenon_L785_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.68/21.86 do 0 intro. intros zenon_H139 zenon_H6c zenon_H77 zenon_H3d zenon_H8a zenon_H111 zenon_H17c zenon_H1b4. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.86 exact (zenon_H6c zenon_H67). % 21.68/21.86 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.86 apply (zenon_L214_); trivial. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.86 apply (zenon_L258_); trivial. % 21.68/21.86 apply (zenon_L347_); trivial. % 21.68/21.86 (* end of lemma zenon_L785_ *) % 21.68/21.86 assert (zenon_L786_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> False). % 21.68/21.86 do 0 intro. intros zenon_H3a zenon_H77 zenon_H111 zenon_H8a zenon_H1b4 zenon_H17c zenon_H139 zenon_H31. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.68/21.86 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 21.68/21.86 exact (zenon_H237 zenon_H31). % 21.68/21.86 apply (zenon_L785_); trivial. % 21.68/21.86 (* end of lemma zenon_L786_ *) % 21.68/21.86 assert (zenon_L787_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e2) (e2)) = (e2)) -> False). % 21.68/21.86 do 0 intro. intros zenon_H5a zenon_H8a. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.68/21.86 apply (zenon_L36_); trivial. % 21.68/21.86 (* end of lemma zenon_L787_ *) % 21.68/21.86 assert (zenon_L788_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> False). % 21.68/21.86 do 0 intro. intros zenon_H61 zenon_H17c zenon_Hbb. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 21.68/21.86 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.68/21.86 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.68/21.86 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.68/21.86 apply (zenon_L783_); trivial. % 21.68/21.86 (* end of lemma zenon_L788_ *) % 21.68/21.86 assert (zenon_L789_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 21.68/21.87 do 0 intro. intros zenon_H63 zenon_H111 zenon_H8a. % 21.68/21.87 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 21.68/21.87 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 21.68/21.87 apply (zenon_L258_); trivial. % 21.68/21.87 (* end of lemma zenon_L789_ *) % 21.68/21.87 assert (zenon_L790_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> False). % 21.68/21.87 do 0 intro. intros zenon_H99 zenon_H17c zenon_Hbb. % 21.68/21.87 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.68/21.87 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.68/21.87 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.68/21.87 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.68/21.87 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.68/21.87 apply (zenon_L783_); trivial. % 21.68/21.87 (* end of lemma zenon_L790_ *) % 21.68/21.87 assert (zenon_L791_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.68/21.87 do 0 intro. intros zenon_H9b zenon_Hbb zenon_Hbc. % 21.68/21.87 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.68/21.87 apply (zenon_L48_); trivial. % 21.68/21.87 (* end of lemma zenon_L791_ *) % 21.68/21.87 assert (zenon_L792_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e2) (e2)) = (e2)) -> False). % 21.68/21.87 do 0 intro. intros zenon_Hc0 zenon_H8a. % 21.68/21.87 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.68/21.87 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.68/21.87 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.68/21.87 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.68/21.87 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.68/21.87 apply (zenon_L36_); trivial. % 21.68/21.87 (* end of lemma zenon_L792_ *) % 21.68/21.87 assert (zenon_L793_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> False). % 21.68/21.87 do 0 intro. intros zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H1b4 zenon_H139 zenon_H1d8 zenon_H271 zenon_H68 zenon_H31 zenon_H77 zenon_H4d zenon_H1cb zenon_H17c zenon_H1cf. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ]. % 21.68/21.87 apply (zenon_L781_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 21.68/21.87 exact (zenon_H181 zenon_H17c). % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.68/21.87 apply (zenon_L2_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.68/21.87 apply (zenon_L700_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.68/21.87 apply (zenon_L782_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.68/21.87 apply (zenon_L784_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.68/21.87 apply (zenon_L786_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.68/21.87 apply (zenon_L11_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.68/21.87 apply (zenon_L787_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.68/21.87 apply (zenon_L788_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.68/21.87 apply (zenon_L789_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.68/21.87 apply (zenon_L343_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.68/21.87 apply (zenon_L37_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.68/21.87 apply (zenon_L790_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.68/21.87 apply (zenon_L791_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.68/21.87 apply (zenon_L361_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.68/21.87 apply (zenon_L792_); trivial. % 21.68/21.87 apply (zenon_L51_); trivial. % 21.68/21.87 (* end of lemma zenon_L793_ *) % 21.68/21.87 assert (zenon_L794_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (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) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (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 (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.68/21.87 do 0 intro. intros zenon_H1bb zenon_H18a zenon_H34 zenon_H1b7 zenon_H7f zenon_H1cf zenon_H77 zenon_H68 zenon_H271 zenon_H1d8 zenon_H139 zenon_H1b4 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H191 zenon_H1cb. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.68/21.87 apply (zenon_L416_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.68/21.87 apply (zenon_L780_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.68/21.87 apply (zenon_L793_); trivial. % 21.68/21.87 apply (zenon_L762_); trivial. % 21.68/21.87 (* end of lemma zenon_L794_ *) % 21.68/21.87 assert (zenon_L795_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.68/21.87 do 0 intro. intros zenon_H12e zenon_H48 zenon_H1cb zenon_H191 zenon_H4d zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H139 zenon_H1d8 zenon_H271 zenon_H68 zenon_H1cf zenon_H1b7 zenon_H34 zenon_H18a zenon_H1bb zenon_H160 zenon_H77 zenon_H155 zenon_H1b4. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.68/21.87 apply (zenon_L456_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.68/21.87 apply (zenon_L794_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.68/21.87 apply (zenon_L367_); trivial. % 21.68/21.87 apply (zenon_L187_); trivial. % 21.68/21.87 (* end of lemma zenon_L795_ *) % 21.68/21.87 assert (zenon_L796_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.68/21.87 do 0 intro. intros zenon_H92 zenon_H13e zenon_H1bf zenon_H2d zenon_H1ef zenon_H89 zenon_H93. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.68/21.87 exact (zenon_H16b zenon_H93). % 21.68/21.87 apply (zenon_L645_); trivial. % 21.68/21.87 (* end of lemma zenon_L796_ *) % 21.68/21.87 assert (zenon_L797_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 21.68/21.87 do 0 intro. intros zenon_H22d zenon_H93 zenon_H89 zenon_H1ef zenon_H1bf zenon_H13e zenon_H92 zenon_H55 zenon_H53 zenon_H7b zenon_Hb9 zenon_H94. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H2d | zenon_intro zenon_H22e ]. % 21.68/21.87 apply (zenon_L796_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H54 | zenon_intro zenon_H22f ]. % 21.68/21.87 apply (zenon_L15_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H65 | zenon_intro zenon_Ha8 ]. % 21.68/21.87 exact (zenon_H7b zenon_H65). % 21.68/21.87 apply (zenon_L47_); trivial. % 21.68/21.87 (* end of lemma zenon_L797_ *) % 21.68/21.87 assert (zenon_L798_ : (((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 (e2) (e1)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (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) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (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 (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((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))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> False). % 21.68/21.87 do 0 intro. intros zenon_H141 zenon_H94 zenon_H55 zenon_H92 zenon_H13e zenon_H1bf zenon_H1ef zenon_H89 zenon_H22d zenon_H191 zenon_Hf0 zenon_H10c zenon_H164 zenon_H1b4 zenon_H155 zenon_H1bb zenon_H18a zenon_H1cf zenon_H271 zenon_H1d8 zenon_H139 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H12e zenon_H1b7 zenon_H26a zenon_H195 zenon_H163 zenon_H13f zenon_H189 zenon_H19a zenon_H48 zenon_H18d zenon_H131 zenon_H25 zenon_Hfa zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H1cb zenon_H26d zenon_H104 zenon_H67 zenon_H7e zenon_H117 zenon_Hef zenon_H156 zenon_H5a zenon_H16a zenon_H7b zenon_H53 zenon_H77 zenon_H8b zenon_H68. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.87 apply (zenon_L644_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.87 apply (zenon_L111_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.87 exact (zenon_H7b zenon_H65). % 21.68/21.87 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.87 apply (zenon_L319_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.87 exact (zenon_H8b zenon_H8a). % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.68/21.87 apply (zenon_L264_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.68/21.87 apply (zenon_L100_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.68/21.87 exact (zenon_H8b zenon_H8a). % 21.68/21.87 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.87 apply (zenon_L795_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.87 apply (zenon_L763_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.87 apply (zenon_L257_); trivial. % 21.68/21.87 apply (zenon_L547_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.87 apply (zenon_L74_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.87 exact (zenon_H191 zenon_H110). % 21.68/21.87 apply (zenon_L797_); trivial. % 21.68/21.87 apply (zenon_L766_); trivial. % 21.68/21.87 (* end of lemma zenon_L798_ *) % 21.68/21.87 assert (zenon_L799_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.68/21.87 do 0 intro. intros zenon_H16a zenon_H7b zenon_H77 zenon_H5a zenon_H8b zenon_H19a zenon_H48 zenon_H155 zenon_Ha5 zenon_Ha0 zenon_H68 zenon_H67 zenon_H7e. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.87 exact (zenon_H7b zenon_H65). % 21.68/21.87 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.87 apply (zenon_L319_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.87 exact (zenon_H8b zenon_H8a). % 21.68/21.87 apply (zenon_L549_); trivial. % 21.68/21.87 (* end of lemma zenon_L799_ *) % 21.68/21.87 assert (zenon_L800_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((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)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (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) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.68/21.87 do 0 intro. intros zenon_H1fe zenon_H125 zenon_H1d5 zenon_H13c zenon_H156 zenon_H117 zenon_H104 zenon_H26d zenon_H1cb zenon_H1a2 zenon_Hfa zenon_H131 zenon_H18d zenon_H189 zenon_H13f zenon_H163 zenon_H195 zenon_H26a zenon_H1b7 zenon_H12e zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H1d8 zenon_H271 zenon_H1cf zenon_H18a zenon_H1bb zenon_H1b4 zenon_H164 zenon_H22d zenon_H89 zenon_H92 zenon_H94 zenon_H141 zenon_Hb6 zenon_H5a zenon_H19a zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H73 zenon_H179 zenon_H15d zenon_H191 zenon_H1bf zenon_H1ef zenon_H13e zenon_H82 zenon_H196 zenon_H8b zenon_Hef zenon_Hf0 zenon_H7b zenon_H16a zenon_H31 zenon_H68 zenon_H173 zenon_H77 zenon_H139 zenon_H4e zenon_H4d zenon_H55 zenon_H53 zenon_H48. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.68/21.87 apply (zenon_L774_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.87 apply (zenon_L775_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.87 apply (zenon_L775_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.87 apply (zenon_L14_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.87 apply (zenon_L15_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.87 apply (zenon_L769_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.87 apply (zenon_L214_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.87 apply (zenon_L264_); trivial. % 21.68/21.87 apply (zenon_L321_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.87 apply (zenon_L184_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.87 apply (zenon_L744_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.87 apply (zenon_L25_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.87 apply (zenon_L15_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.87 apply (zenon_L116_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.87 apply (zenon_L798_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.87 apply (zenon_L124_); trivial. % 21.68/21.87 apply (zenon_L799_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.87 apply (zenon_L226_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.87 apply (zenon_L651_); trivial. % 21.68/21.87 apply (zenon_L621_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.68/21.87 apply (zenon_L644_); trivial. % 21.68/21.87 apply (zenon_L776_); trivial. % 21.68/21.87 (* end of lemma zenon_L800_ *) % 21.68/21.87 assert (zenon_L801_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.68/21.87 do 0 intro. intros zenon_H139 zenon_H1e zenon_Hef zenon_H173 zenon_H68 zenon_H31 zenon_H155 zenon_H77. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.87 apply (zenon_L20_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.87 apply (zenon_L226_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.87 apply (zenon_L264_); trivial. % 21.68/21.87 apply (zenon_L98_); trivial. % 21.68/21.87 (* end of lemma zenon_L801_ *) % 21.68/21.87 assert (zenon_L802_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 21.68/21.87 do 0 intro. intros zenon_H7d zenon_H34 zenon_He0. % 21.68/21.87 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 21.68/21.87 intro zenon_D_pnotp. % 21.68/21.87 apply zenon_H7d. % 21.68/21.87 rewrite <- zenon_D_pnotp. % 21.68/21.87 exact zenon_H34. % 21.68/21.87 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 21.68/21.87 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 21.68/21.87 congruence. % 21.68/21.87 apply zenon_H81. apply refl_equal. % 21.68/21.87 apply zenon_H1f2. apply sym_equal. exact zenon_He0. % 21.68/21.87 (* end of lemma zenon_L802_ *) % 21.68/21.87 assert (zenon_L803_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.68/21.87 do 0 intro. intros zenon_H24e zenon_H34 zenon_H1b7 zenon_H11f zenon_H1cd zenon_H160 zenon_H9d zenon_H7d. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_He0 | zenon_intro zenon_H24f ]. % 21.68/21.87 apply (zenon_L802_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H7f | zenon_intro zenon_H250 ]. % 21.68/21.87 apply (zenon_L780_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H171 | zenon_intro zenon_Hac ]. % 21.68/21.87 apply (zenon_L240_); trivial. % 21.68/21.87 apply (zenon_L44_); trivial. % 21.68/21.87 (* end of lemma zenon_L803_ *) % 21.68/21.87 assert (zenon_L804_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.68/21.87 do 0 intro. intros zenon_H12e zenon_Hb6 zenon_H53 zenon_H1f1 zenon_H77 zenon_H24e zenon_H34 zenon_H1b7 zenon_H1cd zenon_H160 zenon_H9d zenon_H7d. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.68/21.87 apply (zenon_L134_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.68/21.87 apply (zenon_L284_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.68/21.87 apply (zenon_L367_); trivial. % 21.68/21.87 apply (zenon_L803_); trivial. % 21.68/21.87 (* end of lemma zenon_L804_ *) % 21.68/21.87 assert (zenon_L805_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.68/21.87 do 0 intro. intros zenon_H12e zenon_H48 zenon_H34 zenon_H53 zenon_H1f1 zenon_H4d zenon_H163 zenon_Hb6 zenon_Hc3. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.68/21.87 apply (zenon_L456_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.68/21.87 apply (zenon_L284_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.68/21.87 apply (zenon_L285_); trivial. % 21.68/21.87 apply (zenon_L81_); trivial. % 21.68/21.87 (* end of lemma zenon_L805_ *) % 21.68/21.87 assert (zenon_L806_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> False). % 21.68/21.87 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H65 zenon_Hb6 zenon_H53 zenon_H104 zenon_Hbb zenon_Ha0 zenon_H115. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.87 apply (zenon_L43_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.87 apply (zenon_L113_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.87 apply (zenon_L129_); trivial. % 21.68/21.87 apply (zenon_L77_); trivial. % 21.68/21.87 (* end of lemma zenon_L806_ *) % 21.68/21.87 assert (zenon_L807_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> False). % 21.68/21.87 do 0 intro. intros zenon_H1cf zenon_H68 zenon_H31 zenon_H8b zenon_H121 zenon_H1cd zenon_H1b7 zenon_H24e zenon_H77 zenon_H163 zenon_H4d zenon_H1f1 zenon_H34 zenon_H48 zenon_H12e zenon_Hb2 zenon_H47 zenon_H5d zenon_H7d zenon_Hf6 zenon_H26a zenon_H115 zenon_Ha0 zenon_H104 zenon_H53 zenon_H65 zenon_Ha9 zenon_H117 zenon_Hb6. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.68/21.87 apply (zenon_L264_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.68/21.87 apply (zenon_L59_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.68/21.87 exact (zenon_H8b zenon_H8a). % 21.68/21.87 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.68/21.87 apply (zenon_L456_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.68/21.87 apply (zenon_L284_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.68/21.87 apply (zenon_L367_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.68/21.87 apply (zenon_L804_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H9e | zenon_intro zenon_H26b ]. % 21.68/21.87 apply (zenon_L92_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H26c ]. % 21.68/21.87 apply (zenon_L356_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc3 ]. % 21.68/21.87 apply (zenon_L77_); trivial. % 21.68/21.87 apply (zenon_L805_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.68/21.87 apply (zenon_L806_); trivial. % 21.68/21.87 apply (zenon_L81_); trivial. % 21.68/21.87 (* end of lemma zenon_L807_ *) % 21.68/21.87 assert (zenon_L808_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 21.68/21.87 do 0 intro. intros zenon_H12e zenon_H9d zenon_Hb6 zenon_H48 zenon_H160 zenon_H77 zenon_Hef zenon_He0. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.68/21.87 apply (zenon_L134_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.68/21.87 apply (zenon_L57_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.68/21.87 apply (zenon_L367_); trivial. % 21.68/21.87 apply (zenon_L662_); trivial. % 21.68/21.87 (* end of lemma zenon_L808_ *) % 21.68/21.87 assert (zenon_L809_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((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)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (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) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.68/21.87 do 0 intro. intros zenon_H1fe zenon_H2c zenon_Hf0 zenon_H73 zenon_H18d zenon_H186 zenon_H189 zenon_H18a zenon_H125 zenon_H129 zenon_H177 zenon_H164 zenon_H156 zenon_H15d zenon_H16b zenon_H8b zenon_H1cf zenon_H121 zenon_H1cd zenon_H1b7 zenon_H24e zenon_H163 zenon_H1f1 zenon_H12e zenon_Hb2 zenon_H5d zenon_H7d zenon_H26a zenon_H104 zenon_H117 zenon_H16a zenon_H13d zenon_H141 zenon_H4d zenon_Hef zenon_H173 zenon_H82 zenon_H77 zenon_H31 zenon_H68 zenon_H13a zenon_Ha9 zenon_Ha0 zenon_Hb6 zenon_H139 zenon_H4e zenon_H5a zenon_H55 zenon_H53 zenon_H48. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.87 apply (zenon_L13_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.87 apply (zenon_L773_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.87 apply (zenon_L239_); trivial. % 21.68/21.87 apply (zenon_L801_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.87 apply (zenon_L620_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.87 apply (zenon_L226_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.87 apply (zenon_L264_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.68/21.87 apply (zenon_L251_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.68/21.87 apply (zenon_L171_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.68/21.87 apply (zenon_L253_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.68/21.87 apply (zenon_L116_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.68/21.87 apply (zenon_L112_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.87 apply (zenon_L27_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.87 apply (zenon_L111_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.87 exact (zenon_H13d zenon_H14c). % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.68/21.87 apply (zenon_L264_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.68/21.87 apply (zenon_L100_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.68/21.87 exact (zenon_H8b zenon_H8a). % 21.68/21.87 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.87 apply (zenon_L807_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.87 apply (zenon_L808_); trivial. % 21.68/21.87 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.88 apply (zenon_L406_); trivial. % 21.68/21.88 apply (zenon_L298_); trivial. % 21.68/21.88 apply (zenon_L325_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.88 apply (zenon_L771_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.88 apply (zenon_L25_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.88 apply (zenon_L15_); trivial. % 21.68/21.88 apply (zenon_L772_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.88 apply (zenon_L184_); trivial. % 21.68/21.88 apply (zenon_L745_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.68/21.88 apply (zenon_L327_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.88 apply (zenon_L251_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.88 apply (zenon_L226_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.88 apply (zenon_L264_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.88 apply (zenon_L327_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.88 apply (zenon_L111_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.88 exact (zenon_H13d zenon_H14c). % 21.68/21.88 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.68/21.88 apply (zenon_L807_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.68/21.88 apply (zenon_L319_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.68/21.88 exact (zenon_H8b zenon_H8a). % 21.68/21.88 exact (zenon_H16b zenon_H93). % 21.68/21.88 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.88 apply (zenon_L771_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.88 apply (zenon_L14_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.88 apply (zenon_L15_); trivial. % 21.68/21.88 apply (zenon_L456_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.88 apply (zenon_L239_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.88 apply (zenon_L744_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.88 apply (zenon_L16_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.88 apply (zenon_L15_); trivial. % 21.68/21.88 apply (zenon_L456_); trivial. % 21.68/21.88 (* end of lemma zenon_L809_ *) % 21.68/21.88 assert (zenon_L810_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (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) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((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 (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((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))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H1f1 zenon_H121 zenon_Hb2 zenon_H5d zenon_H24e zenon_H7d zenon_H177 zenon_H129 zenon_H2c zenon_H186 zenon_H190 zenon_H139 zenon_Hf0 zenon_H196 zenon_H31 zenon_Hef zenon_H173 zenon_H68 zenon_H82 zenon_H141 zenon_H1cf zenon_H179 zenon_H22d zenon_H26d zenon_H26a zenon_H1cb zenon_H1a2 zenon_H94 zenon_H13f zenon_H19a zenon_H1b7 zenon_Ha0 zenon_H189 zenon_H18d zenon_Hb6 zenon_H163 zenon_H195 zenon_Hfa zenon_H104 zenon_H164 zenon_H1d5 zenon_H125 zenon_H1ef zenon_H131 zenon_H13e zenon_H55 zenon_H48 zenon_H4e zenon_H1fe zenon_H77 zenon_H8b zenon_H16a zenon_H15d zenon_Ha9 zenon_H13a zenon_H1bb zenon_H271 zenon_H1d8 zenon_H1b4 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H18a zenon_H12e zenon_H117 zenon_H156 zenon_H13c zenon_H73 zenon_H5a. % 21.68/21.88 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.68/21.88 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.68/21.88 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.68/21.88 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.68/21.88 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.68/21.88 apply (zenon_L778_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.68/21.88 apply (zenon_L779_); trivial. % 21.68/21.88 apply (zenon_L800_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.68/21.88 apply (zenon_L809_); trivial. % 21.68/21.88 apply (zenon_L176_); trivial. % 21.68/21.88 (* end of lemma zenon_L810_ *) % 21.68/21.88 assert (zenon_L811_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((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)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (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)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H1a8 zenon_H16b zenon_H6f zenon_H67 zenon_H5a zenon_H73 zenon_H13c zenon_H156 zenon_H117 zenon_H12e zenon_H18a zenon_H270 zenon_Hcc zenon_Hbc zenon_H111 zenon_H1b4 zenon_H1d8 zenon_H271 zenon_H1bb zenon_H13a zenon_Ha9 zenon_H15d zenon_H16a zenon_H1fe zenon_H4e zenon_H48 zenon_H55 zenon_H13e zenon_H131 zenon_H1ef zenon_H125 zenon_H1d5 zenon_H164 zenon_H104 zenon_Hfa zenon_H195 zenon_H163 zenon_Hb6 zenon_H18d zenon_H189 zenon_Ha0 zenon_H1b7 zenon_H19a zenon_H13f zenon_H94 zenon_H1a2 zenon_H1cb zenon_H26a zenon_H26d zenon_H22d zenon_H179 zenon_H141 zenon_H82 zenon_H173 zenon_H196 zenon_Hf0 zenon_H139 zenon_H190 zenon_H2c zenon_H129 zenon_H177 zenon_H7d zenon_H24e zenon_H5d zenon_Hb2 zenon_H121 zenon_H1f1 zenon_H53 zenon_H77 zenon_H1cf zenon_H68 zenon_H31 zenon_Hf7 zenon_H186 zenon_H8b zenon_H1cd. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.88 apply (zenon_L714_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.88 apply (zenon_L810_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.88 apply (zenon_L56_); trivial. % 21.68/21.88 apply (zenon_L709_); trivial. % 21.68/21.88 (* end of lemma zenon_L811_ *) % 21.68/21.88 assert (zenon_L812_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (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) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (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 (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (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))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (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) (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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H1cd zenon_H186 zenon_H31 zenon_H1cf zenon_H1f1 zenon_H121 zenon_Hb2 zenon_H5d zenon_H24e zenon_H7d zenon_H177 zenon_H129 zenon_H2c zenon_H190 zenon_H139 zenon_Hf0 zenon_H196 zenon_H173 zenon_H141 zenon_H179 zenon_H22d zenon_H26d zenon_H26a zenon_H1cb zenon_H1a2 zenon_H94 zenon_H13f zenon_H19a zenon_H1b7 zenon_Ha0 zenon_H189 zenon_H18d zenon_Hb6 zenon_H163 zenon_H195 zenon_Hfa zenon_H104 zenon_H164 zenon_H1d5 zenon_H125 zenon_H1ef zenon_H131 zenon_H13e zenon_H1fe zenon_H15d zenon_Ha9 zenon_H13a zenon_H1bb zenon_H271 zenon_H1d8 zenon_H1b4 zenon_H111 zenon_Hbc zenon_Hcc zenon_H270 zenon_H18a zenon_H12e zenon_H117 zenon_H156 zenon_H13c zenon_H73 zenon_H6f zenon_H1a8 zenon_H4d zenon_H16b zenon_H8b zenon_H68 zenon_H16a zenon_H82 zenon_H77 zenon_H67 zenon_H4e zenon_H5a zenon_H55 zenon_H53 zenon_H48. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.68/21.88 apply (zenon_L20_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.88 apply (zenon_L251_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.88 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.88 apply (zenon_L171_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.88 apply (zenon_L773_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.88 apply (zenon_L59_); trivial. % 21.68/21.88 apply (zenon_L811_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.88 apply (zenon_L184_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.88 apply (zenon_L171_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.88 apply (zenon_L745_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.88 apply (zenon_L59_); trivial. % 21.68/21.88 apply (zenon_L811_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.68/21.88 apply (zenon_L327_); trivial. % 21.68/21.88 apply (zenon_L768_); trivial. % 21.68/21.88 (* end of lemma zenon_L812_ *) % 21.68/21.88 assert (zenon_L813_ : ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (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))))) -> (~((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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((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)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((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) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H8f zenon_H6f zenon_H73 zenon_H13c zenon_H156 zenon_H117 zenon_H12e zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H1b4 zenon_H1d8 zenon_H271 zenon_H1bb zenon_H15d zenon_H196 zenon_H190 zenon_H129 zenon_H177 zenon_H7d zenon_H24e zenon_H5d zenon_Hb2 zenon_H121 zenon_H1f1 zenon_H1a8 zenon_H139 zenon_Ha9 zenon_H13a zenon_H173 zenon_H18a zenon_H186 zenon_Hf0 zenon_H2c zenon_H92 zenon_H68 zenon_H67 zenon_H82 zenon_H13e zenon_H4d zenon_H131 zenon_H1ef zenon_H48 zenon_H125 zenon_H1d5 zenon_H164 zenon_H104 zenon_Hfa zenon_H195 zenon_H163 zenon_Hb6 zenon_H18d zenon_H189 zenon_Ha0 zenon_H1b7 zenon_H19a zenon_H13f zenon_H94 zenon_H1a2 zenon_H1cb zenon_H26a zenon_H31 zenon_H26d zenon_H22d zenon_H179 zenon_H1cf zenon_H141 zenon_H55 zenon_H4e zenon_H5a zenon_H1fe zenon_H77 zenon_H53 zenon_H8b zenon_H16a zenon_H89 zenon_H91. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.68/21.88 apply (zenon_L770_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.68/21.88 apply (zenon_L812_); trivial. % 21.68/21.88 apply (zenon_L176_); trivial. % 21.68/21.88 (* end of lemma zenon_L813_ *) % 21.68/21.88 assert (zenon_L814_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H63 zenon_H31 zenon_H68. % 21.68/21.88 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 21.68/21.88 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 21.68/21.88 apply (zenon_L264_); trivial. % 21.68/21.88 (* end of lemma zenon_L814_ *) % 21.68/21.88 assert (zenon_L815_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H121 zenon_H209 zenon_H1c7 zenon_H104 zenon_H110 zenon_Hc4. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.68/21.88 exact (zenon_H209 zenon_H9d). % 21.68/21.88 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.68/21.88 exact (zenon_H1c7 zenon_Hac). % 21.68/21.88 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.68/21.88 apply (zenon_L129_); trivial. % 21.68/21.88 exact (zenon_Hc4 zenon_Hc3). % 21.68/21.88 (* end of lemma zenon_L815_ *) % 21.68/21.88 assert (zenon_L816_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H1bb zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H155 zenon_H181 zenon_Hc4. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.68/21.88 apply (zenon_L560_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.68/21.88 apply (zenon_L187_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.68/21.88 exact (zenon_H181 zenon_H17c). % 21.68/21.88 exact (zenon_Hc4 zenon_Hc3). % 21.68/21.88 (* end of lemma zenon_L816_ *) % 21.68/21.88 assert (zenon_L817_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_H77 zenon_H1e zenon_H68 zenon_H139 zenon_H48 zenon_H31 zenon_H1bb zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.88 apply (zenon_L13_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.88 apply (zenon_L215_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.88 apply (zenon_L239_); trivial. % 21.68/21.88 apply (zenon_L816_); trivial. % 21.68/21.88 (* end of lemma zenon_L817_ *) % 21.68/21.88 assert (zenon_L818_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H139 zenon_H47 zenon_H77 zenon_H3d zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.88 apply (zenon_L251_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.88 apply (zenon_L214_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.88 apply (zenon_L122_); trivial. % 21.68/21.88 apply (zenon_L167_); trivial. % 21.68/21.88 (* end of lemma zenon_L818_ *) % 21.68/21.88 assert (zenon_L819_ : (((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)) = (e3))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H121 zenon_H33 zenon_H9f zenon_H1c7 zenon_H104 zenon_H110 zenon_Hc4. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.68/21.88 apply (zenon_L245_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.68/21.88 exact (zenon_H1c7 zenon_Hac). % 21.68/21.88 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.68/21.88 apply (zenon_L129_); trivial. % 21.68/21.88 exact (zenon_Hc4 zenon_Hc3). % 21.68/21.88 (* end of lemma zenon_L819_ *) % 21.68/21.88 assert (zenon_L820_ : (((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)) = (e2)) -> (~((e1) = (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)) = (e2)) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H160 zenon_H77 zenon_H25e zenon_H195 zenon_H93 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H9f zenon_Hb9 zenon_H196. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.68/21.88 apply (zenon_L456_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.68/21.88 apply (zenon_L146_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.68/21.88 apply (zenon_L367_); trivial. % 21.68/21.88 apply (zenon_L674_); trivial. % 21.68/21.88 (* end of lemma zenon_L820_ *) % 21.68/21.88 assert (zenon_L821_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H19a zenon_H26d zenon_H31 zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_He0 zenon_H1b7. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.68/21.88 apply (zenon_L756_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.68/21.88 apply (zenon_L157_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.68/21.88 apply (zenon_L158_); trivial. % 21.68/21.88 apply (zenon_L556_); trivial. % 21.68/21.88 (* end of lemma zenon_L821_ *) % 21.68/21.88 assert (zenon_L822_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (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)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 21.68/21.88 do 0 intro. intros zenon_H18d zenon_Hc4 zenon_H181 zenon_H1b4 zenon_H24e zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H160 zenon_Hbb zenon_H1cd zenon_H1bb zenon_H1b7 zenon_H68 zenon_H93 zenon_H48 zenon_H31 zenon_H26d zenon_H19a zenon_Hb9 zenon_Hb6 zenon_Hef zenon_He0. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.68/21.88 apply (zenon_L816_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.68/21.88 apply (zenon_L821_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.68/21.88 apply (zenon_L182_); trivial. % 21.68/21.88 apply (zenon_L662_); trivial. % 21.68/21.88 (* end of lemma zenon_L822_ *) % 21.68/21.88 assert (zenon_L823_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (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 (e1) (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))))) -> (~((e1) = (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 (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H164 zenon_H196 zenon_H9f zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H25e zenon_H77 zenon_H192 zenon_H3d zenon_H12e zenon_Hef zenon_Hb6 zenon_Hb9 zenon_H19a zenon_H26d zenon_H48 zenon_H93 zenon_H68 zenon_H1bb zenon_Hbb zenon_H1b4 zenon_H181 zenon_H18d zenon_H31 zenon_H177 zenon_H121 zenon_H11a zenon_H10c zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_Hc4. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.88 apply (zenon_L820_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.88 apply (zenon_L822_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.88 apply (zenon_L406_); trivial. % 21.68/21.88 apply (zenon_L561_); trivial. % 21.68/21.88 (* end of lemma zenon_L823_ *) % 21.68/21.88 assert (zenon_L824_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((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)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (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 (e1) (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))))) -> (~((e1) = (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 (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H117 zenon_H54 zenon_Hf0 zenon_H104 zenon_H1c7 zenon_H33 zenon_H164 zenon_H196 zenon_H9f zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H25e zenon_H77 zenon_H192 zenon_H3d zenon_H12e zenon_Hef zenon_Hb6 zenon_H19a zenon_H26d zenon_H48 zenon_H93 zenon_H68 zenon_H1bb zenon_Hbb zenon_H1b4 zenon_H181 zenon_H18d zenon_H31 zenon_H177 zenon_H121 zenon_H11a zenon_H10c zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_Hc4. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.88 apply (zenon_L151_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.88 apply (zenon_L74_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.88 apply (zenon_L819_); trivial. % 21.68/21.88 apply (zenon_L823_); trivial. % 21.68/21.88 (* end of lemma zenon_L824_ *) % 21.68/21.88 assert (zenon_L825_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.68/21.88 do 0 intro. intros zenon_H13f zenon_H48 zenon_H2d zenon_Hb6 zenon_H10d zenon_H4d zenon_H131 zenon_H77 zenon_H93. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.68/21.88 apply (zenon_L217_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.68/21.88 apply (zenon_L113_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.68/21.88 apply (zenon_L128_); trivial. % 21.68/21.88 apply (zenon_L218_); trivial. % 21.68/21.88 (* end of lemma zenon_L825_ *) % 21.68/21.88 assert (zenon_L826_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha0 zenon_Hdd zenon_H104 zenon_Hbb zenon_Ha5 zenon_H195. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.88 apply (zenon_L151_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.88 apply (zenon_L152_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.88 apply (zenon_L129_); trivial. % 21.68/21.88 apply (zenon_L172_); trivial. % 21.68/21.88 (* end of lemma zenon_L826_ *) % 21.68/21.88 assert (zenon_L827_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 21.68/21.88 do 0 intro. intros zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H93 zenon_H77 zenon_Hef zenon_He0. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.68/21.88 apply (zenon_L246_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.68/21.88 apply (zenon_L413_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.68/21.88 apply (zenon_L218_); trivial. % 21.68/21.88 apply (zenon_L662_); trivial. % 21.68/21.88 (* end of lemma zenon_L827_ *) % 21.68/21.88 assert (zenon_L828_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.88 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H25 zenon_He0 zenon_H77 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H160 zenon_H163 zenon_H93 zenon_H195. % 21.68/21.88 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.88 apply (zenon_L171_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.88 apply (zenon_L827_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.88 apply (zenon_L227_); trivial. % 21.68/21.88 apply (zenon_L228_); trivial. % 21.68/21.88 (* end of lemma zenon_L828_ *) % 21.68/21.88 assert (zenon_L829_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H19a zenon_H195 zenon_H163 zenon_H160 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H25 zenon_Hfa zenon_Ha5 zenon_Ha0 zenon_H93 zenon_H68 zenon_He0 zenon_H1b7. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.68/21.88 apply (zenon_L828_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.68/21.88 apply (zenon_L90_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.68/21.88 apply (zenon_L158_); trivial. % 21.68/21.88 apply (zenon_L556_); trivial. % 21.68/21.88 (* end of lemma zenon_L829_ *) % 21.68/21.88 assert (zenon_L830_ : (((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) (e1)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((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)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.68/21.88 do 0 intro. intros zenon_H141 zenon_H131 zenon_H4d zenon_H10d zenon_H13f zenon_H54 zenon_Hb6 zenon_H117 zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H104 zenon_H19a zenon_H195 zenon_H163 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H25 zenon_Hfa zenon_Ha5 zenon_Ha0 zenon_H179 zenon_H164 zenon_H68 zenon_H93. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.88 apply (zenon_L825_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.88 apply (zenon_L826_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.88 apply (zenon_L297_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.88 apply (zenon_L829_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.88 apply (zenon_L257_); trivial. % 21.68/21.88 apply (zenon_L560_); trivial. % 21.68/21.88 apply (zenon_L158_); trivial. % 21.68/21.88 (* end of lemma zenon_L830_ *) % 21.68/21.88 assert (zenon_L831_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.68/21.88 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_Hdb zenon_H156 zenon_H4d zenon_H55 zenon_H54 zenon_H212 zenon_H25 zenon_H179 zenon_H7d zenon_H160 zenon_Hbb zenon_Hbc. % 21.68/21.88 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.68/21.88 apply (zenon_L55_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.68/21.88 apply (zenon_L486_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.68/21.88 apply (zenon_L15_); trivial. % 21.68/21.88 apply (zenon_L658_); trivial. % 21.68/21.88 (* end of lemma zenon_L831_ *) % 21.68/21.88 assert (zenon_L832_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H117 zenon_Ha0 zenon_H2d zenon_Hb6 zenon_H53 zenon_H104 zenon_Hbb zenon_H9e zenon_H196. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.88 apply (zenon_L67_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.88 apply (zenon_L113_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.88 apply (zenon_L129_); trivial. % 21.68/21.88 apply (zenon_L154_); trivial. % 21.68/21.88 (* end of lemma zenon_L832_ *) % 21.68/21.88 assert (zenon_L833_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.68/21.88 do 0 intro. intros zenon_H13f zenon_H48 zenon_H196 zenon_H9e zenon_Hbb zenon_H104 zenon_Hb6 zenon_H2d zenon_Ha0 zenon_H117 zenon_H4d zenon_H131 zenon_H77 zenon_H93. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.68/21.88 apply (zenon_L217_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.68/21.88 apply (zenon_L832_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.68/21.88 apply (zenon_L128_); trivial. % 21.68/21.88 apply (zenon_L218_); trivial. % 21.68/21.88 (* end of lemma zenon_L833_ *) % 21.68/21.88 assert (zenon_L834_ : (((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)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.68/21.88 do 0 intro. intros zenon_H13f zenon_Hb6 zenon_Ha8 zenon_Hdd zenon_H48 zenon_H4d zenon_H131 zenon_H77 zenon_H93. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.68/21.88 apply (zenon_L151_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.68/21.88 apply (zenon_L111_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.68/21.88 apply (zenon_L128_); trivial. % 21.68/21.88 apply (zenon_L218_); trivial. % 21.68/21.88 (* end of lemma zenon_L834_ *) % 21.68/21.88 assert (zenon_L835_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e3)) = (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) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H117 zenon_H93 zenon_H77 zenon_H131 zenon_H4d zenon_H48 zenon_Hb6 zenon_H13f zenon_Ha0 zenon_Hdd zenon_Hc4 zenon_H104 zenon_H1c7 zenon_H9f zenon_H33 zenon_H121 zenon_H9e zenon_H196. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.88 apply (zenon_L834_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.88 apply (zenon_L152_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.88 apply (zenon_L819_); trivial. % 21.68/21.88 apply (zenon_L154_); trivial. % 21.68/21.88 (* end of lemma zenon_L835_ *) % 21.68/21.88 assert (zenon_L836_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 21.68/21.88 do 0 intro. intros zenon_H18d zenon_Hc4 zenon_H181 zenon_H1b4 zenon_H24e zenon_H1b7 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H160 zenon_Hbb zenon_H1cd zenon_H1bb zenon_H136 zenon_H48 zenon_H93 zenon_H77 zenon_Hef zenon_He0. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.68/21.88 apply (zenon_L816_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.68/21.88 apply (zenon_L157_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.68/21.88 apply (zenon_L218_); trivial. % 21.68/21.88 apply (zenon_L662_); trivial. % 21.68/21.88 (* end of lemma zenon_L836_ *) % 21.68/21.88 assert (zenon_L837_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (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) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.68/21.88 do 0 intro. intros zenon_H19a zenon_H195 zenon_H163 zenon_H129 zenon_H20f zenon_H25 zenon_Hfa zenon_Hef zenon_H77 zenon_H48 zenon_H1bb zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4 zenon_H18d zenon_H93 zenon_H68 zenon_He0 zenon_H1b7. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.68/21.88 apply (zenon_L828_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.68/21.88 apply (zenon_L836_); trivial. % 21.68/21.88 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.68/21.88 apply (zenon_L158_); trivial. % 21.68/21.88 apply (zenon_L556_); trivial. % 21.68/21.88 (* end of lemma zenon_L837_ *) % 21.68/21.88 assert (zenon_L838_ : ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (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) (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((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 (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H7e zenon_H67 zenon_H177 zenon_H31 zenon_H19a zenon_H129 zenon_H20f zenon_H25 zenon_Hfa zenon_H77 zenon_H48 zenon_H1bb zenon_H1cd zenon_Hbb zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4 zenon_H18d zenon_H68 zenon_H1b7 zenon_H179 zenon_H164 zenon_H160 zenon_H163 zenon_H93 zenon_H195. % 21.68/21.89 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.89 apply (zenon_L171_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.89 apply (zenon_L297_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.89 apply (zenon_L837_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.89 apply (zenon_L406_); trivial. % 21.68/21.89 apply (zenon_L547_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.89 apply (zenon_L227_); trivial. % 21.68/21.89 apply (zenon_L228_); trivial. % 21.68/21.89 (* end of lemma zenon_L838_ *) % 21.68/21.89 assert (zenon_L839_ : (((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)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H139 zenon_H195 zenon_H163 zenon_H164 zenon_H179 zenon_H1b7 zenon_H68 zenon_H18d zenon_Hc4 zenon_H181 zenon_H1b4 zenon_H24e zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_Hbb zenon_H1cd zenon_H1bb zenon_H48 zenon_Hfa zenon_H25 zenon_H20f zenon_H129 zenon_H19a zenon_H31 zenon_H7e zenon_H77 zenon_H3d zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.89 apply (zenon_L838_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.89 apply (zenon_L214_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.89 apply (zenon_L122_); trivial. % 21.68/21.89 apply (zenon_L167_); trivial. % 21.68/21.89 (* end of lemma zenon_L839_ *) % 21.68/21.89 assert (zenon_L840_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.68/21.89 do 0 intro. intros zenon_H13f zenon_H48 zenon_H2d zenon_H7f zenon_H1f1 zenon_H4d zenon_H131 zenon_H77 zenon_H93. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.68/21.89 apply (zenon_L217_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.68/21.89 apply (zenon_L284_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.68/21.89 apply (zenon_L128_); trivial. % 21.68/21.89 apply (zenon_L218_); trivial. % 21.68/21.89 (* end of lemma zenon_L840_ *) % 21.68/21.89 assert (zenon_L841_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((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) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.68/21.89 do 0 intro. intros zenon_He4 zenon_H6e zenon_H156 zenon_H196 zenon_H9e zenon_Hbb zenon_H104 zenon_Hb6 zenon_Ha0 zenon_H117 zenon_H13f zenon_H48 zenon_H2d zenon_H1f1 zenon_H4d zenon_H131 zenon_H77 zenon_H93. % 21.68/21.89 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.68/21.89 apply (zenon_L214_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.68/21.89 apply (zenon_L486_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.68/21.89 apply (zenon_L832_); trivial. % 21.68/21.89 apply (zenon_L840_); trivial. % 21.68/21.89 (* end of lemma zenon_L841_ *) % 21.68/21.89 assert (zenon_L842_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((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) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.68/21.89 do 0 intro. intros zenon_H13a zenon_H47 zenon_Ha9 zenon_H31 zenon_He4 zenon_H6e zenon_H156 zenon_H196 zenon_Hbb zenon_H104 zenon_Hb6 zenon_Ha0 zenon_H117 zenon_H13f zenon_H48 zenon_H2d zenon_H1f1 zenon_H4d zenon_H131 zenon_H77 zenon_H93. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.89 apply (zenon_L253_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.89 apply (zenon_L110_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.89 apply (zenon_L68_); trivial. % 21.68/21.89 apply (zenon_L841_); trivial. % 21.68/21.89 (* end of lemma zenon_L842_ *) % 21.68/21.89 assert (zenon_L843_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((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) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H139 zenon_H77 zenon_H131 zenon_H4d zenon_H1f1 zenon_H2d zenon_H48 zenon_H13f zenon_H117 zenon_Ha0 zenon_Hb6 zenon_H104 zenon_Hbb zenon_H156 zenon_He4 zenon_H31 zenon_Ha9 zenon_H47 zenon_H13a zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.89 apply (zenon_L251_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.89 apply (zenon_L842_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.89 apply (zenon_L122_); trivial. % 21.68/21.89 apply (zenon_L167_); trivial. % 21.68/21.89 (* end of lemma zenon_L843_ *) % 21.68/21.89 assert (zenon_L844_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (((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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e2) (e3)))) -> (((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)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.68/21.89 do 0 intro. intros zenon_H13f zenon_Hc4 zenon_H24e zenon_H1b7 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H160 zenon_H1cd zenon_H10c zenon_H11a zenon_H121 zenon_H177 zenon_H31 zenon_H18d zenon_H181 zenon_H1b4 zenon_Hbb zenon_H1bb zenon_H68 zenon_H48 zenon_H26d zenon_H19a zenon_Hb6 zenon_Hef zenon_H12e zenon_H3d zenon_H192 zenon_H25e zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H9f zenon_H196 zenon_H164 zenon_H33 zenon_H1c7 zenon_H104 zenon_H2d zenon_Ha0 zenon_H117 zenon_H4d zenon_H131 zenon_H77 zenon_H93. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.68/21.89 apply (zenon_L217_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.89 apply (zenon_L67_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.89 apply (zenon_L113_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.89 apply (zenon_L819_); trivial. % 21.68/21.89 apply (zenon_L823_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.68/21.89 apply (zenon_L128_); trivial. % 21.68/21.89 apply (zenon_L218_); trivial. % 21.68/21.89 (* end of lemma zenon_L844_ *) % 21.68/21.89 assert (zenon_L845_ : (((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))))) -> (~((e0) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (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 (e1) (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) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H1c6 zenon_H117 zenon_Ha0 zenon_H104 zenon_H33 zenon_H164 zenon_H196 zenon_H9f zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H25e zenon_H192 zenon_H3d zenon_H12e zenon_Hef zenon_H19a zenon_H26d zenon_H68 zenon_H1bb zenon_Hbb zenon_H1b4 zenon_H181 zenon_H18d zenon_H31 zenon_H177 zenon_H121 zenon_H11a zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_Hc4 zenon_H93 zenon_H77 zenon_H131 zenon_H4d zenon_Hb6 zenon_H2d zenon_H48 zenon_H13f zenon_H1c7. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.68/21.89 apply (zenon_L55_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.68/21.89 apply (zenon_L844_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.68/21.89 apply (zenon_L825_); trivial. % 21.68/21.89 exact (zenon_H1c7 zenon_Hac). % 21.68/21.89 (* end of lemma zenon_L845_ *) % 21.68/21.89 assert (zenon_L846_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H11f zenon_H106 zenon_H1cb. % 21.68/21.89 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.68/21.89 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 21.68/21.89 intro zenon_D_pnotp. % 21.68/21.89 apply zenon_H1cb. % 21.68/21.89 rewrite <- zenon_D_pnotp. % 21.68/21.89 exact zenon_H12a. % 21.68/21.89 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.68/21.89 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1cc]. % 21.68/21.89 congruence. % 21.68/21.89 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 21.68/21.89 intro zenon_D_pnotp. % 21.68/21.89 apply zenon_H1cc. % 21.68/21.89 rewrite <- zenon_D_pnotp. % 21.68/21.89 exact zenon_H11f. % 21.68/21.89 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 21.68/21.89 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.68/21.89 congruence. % 21.68/21.89 apply zenon_H12b. apply refl_equal. % 21.68/21.89 apply zenon_H107. apply sym_equal. exact zenon_H106. % 21.68/21.89 apply zenon_H12b. apply refl_equal. % 21.68/21.89 apply zenon_H12b. apply refl_equal. % 21.68/21.89 (* end of lemma zenon_L846_ *) % 21.68/21.89 assert (zenon_L847_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H1bb zenon_H18a zenon_H34 zenon_H106 zenon_H1cb zenon_H160 zenon_Hc4. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.68/21.89 apply (zenon_L416_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.68/21.89 apply (zenon_L846_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.68/21.89 apply (zenon_L236_); trivial. % 21.68/21.89 exact (zenon_Hc4 zenon_Hc3). % 21.68/21.89 (* end of lemma zenon_L847_ *) % 21.68/21.89 assert (zenon_L848_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H11f zenon_H1cd zenon_H160 zenon_H1c7. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_He0 | zenon_intro zenon_H24f ]. % 21.68/21.89 apply (zenon_L802_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H7f | zenon_intro zenon_H250 ]. % 21.68/21.89 apply (zenon_L780_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H171 | zenon_intro zenon_Hac ]. % 21.68/21.89 apply (zenon_L240_); trivial. % 21.68/21.89 exact (zenon_H1c7 zenon_Hac). % 21.68/21.89 (* end of lemma zenon_L848_ *) % 21.68/21.89 assert (zenon_L849_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H12e zenon_H48 zenon_H53 zenon_H1f1 zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H160 zenon_H1c7. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.68/21.89 apply (zenon_L456_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.68/21.89 apply (zenon_L284_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.68/21.89 apply (zenon_L847_); trivial. % 21.68/21.89 apply (zenon_L848_); trivial. % 21.68/21.89 (* end of lemma zenon_L849_ *) % 21.68/21.89 assert (zenon_L850_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H139 zenon_H77 zenon_H155 zenon_Hb6 zenon_Hbb zenon_Ha9 zenon_H47 zenon_H13a zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.89 apply (zenon_L251_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.89 apply (zenon_L253_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.89 apply (zenon_L110_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.89 apply (zenon_L178_); trivial. % 21.68/21.89 apply (zenon_L115_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.89 apply (zenon_L122_); trivial. % 21.68/21.89 apply (zenon_L167_); trivial. % 21.68/21.89 (* end of lemma zenon_L850_ *) % 21.68/21.89 assert (zenon_L851_ : (((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)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H19a zenon_Ha0 zenon_H9e zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H34 zenon_H18a. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.68/21.89 apply (zenon_L156_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.68/21.89 apply (zenon_L157_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.68/21.89 apply (zenon_L158_); trivial. % 21.68/21.89 apply (zenon_L416_); trivial. % 21.68/21.89 (* end of lemma zenon_L851_ *) % 21.68/21.89 assert (zenon_L852_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (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) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H18d zenon_H196 zenon_H177 zenon_H160 zenon_H13a zenon_H47 zenon_Ha9 zenon_Hbb zenon_Hb6 zenon_H139 zenon_H18a zenon_H34 zenon_H68 zenon_H48 zenon_H9e zenon_Ha0 zenon_H19a zenon_H93 zenon_H77 zenon_H7f zenon_H1b7. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.68/21.89 apply (zenon_L850_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.68/21.89 apply (zenon_L851_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.68/21.89 apply (zenon_L218_); trivial. % 21.68/21.89 apply (zenon_L780_); trivial. % 21.68/21.89 (* end of lemma zenon_L852_ *) % 21.68/21.89 assert (zenon_L853_ : (((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)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H12e zenon_H48 zenon_H3d zenon_H192 zenon_H4d zenon_H163 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H160 zenon_H1c7. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.68/21.89 apply (zenon_L456_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.68/21.89 apply (zenon_L146_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.68/21.89 apply (zenon_L285_); trivial. % 21.68/21.89 apply (zenon_L848_); trivial. % 21.68/21.89 (* end of lemma zenon_L853_ *) % 21.68/21.89 assert (zenon_L854_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e0)) = (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) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_He4 zenon_H156 zenon_H1cb zenon_H1f1 zenon_H18d zenon_H13a zenon_Ha9 zenon_Hb6 zenon_H139 zenon_H68 zenon_Ha0 zenon_H19a zenon_H77 zenon_H1c7 zenon_H34 zenon_H163 zenon_H192 zenon_H48 zenon_H12e zenon_H73 zenon_H4d zenon_H1bb zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.89 apply (zenon_L251_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.89 apply (zenon_L253_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.89 apply (zenon_L110_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.89 apply (zenon_L178_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.68/21.89 apply (zenon_L214_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.68/21.89 apply (zenon_L486_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.68/21.89 apply (zenon_L849_); trivial. % 21.68/21.89 apply (zenon_L852_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.89 apply (zenon_L122_); trivial. % 21.68/21.89 apply (zenon_L167_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.89 apply (zenon_L853_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.89 apply (zenon_L184_); trivial. % 21.68/21.89 apply (zenon_L816_); trivial. % 21.68/21.89 (* end of lemma zenon_L854_ *) % 21.68/21.89 assert (zenon_L855_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((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 (e1) (e1)) = (op (e2) (e1)))) -> (((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e2) (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 (e0) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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 (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> (~((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) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H1fe zenon_H82 zenon_H13c zenon_Hf0 zenon_H141 zenon_Hb2 zenon_H55 zenon_H179 zenon_Hfa zenon_H129 zenon_H125 zenon_H94 zenon_H11a zenon_H121 zenon_H26d zenon_Hef zenon_H25e zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H164 zenon_H33 zenon_H1c6 zenon_H31 zenon_H13f zenon_H104 zenon_H117 zenon_H131 zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_He4 zenon_H156 zenon_H1cb zenon_H1f1 zenon_H18d zenon_H13a zenon_Ha9 zenon_Hb6 zenon_H139 zenon_H68 zenon_Ha0 zenon_H19a zenon_H77 zenon_H1c7 zenon_H163 zenon_H192 zenon_H48 zenon_H12e zenon_H73 zenon_H4d zenon_H1bb zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.68/21.89 apply (zenon_L817_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.89 apply (zenon_L541_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.89 apply (zenon_L818_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.89 apply (zenon_L25_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.89 apply (zenon_L116_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.89 apply (zenon_L824_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.89 apply (zenon_L124_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.68/21.89 apply (zenon_L55_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.68/21.89 apply (zenon_L824_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.68/21.89 apply (zenon_L830_); trivial. % 21.68/21.89 exact (zenon_H1c7 zenon_Hac). % 21.68/21.89 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.89 apply (zenon_L831_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.89 apply (zenon_L178_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.89 apply (zenon_L116_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.89 apply (zenon_L833_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.89 apply (zenon_L835_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.89 apply (zenon_L581_); trivial. % 21.68/21.89 apply (zenon_L158_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.89 apply (zenon_L124_); trivial. % 21.68/21.89 apply (zenon_L262_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.68/21.89 apply (zenon_L116_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.68/21.89 apply (zenon_L151_); trivial. % 21.68/21.89 exact (zenon_H209 zenon_H9d). % 21.68/21.89 apply (zenon_L839_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.89 apply (zenon_L239_); trivial. % 21.68/21.89 apply (zenon_L816_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.89 apply (zenon_L843_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.89 apply (zenon_L845_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.89 apply (zenon_L55_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.89 apply (zenon_L68_); trivial. % 21.68/21.89 apply (zenon_L833_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.89 apply (zenon_L184_); trivial. % 21.68/21.89 apply (zenon_L816_); trivial. % 21.68/21.89 apply (zenon_L854_); trivial. % 21.68/21.89 (* end of lemma zenon_L855_ *) % 21.68/21.89 assert (zenon_L856_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.89 do 0 intro. intros zenon_He4 zenon_H77 zenon_H6e zenon_H156 zenon_H4d zenon_H55 zenon_H54 zenon_H1bb zenon_H209 zenon_H160 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H120 zenon_H129 zenon_H93 zenon_Hc4. % 21.68/21.89 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.68/21.89 apply (zenon_L214_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.68/21.89 apply (zenon_L486_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.68/21.89 apply (zenon_L15_); trivial. % 21.68/21.89 apply (zenon_L527_); trivial. % 21.68/21.89 (* end of lemma zenon_L856_ *) % 21.68/21.89 assert (zenon_L857_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (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 (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H139 zenon_H68 zenon_H1e zenon_Hc4 zenon_H129 zenon_H120 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H54 zenon_H55 zenon_H4d zenon_H156 zenon_H77 zenon_He4 zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.89 apply (zenon_L20_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.89 apply (zenon_L856_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.89 apply (zenon_L122_); trivial. % 21.68/21.89 apply (zenon_L167_); trivial. % 21.68/21.89 (* end of lemma zenon_L857_ *) % 21.68/21.89 assert (zenon_L858_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.68/21.89 do 0 intro. intros zenon_H141 zenon_H1e zenon_H2c zenon_H53 zenon_H48 zenon_H110 zenon_Ha0 zenon_H68 zenon_H93. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.89 apply (zenon_L5_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.89 apply (zenon_L111_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.89 apply (zenon_L278_); trivial. % 21.68/21.89 apply (zenon_L158_); trivial. % 21.68/21.89 (* end of lemma zenon_L858_ *) % 21.68/21.89 assert (zenon_L859_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (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) (e2)) = (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) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H82 zenon_H4e zenon_H55 zenon_H120 zenon_H129 zenon_H7d zenon_H1a2 zenon_Hb6 zenon_H4d zenon_Ha0 zenon_H2c zenon_H141 zenon_H15d zenon_H177 zenon_H77 zenon_H1e zenon_H139 zenon_H48 zenon_H1bb zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4 zenon_H156 zenon_He4 zenon_H68 zenon_H31 zenon_H93 zenon_H196. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.89 apply (zenon_L13_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.89 apply (zenon_L14_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.89 apply (zenon_L857_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.89 apply (zenon_L20_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.68/21.89 apply (zenon_L214_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.68/21.89 apply (zenon_L486_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.68/21.89 apply (zenon_L68_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.68/21.89 apply (zenon_L124_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.68/21.89 apply (zenon_L858_); trivial. % 21.68/21.89 apply (zenon_L817_); trivial. % 21.68/21.89 apply (zenon_L31_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.89 apply (zenon_L264_); trivial. % 21.68/21.89 apply (zenon_L167_); trivial. % 21.68/21.89 (* end of lemma zenon_L859_ *) % 21.68/21.89 assert (zenon_L860_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H19a zenon_H77 zenon_H93 zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H120 zenon_H1bb zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_Hb9 zenon_H195. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.68/21.89 apply (zenon_L555_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.68/21.89 apply (zenon_L422_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.68/21.89 apply (zenon_L77_); trivial. % 21.68/21.89 apply (zenon_L684_); trivial. % 21.68/21.89 (* end of lemma zenon_L860_ *) % 21.68/21.89 assert (zenon_L861_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H117 zenon_H131 zenon_Hb6 zenon_H13f zenon_Hdd zenon_H104 zenon_Hbb zenon_H19a zenon_H77 zenon_H93 zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H120 zenon_H1bb zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_H195. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.89 apply (zenon_L834_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.89 apply (zenon_L152_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.89 apply (zenon_L129_); trivial. % 21.68/21.89 apply (zenon_L860_); trivial. % 21.68/21.89 (* end of lemma zenon_L861_ *) % 21.68/21.89 assert (zenon_L862_ : (((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)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H164 zenon_H179 zenon_H1b7 zenon_H68 zenon_H93 zenon_Ha0 zenon_Ha5 zenon_Hfa zenon_H25 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H163 zenon_H195 zenon_H19a zenon_H31 zenon_H177 zenon_H12e zenon_H67 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H160 zenon_H77 zenon_H120. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.89 apply (zenon_L297_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.89 apply (zenon_L829_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.89 apply (zenon_L406_); trivial. % 21.68/21.89 apply (zenon_L558_); trivial. % 21.68/21.89 (* end of lemma zenon_L862_ *) % 21.68/21.89 assert (zenon_L863_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.68/21.89 do 0 intro. intros zenon_H19a zenon_He0 zenon_Hef zenon_H77 zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H120 zenon_H20f zenon_H1bb zenon_H93 zenon_H68 zenon_H67 zenon_H7e. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.68/21.89 apply (zenon_L827_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.68/21.89 apply (zenon_L422_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.68/21.89 apply (zenon_L158_); trivial. % 21.68/21.89 apply (zenon_L547_); trivial. % 21.68/21.89 (* end of lemma zenon_L863_ *) % 21.68/21.89 assert (zenon_L864_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (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 (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.68/21.89 do 0 intro. intros zenon_H164 zenon_H68 zenon_H93 zenon_H1bb zenon_H20f zenon_H120 zenon_H181 zenon_Hc4 zenon_H18d zenon_H48 zenon_H129 zenon_H1b4 zenon_H77 zenon_Hef zenon_H19a zenon_H31 zenon_H177 zenon_H67 zenon_H7e. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.89 apply (zenon_L456_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.89 apply (zenon_L863_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.89 apply (zenon_L406_); trivial. % 21.68/21.89 apply (zenon_L547_); trivial. % 21.68/21.89 (* end of lemma zenon_L864_ *) % 21.68/21.89 assert (zenon_L865_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((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))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H1a8 zenon_H3d zenon_H7e zenon_H67 zenon_H177 zenon_H31 zenon_H19a zenon_H77 zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H120 zenon_H20f zenon_H1bb zenon_H68 zenon_H164 zenon_H189 zenon_H93 zenon_H160 zenon_H1cd. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.89 apply (zenon_L214_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.89 apply (zenon_L864_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.89 apply (zenon_L439_); trivial. % 21.68/21.89 apply (zenon_L240_); trivial. % 21.68/21.89 (* end of lemma zenon_L865_ *) % 21.68/21.89 assert (zenon_L866_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H139 zenon_H1cd zenon_H160 zenon_H189 zenon_H164 zenon_H1bb zenon_H20f zenon_H120 zenon_H181 zenon_Hc4 zenon_H18d zenon_H48 zenon_H129 zenon_H1b4 zenon_H19a zenon_H177 zenon_H7e zenon_H1a8 zenon_H77 zenon_H3d zenon_H68 zenon_H31 zenon_H93 zenon_H196. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.89 apply (zenon_L865_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.89 apply (zenon_L214_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.89 apply (zenon_L264_); trivial. % 21.68/21.89 apply (zenon_L167_); trivial. % 21.68/21.89 (* end of lemma zenon_L866_ *) % 21.68/21.89 assert (zenon_L867_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.68/21.89 do 0 intro. intros zenon_H164 zenon_H7e zenon_H68 zenon_H93 zenon_H1bb zenon_H20f zenon_H120 zenon_H181 zenon_Hc4 zenon_H18d zenon_H48 zenon_H129 zenon_H1b4 zenon_H77 zenon_H19a zenon_H31 zenon_H177 zenon_H24e zenon_H1b7 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H160 zenon_Hbb zenon_H1cd. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.89 apply (zenon_L456_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.89 apply (zenon_L557_); trivial. % 21.68/21.89 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.89 apply (zenon_L406_); trivial. % 21.68/21.89 apply (zenon_L560_); trivial. % 21.68/21.89 (* end of lemma zenon_L867_ *) % 21.68/21.89 assert (zenon_L868_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (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) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (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) (e3)) = (op (e2) (e3)))) -> (((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)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H1fe zenon_H2c zenon_H1a2 zenon_H55 zenon_H13c zenon_H121 zenon_H11a zenon_H25b zenon_H186 zenon_H141 zenon_H179 zenon_Hfa zenon_H163 zenon_H195 zenon_H189 zenon_H1a8 zenon_H125 zenon_H94 zenon_H181 zenon_H1b4 zenon_H24e zenon_H1b7 zenon_Hbb zenon_H1cd zenon_H4d zenon_H73 zenon_H82 zenon_H196 zenon_H139 zenon_H4e zenon_H164 zenon_H68 zenon_H20f zenon_H18d zenon_H19a zenon_H31 zenon_H177 zenon_H131 zenon_H1f1 zenon_H13f zenon_H117 zenon_Ha0 zenon_Hb6 zenon_H104 zenon_H156 zenon_He4 zenon_Ha9 zenon_H13a zenon_H15d zenon_H12e zenon_H48 zenon_Hc4 zenon_H93 zenon_H129 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H160 zenon_H77 zenon_H120. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.68/21.90 apply (zenon_L859_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.90 apply (zenon_L541_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.90 apply (zenon_L818_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.90 apply (zenon_L25_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.90 apply (zenon_L116_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.90 apply (zenon_L217_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.90 apply (zenon_L861_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.90 apply (zenon_L562_); trivial. % 21.68/21.90 apply (zenon_L415_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.90 apply (zenon_L124_); trivial. % 21.68/21.90 apply (zenon_L862_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.90 apply (zenon_L856_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.90 apply (zenon_L264_); trivial. % 21.68/21.90 apply (zenon_L167_); trivial. % 21.68/21.90 apply (zenon_L866_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.90 apply (zenon_L239_); trivial. % 21.68/21.90 apply (zenon_L816_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.90 apply (zenon_L843_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.90 apply (zenon_L818_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.90 apply (zenon_L14_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.90 apply (zenon_L217_); trivial. % 21.68/21.90 apply (zenon_L867_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.90 apply (zenon_L184_); trivial. % 21.68/21.90 apply (zenon_L816_); trivial. % 21.68/21.90 apply (zenon_L528_); trivial. % 21.68/21.90 (* end of lemma zenon_L868_ *) % 21.68/21.90 assert (zenon_L869_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e2) (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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 (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 (e3) (e2)))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((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))))) -> (~((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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 21.68/21.90 do 0 intro. intros zenon_Hcb zenon_H1fe zenon_Ha9 zenon_H1f1 zenon_H13a zenon_H73 zenon_H125 zenon_H94 zenon_H1a8 zenon_H189 zenon_H13c zenon_H179 zenon_H163 zenon_Hfa zenon_H117 zenon_H18d zenon_H20f zenon_H25b zenon_H195 zenon_H186 zenon_H19a zenon_H104 zenon_H131 zenon_H13f zenon_H164 zenon_H11a zenon_H121 zenon_H12e zenon_H48 zenon_H4e zenon_H4d zenon_H139 zenon_H196 zenon_H177 zenon_H77 zenon_H156 zenon_H55 zenon_H1bb zenon_H93 zenon_H129 zenon_H120 zenon_H18a zenon_H7d zenon_Hbc zenon_H160 zenon_H209 zenon_H212 zenon_He4 zenon_H68 zenon_H1a2 zenon_H1b4 zenon_H1b7 zenon_H1cd zenon_H24e zenon_H15d zenon_H2c zenon_H141 zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H82 zenon_Hc2 zenon_Hbb. % 21.68/21.90 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.68/21.90 exact (zenon_H1a3 zenon_Hbb). % 21.68/21.90 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.68/21.90 apply (zenon_L868_); trivial. % 21.68/21.90 apply (zenon_L868_); trivial. % 21.68/21.90 (* end of lemma zenon_L869_ *) % 21.68/21.90 assert (zenon_L870_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H1bb zenon_H162 zenon_H1c7 zenon_H160 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H181 zenon_Hc4. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.68/21.90 exact (zenon_H162 zenon_H167). % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.68/21.90 apply (zenon_L848_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.68/21.90 exact (zenon_H181 zenon_H17c). % 21.68/21.90 exact (zenon_Hc4 zenon_Hc3). % 21.68/21.90 (* end of lemma zenon_L870_ *) % 21.68/21.90 assert (zenon_L871_ : (((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)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.68/21.90 do 0 intro. intros zenon_H13a zenon_H33 zenon_H9d zenon_Ha9 zenon_H6e zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H155. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.90 apply (zenon_L245_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.90 apply (zenon_L110_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.90 apply (zenon_L68_); trivial. % 21.68/21.90 apply (zenon_L115_); trivial. % 21.68/21.90 (* end of lemma zenon_L871_ *) % 21.68/21.90 assert (zenon_L872_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.68/21.90 do 0 intro. intros zenon_H212 zenon_He0 zenon_H7f zenon_H7d zenon_Hbc zenon_H160 zenon_H13a zenon_H33 zenon_Ha9 zenon_H6e zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H155. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H34 | zenon_intro zenon_H213 ]. % 21.68/21.90 apply (zenon_L802_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H7e | zenon_intro zenon_H214 ]. % 21.68/21.90 apply (zenon_L31_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H102 | zenon_intro zenon_H9d ]. % 21.68/21.90 apply (zenon_L104_); trivial. % 21.68/21.90 apply (zenon_L871_); trivial. % 21.68/21.90 (* end of lemma zenon_L872_ *) % 21.68/21.90 assert (zenon_L873_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H212 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H18a zenon_H11f zenon_H160 zenon_Hbb zenon_Hbc. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H34 | zenon_intro zenon_H213 ]. % 21.68/21.90 apply (zenon_L848_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H7e | zenon_intro zenon_H214 ]. % 21.68/21.90 apply (zenon_L140_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H102 | zenon_intro zenon_H9d ]. % 21.68/21.90 apply (zenon_L104_); trivial. % 21.68/21.90 apply (zenon_L48_); trivial. % 21.68/21.90 (* end of lemma zenon_L873_ *) % 21.68/21.90 assert (zenon_L874_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((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)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H18d zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H6e zenon_Ha9 zenon_H33 zenon_H13a zenon_H7f zenon_He0 zenon_H136 zenon_H48 zenon_H93 zenon_H77 zenon_H212 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H18a zenon_H160 zenon_Hbb zenon_Hbc. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.68/21.90 apply (zenon_L872_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.68/21.90 apply (zenon_L157_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.68/21.90 apply (zenon_L218_); trivial. % 21.68/21.90 apply (zenon_L873_); trivial. % 21.68/21.90 (* end of lemma zenon_L874_ *) % 21.68/21.90 assert (zenon_L875_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H12e zenon_Hc4 zenon_H181 zenon_H162 zenon_H1bb zenon_H77 zenon_H93 zenon_H48 zenon_H136 zenon_He0 zenon_H13a zenon_H33 zenon_Ha9 zenon_H6e zenon_Ha0 zenon_H31 zenon_H18d zenon_Hb6 zenon_H212 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H18a zenon_H160 zenon_Hbb zenon_Hbc. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.68/21.90 apply (zenon_L211_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.68/21.90 apply (zenon_L874_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.68/21.90 apply (zenon_L363_); trivial. % 21.68/21.90 apply (zenon_L873_); trivial. % 21.68/21.90 (* end of lemma zenon_L875_ *) % 21.68/21.90 assert (zenon_L876_ : (((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)) = (e3)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((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)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H164 zenon_Hbc zenon_Hbb zenon_H160 zenon_H18a zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H212 zenon_Hb6 zenon_H18d zenon_Ha0 zenon_H6e zenon_Ha9 zenon_H33 zenon_H13a zenon_H136 zenon_H48 zenon_H93 zenon_H77 zenon_H1bb zenon_H181 zenon_Hc4 zenon_H12e zenon_H31 zenon_H177 zenon_H162. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.90 apply (zenon_L870_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.90 apply (zenon_L875_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.90 apply (zenon_L406_); trivial. % 21.68/21.90 exact (zenon_H162 zenon_H167). % 21.68/21.90 (* end of lemma zenon_L876_ *) % 21.68/21.90 assert (zenon_L877_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (((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)) = (e3)) -> (~((op (e3) (e0)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H139 zenon_H1e zenon_H162 zenon_H68 zenon_H164 zenon_Hbc zenon_Hbb zenon_H18a zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H212 zenon_Hb6 zenon_H18d zenon_Ha0 zenon_Ha9 zenon_H33 zenon_H13a zenon_H48 zenon_H77 zenon_H1bb zenon_H181 zenon_Hc4 zenon_H12e zenon_H31 zenon_H26d zenon_H19a zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.90 apply (zenon_L20_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.68/21.90 apply (zenon_L756_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.68/21.90 apply (zenon_L876_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.68/21.90 apply (zenon_L158_); trivial. % 21.68/21.90 exact (zenon_H162 zenon_H167). % 21.68/21.90 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.90 apply (zenon_L122_); trivial. % 21.68/21.90 apply (zenon_L167_); trivial. % 21.68/21.90 (* end of lemma zenon_L877_ *) % 21.68/21.90 assert (zenon_L878_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 21.68/21.90 do 0 intro. intros zenon_H12e zenon_Hc4 zenon_H181 zenon_H18a zenon_H162 zenon_H1bb zenon_H3d zenon_H192 zenon_H4d zenon_H163 zenon_Hef zenon_He0. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.68/21.90 apply (zenon_L211_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.68/21.90 apply (zenon_L146_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.68/21.90 apply (zenon_L285_); trivial. % 21.68/21.90 apply (zenon_L662_); trivial. % 21.68/21.90 (* end of lemma zenon_L878_ *) % 21.68/21.90 assert (zenon_L879_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (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) (e3)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.90 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H25 zenon_He0 zenon_H163 zenon_H192 zenon_H3d zenon_H1bb zenon_H162 zenon_H18a zenon_H181 zenon_Hc4 zenon_H12e zenon_H77 zenon_H4d zenon_H93 zenon_H195. % 21.68/21.90 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.68/21.90 apply (zenon_L171_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.68/21.90 apply (zenon_L878_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.68/21.90 apply (zenon_L59_); trivial. % 21.68/21.90 apply (zenon_L228_); trivial. % 21.68/21.90 (* end of lemma zenon_L879_ *) % 21.68/21.90 assert (zenon_L880_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e0) (e0)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H164 zenon_H196 zenon_Hb9 zenon_H9f zenon_H1b4 zenon_H25b zenon_Hf5 zenon_H20f zenon_H25e zenon_H160 zenon_H48 zenon_H195 zenon_H93 zenon_H4d zenon_H77 zenon_H12e zenon_Hc4 zenon_H181 zenon_H18a zenon_H1bb zenon_H3d zenon_H192 zenon_H163 zenon_H25 zenon_H68 zenon_Hfa zenon_H31 zenon_H177 zenon_H162. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.90 apply (zenon_L820_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.90 apply (zenon_L879_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.90 apply (zenon_L406_); trivial. % 21.68/21.90 exact (zenon_H162 zenon_H167). % 21.68/21.90 (* end of lemma zenon_L880_ *) % 21.68/21.90 assert (zenon_L881_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((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) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H117 zenon_H131 zenon_Hb6 zenon_H13f zenon_Ha0 zenon_Hdd zenon_H104 zenon_H1c7 zenon_H33 zenon_H121 zenon_H164 zenon_H196 zenon_H9f zenon_H1b4 zenon_H25b zenon_Hf5 zenon_H20f zenon_H25e zenon_H160 zenon_H48 zenon_H195 zenon_H93 zenon_H4d zenon_H77 zenon_H12e zenon_Hc4 zenon_H181 zenon_H18a zenon_H1bb zenon_H3d zenon_H192 zenon_H163 zenon_H25 zenon_H68 zenon_Hfa zenon_H31 zenon_H177 zenon_H162. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.90 apply (zenon_L834_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.90 apply (zenon_L152_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.90 apply (zenon_L819_); trivial. % 21.68/21.90 apply (zenon_L880_); trivial. % 21.68/21.90 (* end of lemma zenon_L881_ *) % 21.68/21.90 assert (zenon_L882_ : (((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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((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 (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.68/21.90 do 0 intro. intros zenon_H141 zenon_H121 zenon_H33 zenon_H1c7 zenon_H104 zenon_H13f zenon_H131 zenon_H162 zenon_H177 zenon_H31 zenon_Hfa zenon_H25 zenon_H163 zenon_H192 zenon_H3d zenon_H1bb zenon_H18a zenon_H181 zenon_Hc4 zenon_H12e zenon_H77 zenon_H4d zenon_H195 zenon_H48 zenon_H160 zenon_H25e zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H9f zenon_H196 zenon_H164 zenon_Ha0 zenon_Hf0 zenon_H10c zenon_H54 zenon_Hb6 zenon_H117 zenon_H68 zenon_H93. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.90 apply (zenon_L217_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.90 apply (zenon_L881_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.68/21.90 apply (zenon_L151_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.68/21.90 apply (zenon_L74_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.68/21.90 apply (zenon_L278_); trivial. % 21.68/21.90 apply (zenon_L880_); trivial. % 21.68/21.90 apply (zenon_L158_); trivial. % 21.68/21.90 (* end of lemma zenon_L882_ *) % 21.68/21.90 assert (zenon_L883_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H164 zenon_H1c7 zenon_H1cd zenon_H7d zenon_H24e zenon_H4d zenon_H192 zenon_H3d zenon_H12e zenon_H1b7 zenon_H68 zenon_H93 zenon_Ha0 zenon_Ha5 zenon_Hfa zenon_H25 zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H160 zenon_H163 zenon_H195 zenon_H19a zenon_H14c zenon_H104 zenon_H162. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.90 apply (zenon_L853_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.90 apply (zenon_L829_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.90 apply (zenon_L257_); trivial. % 21.68/21.90 exact (zenon_H162 zenon_H167). % 21.68/21.90 (* end of lemma zenon_L883_ *) % 21.68/21.90 assert (zenon_L884_ : (~((e1) = (e2))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> False). % 21.68/21.90 do 0 intro. intros zenon_H77 zenon_H17c zenon_H11f. % 21.68/21.90 cut (((op (e3) (e3)) = (e2)) = ((e1) = (e2))). % 21.68/21.90 intro zenon_D_pnotp. % 21.68/21.90 apply zenon_H77. % 21.68/21.90 rewrite <- zenon_D_pnotp. % 21.68/21.90 exact zenon_H17c. % 21.68/21.90 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.68/21.90 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 21.68/21.90 congruence. % 21.68/21.90 exact (zenon_H120 zenon_H11f). % 21.68/21.90 apply zenon_H6a. apply refl_equal. % 21.68/21.90 (* end of lemma zenon_L884_ *) % 21.68/21.90 assert (zenon_L885_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> False). % 21.68/21.90 do 0 intro. intros zenon_H1c3 zenon_H9f zenon_Ha5 zenon_Ha9 zenon_H115 zenon_H68 zenon_H77 zenon_H11f. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.68/21.90 apply (zenon_L673_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.68/21.90 apply (zenon_L299_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.68/21.90 apply (zenon_L158_); trivial. % 21.68/21.90 apply (zenon_L884_); trivial. % 21.68/21.90 (* end of lemma zenon_L885_ *) % 21.68/21.90 assert (zenon_L886_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H1bb zenon_H162 zenon_H77 zenon_H68 zenon_H115 zenon_Ha9 zenon_Ha5 zenon_H9f zenon_H1c3 zenon_H181 zenon_Hc4. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.68/21.90 exact (zenon_H162 zenon_H167). % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.68/21.90 apply (zenon_L885_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.68/21.90 exact (zenon_H181 zenon_H17c). % 21.68/21.90 exact (zenon_Hc4 zenon_Hc3). % 21.68/21.90 (* end of lemma zenon_L886_ *) % 21.68/21.90 assert (zenon_L887_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e1)) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (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)) = (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) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H141 zenon_H131 zenon_Hb6 zenon_H13f zenon_H10d zenon_H104 zenon_H19a zenon_H195 zenon_H163 zenon_H160 zenon_H18d zenon_H48 zenon_H129 zenon_H20f zenon_H1b4 zenon_H25 zenon_Hfa zenon_Ha0 zenon_H93 zenon_H1b7 zenon_H12e zenon_H3d zenon_H192 zenon_H4d zenon_H24e zenon_H7d zenon_H1cd zenon_H1c7 zenon_H164 zenon_H1bb zenon_H162 zenon_H77 zenon_H68 zenon_Ha9 zenon_Ha5 zenon_H9f zenon_H1c3 zenon_H181 zenon_Hc4. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.68/21.90 apply (zenon_L825_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.68/21.90 apply (zenon_L152_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.68/21.90 apply (zenon_L883_); trivial. % 21.68/21.90 apply (zenon_L886_); trivial. % 21.68/21.90 (* end of lemma zenon_L887_ *) % 21.68/21.90 assert (zenon_L888_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H139 zenon_H77 zenon_H155 zenon_Hb6 zenon_H31 zenon_Ha0 zenon_Ha9 zenon_H47 zenon_H13a zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.90 apply (zenon_L251_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.90 apply (zenon_L743_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.90 apply (zenon_L122_); trivial. % 21.68/21.90 apply (zenon_L167_); trivial. % 21.68/21.90 (* end of lemma zenon_L888_ *) % 21.68/21.90 assert (zenon_L889_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H13c zenon_H117 zenon_H54 zenon_Hf0 zenon_H164 zenon_H196 zenon_H9f zenon_H1b4 zenon_H25b zenon_Hf5 zenon_H20f zenon_H25e zenon_H160 zenon_H195 zenon_H77 zenon_H12e zenon_Hc4 zenon_H181 zenon_H18a zenon_H1bb zenon_H3d zenon_H192 zenon_H163 zenon_H25 zenon_Hfa zenon_H31 zenon_H177 zenon_H131 zenon_H13f zenon_H104 zenon_H1c7 zenon_H33 zenon_H121 zenon_H141 zenon_Hb6 zenon_H4d zenon_H19a zenon_H48 zenon_H155 zenon_Ha0 zenon_H93 zenon_H68 zenon_H162. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.90 apply (zenon_L116_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.90 apply (zenon_L882_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.90 apply (zenon_L124_); trivial. % 21.68/21.90 apply (zenon_L247_); trivial. % 21.68/21.90 (* end of lemma zenon_L889_ *) % 21.68/21.90 assert (zenon_L890_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((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)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H19a zenon_H9e zenon_Hbc zenon_Hbb zenon_H160 zenon_H18a zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H212 zenon_Hb6 zenon_H18d zenon_H31 zenon_Ha0 zenon_H6e zenon_Ha9 zenon_H33 zenon_H13a zenon_He0 zenon_H48 zenon_H77 zenon_H1bb zenon_H181 zenon_Hc4 zenon_H12e zenon_H93 zenon_H68 zenon_H162. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.68/21.90 apply (zenon_L156_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.68/21.90 apply (zenon_L875_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.68/21.90 apply (zenon_L158_); trivial. % 21.68/21.90 exact (zenon_H162 zenon_H167). % 21.68/21.90 (* end of lemma zenon_L890_ *) % 21.68/21.90 assert (zenon_L891_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H139 zenon_H162 zenon_Ha0 zenon_Hbb zenon_H19a zenon_Hbc zenon_H18a zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H212 zenon_Hb6 zenon_H18d zenon_H31 zenon_Ha9 zenon_H33 zenon_H13a zenon_H48 zenon_H77 zenon_H1bb zenon_H181 zenon_Hc4 zenon_H12e zenon_H68 zenon_H109 zenon_H2d zenon_H164 zenon_H47 zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.68/21.90 apply (zenon_L251_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.90 apply (zenon_L253_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.90 apply (zenon_L110_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.90 apply (zenon_L68_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.68/21.90 apply (zenon_L359_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.68/21.90 apply (zenon_L890_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.68/21.90 apply (zenon_L80_); trivial. % 21.68/21.90 exact (zenon_H162 zenon_H167). % 21.68/21.90 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.68/21.90 apply (zenon_L122_); trivial. % 21.68/21.90 apply (zenon_L167_); trivial. % 21.68/21.90 (* end of lemma zenon_L891_ *) % 21.68/21.90 assert (zenon_L892_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (((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) (e3)) = (e3))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H82 zenon_H196 zenon_H93 zenon_H177 zenon_H160 zenon_H3d zenon_H77 zenon_H139 zenon_H4e zenon_H4d zenon_H48 zenon_H2d zenon_H1bb zenon_H162 zenon_H18a zenon_H181 zenon_Hc4. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.90 apply (zenon_L818_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.90 apply (zenon_L14_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.90 apply (zenon_L217_); trivial. % 21.68/21.90 apply (zenon_L211_); trivial. % 21.68/21.90 (* end of lemma zenon_L892_ *) % 21.68/21.90 assert (zenon_L893_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (((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) (e3)) = (e3))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H82 zenon_H196 zenon_H93 zenon_H177 zenon_H160 zenon_H13a zenon_Ha9 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H155 zenon_H77 zenon_H139 zenon_H4e zenon_H4d zenon_H48 zenon_H2d zenon_H1bb zenon_H162 zenon_H18a zenon_H181 zenon_Hc4. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.90 apply (zenon_L888_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.90 apply (zenon_L14_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.90 apply (zenon_L217_); trivial. % 21.68/21.90 apply (zenon_L211_); trivial. % 21.68/21.90 (* end of lemma zenon_L893_ *) % 21.68/21.90 assert (zenon_L894_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.90 do 0 intro. intros zenon_H1fe zenon_H26d zenon_H13c zenon_H117 zenon_Hf0 zenon_H1b4 zenon_H25b zenon_Hf5 zenon_H20f zenon_H25e zenon_H195 zenon_H192 zenon_H163 zenon_Hfa zenon_H131 zenon_H13f zenon_H104 zenon_H121 zenon_H141 zenon_H179 zenon_H55 zenon_H156 zenon_He4 zenon_H94 zenon_H125 zenon_Hb2 zenon_H1c6 zenon_H1c3 zenon_H129 zenon_H18a zenon_H48 zenon_H4d zenon_H4e zenon_H139 zenon_H77 zenon_Hb6 zenon_H31 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H177 zenon_H93 zenon_H196 zenon_H82 zenon_H73 zenon_Hbb zenon_H19a zenon_Hbc zenon_H212 zenon_H18d zenon_H33 zenon_H12e zenon_H68 zenon_H109 zenon_H164 zenon_H15d zenon_H1bb zenon_H162 zenon_H1c7 zenon_H160 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H181 zenon_Hc4. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.68/21.90 apply (zenon_L877_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.90 apply (zenon_L541_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.90 apply (zenon_L541_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.90 apply (zenon_L25_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.90 apply (zenon_L116_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.90 apply (zenon_L882_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.90 apply (zenon_L124_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.68/21.90 apply (zenon_L831_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.68/21.90 apply (zenon_L882_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.68/21.90 apply (zenon_L887_); trivial. % 21.68/21.90 exact (zenon_H1c7 zenon_Hac). % 21.68/21.90 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.90 apply (zenon_L55_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.90 apply (zenon_L68_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.68/21.90 apply (zenon_L116_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.68/21.90 apply (zenon_L882_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.68/21.90 apply (zenon_L617_); trivial. % 21.68/21.90 apply (zenon_L262_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.68/21.90 apply (zenon_L116_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.68/21.90 apply (zenon_L151_); trivial. % 21.68/21.90 apply (zenon_L48_); trivial. % 21.68/21.90 apply (zenon_L211_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.90 apply (zenon_L239_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.68/21.90 apply (zenon_L888_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.68/21.90 apply (zenon_L14_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.68/21.90 apply (zenon_L889_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.68/21.90 apply (zenon_L486_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.68/21.90 apply (zenon_L15_); trivial. % 21.68/21.90 apply (zenon_L658_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.68/21.90 apply (zenon_L831_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.68/21.90 apply (zenon_L178_); trivial. % 21.68/21.90 apply (zenon_L115_); trivial. % 21.68/21.90 apply (zenon_L211_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.90 apply (zenon_L891_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.90 apply (zenon_L892_); trivial. % 21.68/21.90 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.90 apply (zenon_L184_); trivial. % 21.68/21.90 apply (zenon_L893_); trivial. % 21.68/21.90 apply (zenon_L870_); trivial. % 21.68/21.90 (* end of lemma zenon_L894_ *) % 21.68/21.90 assert (zenon_L895_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 21.68/21.90 do 0 intro. intros zenon_Hcb zenon_H1bb zenon_H120 zenon_H162 zenon_Hc2 zenon_Hbb. % 21.68/21.90 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.68/21.90 exact (zenon_H1a3 zenon_Hbb). % 21.68/21.90 apply (zenon_L434_); trivial. % 21.68/21.90 (* end of lemma zenon_L895_ *) % 21.68/21.90 assert (zenon_L896_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> ((op (e3) (e2)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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 (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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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)) = (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> False). % 21.68/21.90 do 0 intro. intros zenon_Hca zenon_Hbb zenon_Hc2 zenon_H139 zenon_H196 zenon_H26d zenon_H31 zenon_H164 zenon_H177 zenon_H18a zenon_H18d zenon_H93 zenon_H77 zenon_H48 zenon_Hbc zenon_H13a zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H33 zenon_H212 zenon_H12e zenon_H162 zenon_H24e zenon_H160 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H1bb zenon_H19a zenon_H68 zenon_H15d zenon_H4e zenon_Hb2 zenon_H141 zenon_Hf0 zenon_H13f zenon_H4d zenon_H131 zenon_H121 zenon_H104 zenon_H163 zenon_Hfa zenon_H192 zenon_H25e zenon_H1b4 zenon_Hf5 zenon_H20f zenon_H195 zenon_H25b zenon_H117 zenon_H1c6 zenon_H129 zenon_H1c3 zenon_H156 zenon_H55 zenon_H179 zenon_He4 zenon_H13c zenon_H82 zenon_H94 zenon_H125 zenon_H73 zenon_H109 zenon_H1fe zenon_Hcb. % 21.68/21.90 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.68/21.90 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.68/21.90 exact (zenon_H1a3 zenon_Hbb). % 21.68/21.90 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.68/21.90 apply (zenon_L894_); trivial. % 21.68/21.90 apply (zenon_L894_); trivial. % 21.68/21.90 apply (zenon_L895_); trivial. % 21.68/21.90 (* end of lemma zenon_L896_ *) % 21.68/21.90 assert (zenon_L897_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (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 (e2) (e0)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (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))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((op (e3) (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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> False). % 21.68/21.91 do 0 intro. intros zenon_Hc8 zenon_H109 zenon_H1c3 zenon_Hcb zenon_H1fe zenon_H1cb zenon_Ha9 zenon_H1f1 zenon_H73 zenon_H125 zenon_H94 zenon_H82 zenon_H13c zenon_H141 zenon_H179 zenon_H129 zenon_H163 zenon_Hfa zenon_H131 zenon_H13f zenon_H1c6 zenon_H4d zenon_Hb6 zenon_Hf0 zenon_H121 zenon_H104 zenon_H33 zenon_H164 zenon_H11a zenon_H19a zenon_H26d zenon_Hef zenon_H18d zenon_H192 zenon_H25e zenon_Hf5 zenon_H20f zenon_H195 zenon_H25b zenon_H12e zenon_H117 zenon_Ha0 zenon_He4 zenon_H55 zenon_H156 zenon_Hb2 zenon_H13a zenon_H48 zenon_H139 zenon_H93 zenon_H196 zenon_H160 zenon_H177 zenon_H77 zenon_H68 zenon_H31 zenon_H1bb zenon_H1b4 zenon_H1b7 zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H1cd zenon_H24e zenon_H15d zenon_Hc2 zenon_Hbb zenon_H1a8 zenon_H189 zenon_H186 zenon_H4e zenon_H1a2 zenon_H2c zenon_Hca. % 21.68/21.91 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.68/21.91 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.68/21.91 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.68/21.91 exact (zenon_H1a3 zenon_Hbb). % 21.68/21.91 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.68/21.91 apply (zenon_L855_); trivial. % 21.68/21.91 apply (zenon_L855_); trivial. % 21.68/21.91 apply (zenon_L869_); trivial. % 21.68/21.91 apply (zenon_L896_); trivial. % 21.68/21.91 (* end of lemma zenon_L897_ *) % 21.68/21.91 assert (zenon_L898_ : (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (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 (e2) (e0)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (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))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> False). % 21.68/21.91 do 0 intro. intros zenon_Hc4 zenon_H1c7 zenon_H209 zenon_Hc8 zenon_H109 zenon_H1c3 zenon_Hcb zenon_H1fe zenon_H1cb zenon_Ha9 zenon_H1f1 zenon_H73 zenon_H125 zenon_H94 zenon_H82 zenon_H13c zenon_H141 zenon_H179 zenon_H129 zenon_H163 zenon_Hfa zenon_H131 zenon_H13f zenon_H1c6 zenon_H4d zenon_Hb6 zenon_Hf0 zenon_H121 zenon_H104 zenon_H33 zenon_H164 zenon_H11a zenon_H19a zenon_H26d zenon_Hef zenon_H18d zenon_H192 zenon_H25e zenon_Hf5 zenon_H20f zenon_H195 zenon_H25b zenon_H12e zenon_H117 zenon_Ha0 zenon_He4 zenon_H55 zenon_H156 zenon_Hb2 zenon_H13a zenon_H48 zenon_H139 zenon_H93 zenon_H196 zenon_H160 zenon_H177 zenon_H77 zenon_H68 zenon_H31 zenon_H1bb zenon_H1b4 zenon_H1b7 zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H1cd zenon_H24e zenon_H15d zenon_Hc2 zenon_H1a8 zenon_H189 zenon_H186 zenon_H4e zenon_H1a2 zenon_H2c zenon_Hca. % 21.68/21.91 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.68/21.91 apply (zenon_L68_); trivial. % 21.68/21.91 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.68/21.91 apply (zenon_L124_); trivial. % 21.68/21.91 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.68/21.91 apply (zenon_L815_); trivial. % 21.68/21.91 apply (zenon_L897_); trivial. % 21.68/21.91 (* end of lemma zenon_L898_ *) % 21.68/21.91 assert (zenon_L899_ : (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (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 (e2) (e0)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (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))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> False). % 21.68/21.91 do 0 intro. intros zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H121 zenon_H104 zenon_H1c7 zenon_H209 zenon_Hc8 zenon_H109 zenon_H1c3 zenon_Hcb zenon_H1fe zenon_H1cb zenon_Ha9 zenon_H1f1 zenon_H73 zenon_H125 zenon_H94 zenon_H82 zenon_H13c zenon_H141 zenon_H179 zenon_H129 zenon_H163 zenon_Hfa zenon_H131 zenon_H13f zenon_H1c6 zenon_Hf0 zenon_H33 zenon_H164 zenon_H11a zenon_H19a zenon_H26d zenon_Hef zenon_H18d zenon_H192 zenon_H25e zenon_Hf5 zenon_H20f zenon_H195 zenon_H25b zenon_H12e zenon_H117 zenon_He4 zenon_H55 zenon_H156 zenon_Hb2 zenon_H13a zenon_H48 zenon_H139 zenon_H93 zenon_H196 zenon_H160 zenon_H177 zenon_H77 zenon_H68 zenon_H1bb zenon_H1b4 zenon_H1b7 zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H1cd zenon_H24e zenon_H15d zenon_Hc2 zenon_H1a8 zenon_H189 zenon_H186 zenon_H4e zenon_H1a2 zenon_H2c zenon_Hca. % 21.68/21.91 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.68/21.91 apply (zenon_L898_); trivial. % 21.68/21.91 apply (zenon_L898_); trivial. % 21.68/21.91 (* end of lemma zenon_L899_ *) % 21.68/21.91 assert (zenon_L900_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> False). % 21.68/21.91 do 0 intro. intros zenon_H24 zenon_H9f zenon_Ha6. % 21.68/21.91 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 21.68/21.91 intro zenon_D_pnotp. % 21.68/21.91 apply zenon_H24. % 21.68/21.91 rewrite <- zenon_D_pnotp. % 21.68/21.91 exact zenon_H9f. % 21.68/21.91 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 21.68/21.91 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 21.68/21.91 congruence. % 21.68/21.91 apply zenon_H27. apply refl_equal. % 21.68/21.91 apply zenon_Ha7. apply sym_equal. exact zenon_Ha6. % 21.68/21.91 (* end of lemma zenon_L900_ *) % 21.68/21.91 assert (zenon_L901_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (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 (e2) (e0)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (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))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> False). % 21.68/21.91 do 0 intro. intros zenon_H99 zenon_H109 zenon_H1c3 zenon_H1fe zenon_H1cb zenon_Ha9 zenon_H1f1 zenon_H73 zenon_H125 zenon_H94 zenon_H82 zenon_H13c zenon_H141 zenon_H179 zenon_H129 zenon_H163 zenon_Hfa zenon_H131 zenon_H13f zenon_H1c6 zenon_H4d zenon_Hb6 zenon_Hf0 zenon_H121 zenon_H104 zenon_H33 zenon_H164 zenon_H11a zenon_H19a zenon_H26d zenon_Hef zenon_H18d zenon_H192 zenon_H25e zenon_Hf5 zenon_H20f zenon_H195 zenon_H25b zenon_H12e zenon_H117 zenon_Ha0 zenon_He4 zenon_H55 zenon_H156 zenon_Hb2 zenon_H13a zenon_H48 zenon_H139 zenon_H196 zenon_H177 zenon_H77 zenon_H68 zenon_H31 zenon_H1bb zenon_H1b4 zenon_H1b7 zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H1cd zenon_H24e zenon_H15d zenon_Hbb zenon_H1a8 zenon_H189 zenon_H186 zenon_H4e zenon_H1a2 zenon_H2c. % 21.68/21.91 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.68/21.91 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.68/21.91 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.68/21.91 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.68/21.91 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.68/21.91 apply (zenon_L897_); trivial. % 21.68/21.91 (* end of lemma zenon_L901_ *) % 21.68/21.91 assert (zenon_L902_ : ((op (e0) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (((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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (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 (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((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) (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.68/21.91 do 0 intro. intros zenon_H3d zenon_H2c zenon_H1a2 zenon_H4e zenon_H186 zenon_H1a8 zenon_Hbb zenon_H15d zenon_H24e zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1b7 zenon_H1b4 zenon_H1bb zenon_H31 zenon_H68 zenon_H77 zenon_H177 zenon_H196 zenon_H139 zenon_H48 zenon_H13a zenon_Hb2 zenon_H156 zenon_H55 zenon_He4 zenon_Ha0 zenon_H117 zenon_H12e zenon_H25b zenon_H195 zenon_H20f zenon_Hf5 zenon_H25e zenon_H192 zenon_H18d zenon_H26d zenon_H19a zenon_H11a zenon_H164 zenon_H33 zenon_H104 zenon_H121 zenon_Hf0 zenon_Hb6 zenon_H4d zenon_H1c6 zenon_H13f zenon_H131 zenon_Hfa zenon_H163 zenon_H129 zenon_H179 zenon_H141 zenon_H13c zenon_H82 zenon_H94 zenon_H125 zenon_H73 zenon_H1f1 zenon_Ha9 zenon_H1cb zenon_H1fe zenon_H1c3 zenon_H109 zenon_H99 zenon_H189 zenon_H93 zenon_H160 zenon_H1cd. % 21.68/21.91 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.68/21.91 apply (zenon_L214_); trivial. % 21.68/21.91 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.68/21.91 apply (zenon_L901_); trivial. % 21.68/21.91 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.68/21.91 apply (zenon_L439_); trivial. % 21.68/21.91 apply (zenon_L240_); trivial. % 21.68/21.91 (* end of lemma zenon_L902_ *) % 21.68/21.91 assert (zenon_L903_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (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 (e2) (e0)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (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))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.91 do 0 intro. intros zenon_H2d zenon_H93 zenon_H189 zenon_H99 zenon_H109 zenon_H1c3 zenon_H1fe zenon_H1cb zenon_Ha9 zenon_H1f1 zenon_H73 zenon_H125 zenon_H94 zenon_H82 zenon_H13c zenon_H141 zenon_H179 zenon_H129 zenon_H163 zenon_Hfa zenon_H131 zenon_H13f zenon_H1c6 zenon_H4d zenon_Hb6 zenon_Hf0 zenon_H121 zenon_H104 zenon_H33 zenon_H164 zenon_H11a zenon_H19a zenon_H26d zenon_H18d zenon_H192 zenon_H25e zenon_Hf5 zenon_H20f zenon_H195 zenon_H25b zenon_H12e zenon_H117 zenon_Ha0 zenon_He4 zenon_H55 zenon_H156 zenon_Hb2 zenon_H13a zenon_H139 zenon_H196 zenon_H177 zenon_H77 zenon_H68 zenon_H15d zenon_H1a8 zenon_H186 zenon_H4e zenon_H1a2 zenon_H2c zenon_H48 zenon_H31 zenon_H1bb zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.68/21.91 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.68/21.91 apply (zenon_L843_); trivial. % 21.68/21.91 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.68/21.91 apply (zenon_L902_); trivial. % 21.68/21.91 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.68/21.91 apply (zenon_L239_); trivial. % 21.68/21.91 apply (zenon_L816_); trivial. % 21.68/21.91 (* end of lemma zenon_L903_ *) % 21.68/21.91 assert (zenon_L904_ : ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (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 (e2) (e0)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (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))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.68/21.91 do 0 intro. intros zenon_H10c zenon_H1c7 zenon_H2d zenon_H93 zenon_H189 zenon_H99 zenon_H109 zenon_H1c3 zenon_H1fe zenon_H1cb zenon_Ha9 zenon_H1f1 zenon_H73 zenon_H125 zenon_H94 zenon_H82 zenon_H13c zenon_H141 zenon_H179 zenon_H129 zenon_H163 zenon_Hfa zenon_H131 zenon_H13f zenon_H1c6 zenon_H4d zenon_Hb6 zenon_Hf0 zenon_H121 zenon_H104 zenon_H33 zenon_H164 zenon_H11a zenon_H19a zenon_H26d zenon_H18d zenon_H192 zenon_H25e zenon_Hf5 zenon_H20f zenon_H195 zenon_H25b zenon_H12e zenon_H117 zenon_Ha0 zenon_He4 zenon_H55 zenon_H156 zenon_Hb2 zenon_H13a zenon_H139 zenon_H196 zenon_H177 zenon_H77 zenon_H68 zenon_H15d zenon_H1a8 zenon_H186 zenon_H4e zenon_H1a2 zenon_H2c zenon_H48 zenon_H31 zenon_H1bb zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.68/21.91 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.68/21.91 apply (zenon_L393_); trivial. % 21.68/21.91 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.68/21.91 apply (zenon_L124_); trivial. % 21.68/21.91 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.68/21.91 apply (zenon_L815_); trivial. % 21.68/21.91 apply (zenon_L903_); trivial. % 21.68/21.91 (* end of lemma zenon_L904_ *) % 21.68/21.91 assert (zenon_L905_ : ((op (e0) (e1)) = (e3)) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (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 (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (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 (e1) (e1)) = (op (e2) (e1)))) -> (((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) (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (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 (e3) (e3)) = (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.78/21.91 do 0 intro. intros zenon_Hdb zenon_Hca zenon_H2c zenon_H1a2 zenon_H4e zenon_H186 zenon_H189 zenon_H1a8 zenon_Hc2 zenon_H15d zenon_H24e zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1b7 zenon_H1b4 zenon_H1bb zenon_H68 zenon_H177 zenon_H196 zenon_H93 zenon_H139 zenon_H48 zenon_H13a zenon_Hb2 zenon_H156 zenon_H55 zenon_He4 zenon_H117 zenon_H12e zenon_H25b zenon_H195 zenon_H20f zenon_Hf5 zenon_H25e zenon_H192 zenon_H18d zenon_H26d zenon_H19a zenon_H11a zenon_H164 zenon_H33 zenon_Hf0 zenon_H1c6 zenon_H13f zenon_H131 zenon_Hfa zenon_H163 zenon_H129 zenon_H179 zenon_H141 zenon_H13c zenon_H82 zenon_H94 zenon_H125 zenon_H73 zenon_H1f1 zenon_Ha9 zenon_H1cb zenon_H1fe zenon_Hcb zenon_H1c3 zenon_H109 zenon_Hc8 zenon_H209 zenon_H1c7 zenon_H104 zenon_H121 zenon_H4d zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H53 zenon_H77 zenon_H160 zenon_H1cd. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.91 apply (zenon_L110_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.91 apply (zenon_L899_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.91 apply (zenon_L56_); trivial. % 21.78/21.91 apply (zenon_L240_); trivial. % 21.78/21.91 (* end of lemma zenon_L905_ *) % 21.78/21.91 assert (zenon_L906_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (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 (e2) (e0)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (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))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 21.78/21.91 do 0 intro. intros zenon_H1cd zenon_H160 zenon_H77 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H121 zenon_H104 zenon_H1c7 zenon_H209 zenon_Hc8 zenon_H109 zenon_H1c3 zenon_Hcb zenon_H1fe zenon_H1cb zenon_Ha9 zenon_H1f1 zenon_H73 zenon_H125 zenon_H94 zenon_H82 zenon_H13c zenon_H141 zenon_H179 zenon_H129 zenon_H163 zenon_Hfa zenon_H131 zenon_H13f zenon_H1c6 zenon_Hf0 zenon_H33 zenon_H164 zenon_H11a zenon_H19a zenon_H26d zenon_H18d zenon_H192 zenon_H25e zenon_Hf5 zenon_H20f zenon_H195 zenon_H25b zenon_H12e zenon_H117 zenon_He4 zenon_H55 zenon_H156 zenon_Hb2 zenon_H13a zenon_H48 zenon_H139 zenon_H93 zenon_H196 zenon_H177 zenon_H68 zenon_H1bb zenon_H1b4 zenon_H1b7 zenon_H212 zenon_Hbc zenon_H18a zenon_H24e zenon_H15d zenon_Hc2 zenon_H1a8 zenon_H189 zenon_H186 zenon_H4e zenon_H1a2 zenon_H2c zenon_Hca zenon_Hdb zenon_H7d zenon_H7e. % 21.78/21.91 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.91 apply (zenon_L55_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.91 apply (zenon_L486_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.91 apply (zenon_L905_); trivial. % 21.78/21.91 apply (zenon_L31_); trivial. % 21.78/21.91 (* end of lemma zenon_L906_ *) % 21.78/21.91 assert (zenon_L907_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e0)) = (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) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.78/21.91 do 0 intro. intros zenon_H1a2 zenon_H31 zenon_H104 zenon_H121 zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_He4 zenon_H156 zenon_H1cb zenon_H1f1 zenon_H18d zenon_H13a zenon_Ha9 zenon_Hb6 zenon_H139 zenon_H68 zenon_Ha0 zenon_H19a zenon_H77 zenon_H1c7 zenon_H34 zenon_H163 zenon_H192 zenon_H48 zenon_H12e zenon_H73 zenon_H4d zenon_H1bb zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.78/21.91 apply (zenon_L68_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.78/21.91 apply (zenon_L124_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.78/21.91 apply (zenon_L815_); trivial. % 21.78/21.91 apply (zenon_L854_); trivial. % 21.78/21.91 (* end of lemma zenon_L907_ *) % 21.78/21.91 assert (zenon_L908_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (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 (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 (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> (~((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) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.78/21.91 do 0 intro. intros zenon_Hc8 zenon_H109 zenon_H1c3 zenon_Hcb zenon_H1fe zenon_H125 zenon_H94 zenon_H82 zenon_H13c zenon_H141 zenon_H179 zenon_H129 zenon_Hfa zenon_H131 zenon_H13f zenon_H1c6 zenon_Hf0 zenon_H33 zenon_H164 zenon_H11a zenon_H26d zenon_H25e zenon_Hf5 zenon_H20f zenon_H195 zenon_H25b zenon_H117 zenon_H55 zenon_Hb2 zenon_Hc2 zenon_H1a8 zenon_H189 zenon_H186 zenon_H4e zenon_H2c zenon_Hca zenon_H24 zenon_H99 zenon_H67 zenon_H1a2 zenon_H31 zenon_H104 zenon_H121 zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_He4 zenon_H156 zenon_H1cb zenon_H1f1 zenon_H18d zenon_H13a zenon_Ha9 zenon_Hb6 zenon_H139 zenon_H68 zenon_Ha0 zenon_H19a zenon_H77 zenon_H1c7 zenon_H163 zenon_H192 zenon_H48 zenon_H12e zenon_H73 zenon_H4d zenon_H1bb zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.91 apply (zenon_L20_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.91 apply (zenon_L171_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.91 apply (zenon_L898_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.91 apply (zenon_L59_); trivial. % 21.78/21.91 apply (zenon_L228_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.91 apply (zenon_L251_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.91 apply (zenon_L214_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.91 apply (zenon_L899_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.91 apply (zenon_L458_); trivial. % 21.78/21.91 apply (zenon_L240_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.91 apply (zenon_L239_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.91 apply (zenon_L744_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.91 apply (zenon_L14_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.91 apply (zenon_L217_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.91 apply (zenon_L900_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.91 apply (zenon_L904_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.91 apply (zenon_L124_); trivial. % 21.78/21.91 apply (zenon_L549_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.91 apply (zenon_L906_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.91 apply (zenon_L68_); trivial. % 21.78/21.91 apply (zenon_L115_); trivial. % 21.78/21.91 apply (zenon_L907_); trivial. % 21.78/21.91 (* end of lemma zenon_L908_ *) % 21.78/21.91 assert (zenon_L909_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.78/21.91 do 0 intro. intros zenon_H19a zenon_H48 zenon_H155 zenon_Hc4 zenon_H181 zenon_H20f zenon_H1bb zenon_H93 zenon_H68 zenon_H12e zenon_H67 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H160 zenon_H77 zenon_H120. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.78/21.91 apply (zenon_L246_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.78/21.91 apply (zenon_L422_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.78/21.91 apply (zenon_L158_); trivial. % 21.78/21.91 apply (zenon_L558_); trivial. % 21.78/21.91 (* end of lemma zenon_L909_ *) % 21.78/21.91 assert (zenon_L910_ : (((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 (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (~((e1) = (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) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (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))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.78/21.91 do 0 intro. intros zenon_H1fe zenon_He4 zenon_H156 zenon_H24e zenon_H141 zenon_H2c zenon_Ha0 zenon_Hb6 zenon_H1a2 zenon_H55 zenon_H1b7 zenon_H179 zenon_H67 zenon_H68 zenon_H20f zenon_H181 zenon_H19a zenon_H4d zenon_H73 zenon_H82 zenon_H196 zenon_H139 zenon_H4e zenon_H1a8 zenon_H177 zenon_H31 zenon_H1b4 zenon_H18d zenon_H164 zenon_H189 zenon_H1cd zenon_H15d zenon_H12e zenon_H48 zenon_Hc4 zenon_H93 zenon_H129 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H160 zenon_H77 zenon_H120. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.91 apply (zenon_L859_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.91 apply (zenon_L559_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.91 apply (zenon_L251_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.91 apply (zenon_L818_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.91 apply (zenon_L14_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.91 apply (zenon_L217_); trivial. % 21.78/21.91 apply (zenon_L865_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.91 apply (zenon_L184_); trivial. % 21.78/21.91 apply (zenon_L909_); trivial. % 21.78/21.91 apply (zenon_L528_); trivial. % 21.78/21.91 (* end of lemma zenon_L910_ *) % 21.78/21.91 assert (zenon_L911_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.78/21.91 do 0 intro. intros zenon_He4 zenon_H77 zenon_H156 zenon_H4d zenon_H55 zenon_H54 zenon_H164 zenon_Hc4 zenon_H181 zenon_H24e zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H1bb zenon_H155 zenon_Hb6 zenon_Ha0 zenon_H6e zenon_Ha9 zenon_H33 zenon_H13a zenon_H160 zenon_Hbc zenon_H7d zenon_H212 zenon_H31 zenon_H177 zenon_H162. % 21.78/21.91 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.91 apply (zenon_L214_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.91 apply (zenon_L486_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.91 apply (zenon_L15_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.78/21.91 apply (zenon_L870_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.78/21.91 apply (zenon_L872_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.78/21.91 apply (zenon_L406_); trivial. % 21.78/21.91 exact (zenon_H162 zenon_H167). % 21.78/21.91 (* end of lemma zenon_L911_ *) % 21.78/21.91 assert (zenon_L912_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (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) (e3)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.91 do 0 intro. intros zenon_H139 zenon_H68 zenon_H1e zenon_H162 zenon_H31 zenon_H212 zenon_H7d zenon_Hbc zenon_H13a zenon_H33 zenon_Ha9 zenon_Ha0 zenon_Hb6 zenon_H155 zenon_H1bb zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H24e zenon_H181 zenon_Hc4 zenon_H164 zenon_H54 zenon_H55 zenon_H4d zenon_H156 zenon_H77 zenon_He4 zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.91 apply (zenon_L20_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.91 apply (zenon_L911_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.91 apply (zenon_L122_); trivial. % 21.78/21.91 apply (zenon_L167_); trivial. % 21.78/21.91 (* end of lemma zenon_L912_ *) % 21.78/21.91 assert (zenon_L913_ : (((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) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.78/21.91 do 0 intro. intros zenon_H15d zenon_H48 zenon_H82 zenon_H4e zenon_H196 zenon_H93 zenon_H177 zenon_H160 zenon_He4 zenon_H77 zenon_H156 zenon_H4d zenon_H55 zenon_H164 zenon_H24e zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H33 zenon_H13a zenon_Hbc zenon_H7d zenon_H212 zenon_H31 zenon_H1e zenon_H68 zenon_H139 zenon_H1bb zenon_H162 zenon_H18a zenon_H181 zenon_Hc4. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.91 apply (zenon_L13_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.91 apply (zenon_L215_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.91 apply (zenon_L239_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.91 apply (zenon_L888_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.91 apply (zenon_L14_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.91 apply (zenon_L912_); trivial. % 21.78/21.91 apply (zenon_L211_); trivial. % 21.78/21.91 (* end of lemma zenon_L913_ *) % 21.78/21.91 assert (zenon_L914_ : (((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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (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)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.78/21.91 do 0 intro. intros zenon_H13c zenon_H1c6 zenon_H117 zenon_H54 zenon_Hf0 zenon_H196 zenon_H25b zenon_Hf5 zenon_H25e zenon_H18a zenon_H31 zenon_H177 zenon_H33 zenon_H121 zenon_Hc4 zenon_H181 zenon_H1c3 zenon_H9f zenon_Ha9 zenon_H68 zenon_H77 zenon_H162 zenon_H1bb zenon_H164 zenon_H1cd zenon_H7d zenon_H24e zenon_H4d zenon_H192 zenon_H3d zenon_H12e zenon_H1b7 zenon_H93 zenon_Ha0 zenon_Hfa zenon_H25 zenon_H1b4 zenon_H20f zenon_H129 zenon_H48 zenon_H18d zenon_H160 zenon_H163 zenon_H195 zenon_H19a zenon_H104 zenon_H13f zenon_Hb6 zenon_H131 zenon_H141 zenon_H1c7. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.91 apply (zenon_L116_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.91 apply (zenon_L882_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.91 apply (zenon_L124_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.78/21.91 apply (zenon_L55_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.78/21.91 apply (zenon_L882_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.78/21.91 apply (zenon_L887_); trivial. % 21.78/21.91 exact (zenon_H1c7 zenon_Hac). % 21.78/21.91 (* end of lemma zenon_L914_ *) % 21.78/21.91 assert (zenon_L915_ : (((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)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.78/21.91 do 0 intro. intros zenon_H1bb zenon_H18a zenon_H7d zenon_H9d zenon_H160 zenon_H1cd zenon_H1b7 zenon_H34 zenon_H24e zenon_H181 zenon_H9e zenon_H1b4. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.78/21.91 apply (zenon_L416_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.78/21.91 apply (zenon_L803_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.78/21.91 exact (zenon_H181 zenon_H17c). % 21.78/21.91 apply (zenon_L602_); trivial. % 21.78/21.91 (* end of lemma zenon_L915_ *) % 21.78/21.91 assert (zenon_L916_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e0)) -> False). % 21.78/21.91 do 0 intro. intros zenon_He4 zenon_Hef zenon_H163 zenon_H192 zenon_H1bb zenon_H162 zenon_H18a zenon_H181 zenon_Hc4 zenon_H12e zenon_H156 zenon_H4d zenon_H55 zenon_H54 zenon_H48 zenon_He0. % 21.78/21.91 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.91 apply (zenon_L878_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.91 apply (zenon_L486_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.91 apply (zenon_L15_); trivial. % 21.78/21.91 apply (zenon_L57_); trivial. % 21.78/21.91 (* end of lemma zenon_L916_ *) % 21.78/21.91 assert (zenon_L917_ : (((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 (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (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)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (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) (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) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (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 (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 21.78/21.91 do 0 intro. intros zenon_Hb2 zenon_Hf5 zenon_H141 zenon_H121 zenon_H33 zenon_H1c7 zenon_H104 zenon_H13f zenon_H131 zenon_Hfa zenon_H3d zenon_H77 zenon_H195 zenon_H25e zenon_H20f zenon_H25b zenon_H196 zenon_Hf0 zenon_H117 zenon_H68 zenon_H93 zenon_H13c zenon_Ha0 zenon_H25 zenon_Hb6 zenon_H164 zenon_H1b4 zenon_H9e zenon_H24e zenon_H1b7 zenon_H1cd zenon_H160 zenon_H7d zenon_H48 zenon_H54 zenon_H55 zenon_H4d zenon_H156 zenon_H12e zenon_Hc4 zenon_H181 zenon_H18a zenon_H1bb zenon_H192 zenon_H163 zenon_Hef zenon_He4 zenon_H31 zenon_H177 zenon_H162. % 21.78/21.91 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.91 apply (zenon_L116_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.91 apply (zenon_L882_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.91 apply (zenon_L124_); trivial. % 21.78/21.91 apply (zenon_L262_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.78/21.91 apply (zenon_L116_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.78/21.91 apply (zenon_L151_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.78/21.91 apply (zenon_L915_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.78/21.91 apply (zenon_L916_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.78/21.91 apply (zenon_L406_); trivial. % 21.78/21.91 exact (zenon_H162 zenon_H167). % 21.78/21.91 (* end of lemma zenon_L917_ *) % 21.78/21.91 assert (zenon_L918_ : (((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)) = (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) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.78/21.91 do 0 intro. intros zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_Hc4 zenon_H104 zenon_H1c7 zenon_H9f zenon_H33 zenon_H121 zenon_H212 zenon_H25 zenon_H179 zenon_H7f zenon_H7d zenon_H160 zenon_Hbc. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.78/21.91 apply (zenon_L68_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.78/21.91 apply (zenon_L124_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.78/21.91 apply (zenon_L819_); trivial. % 21.78/21.91 apply (zenon_L658_); trivial. % 21.78/21.91 (* end of lemma zenon_L918_ *) % 21.78/21.91 assert (zenon_L919_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (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) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((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) (e3)) = (e3))) -> False). % 21.78/21.91 do 0 intro. intros zenon_H82 zenon_Ha9 zenon_H139 zenon_H155 zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H13c zenon_H25 zenon_H173 zenon_H4d zenon_H19a zenon_H48 zenon_H93 zenon_H68 zenon_He4 zenon_H141 zenon_H13f zenon_H131 zenon_H177 zenon_Hfa zenon_H163 zenon_H192 zenon_H12e zenon_H77 zenon_H195 zenon_H25e zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H196 zenon_H164 zenon_Hf0 zenon_H117 zenon_H156 zenon_H55 zenon_H1a2 zenon_H104 zenon_H1c7 zenon_H33 zenon_H121 zenon_H212 zenon_H179 zenon_H7d zenon_H160 zenon_Hbc zenon_H13a zenon_H1bb zenon_H162 zenon_H18a zenon_H181 zenon_Hc4. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.91 apply (zenon_L888_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.91 apply (zenon_L25_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.91 apply (zenon_L889_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.91 apply (zenon_L486_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.91 apply (zenon_L15_); trivial. % 21.78/21.91 apply (zenon_L918_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.91 apply (zenon_L116_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.91 apply (zenon_L120_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.91 apply (zenon_L124_); trivial. % 21.78/21.91 apply (zenon_L247_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.91 apply (zenon_L68_); trivial. % 21.78/21.91 apply (zenon_L115_); trivial. % 21.78/21.91 apply (zenon_L211_); trivial. % 21.78/21.91 (* end of lemma zenon_L919_ *) % 21.78/21.91 assert (zenon_L920_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (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) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (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))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (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) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.78/21.91 do 0 intro. intros zenon_H1fe zenon_Hbc zenon_H179 zenon_H212 zenon_H121 zenon_H33 zenon_H104 zenon_H1a2 zenon_H55 zenon_H156 zenon_H117 zenon_Hf0 zenon_H164 zenon_H1b4 zenon_H25b zenon_Hf5 zenon_H20f zenon_H25e zenon_H195 zenon_H12e zenon_H192 zenon_H163 zenon_Hfa zenon_H131 zenon_H13f zenon_H141 zenon_He4 zenon_H68 zenon_H19a zenon_H173 zenon_H13c zenon_Hb2 zenon_H1c6 zenon_H1c3 zenon_H129 zenon_H18d zenon_H18a zenon_H48 zenon_H4d zenon_H4e zenon_H139 zenon_H77 zenon_Hb6 zenon_H31 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H177 zenon_H93 zenon_H196 zenon_H82 zenon_H73 zenon_H67 zenon_H15d zenon_H1bb zenon_H162 zenon_H1c7 zenon_H160 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H181 zenon_Hc4. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.91 apply (zenon_L913_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.91 apply (zenon_L251_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.91 apply (zenon_L818_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.91 apply (zenon_L25_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.91 apply (zenon_L914_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.91 apply (zenon_L55_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.91 apply (zenon_L68_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.91 apply (zenon_L171_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.91 apply (zenon_L917_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.91 apply (zenon_L227_); trivial. % 21.78/21.91 apply (zenon_L228_); trivial. % 21.78/21.91 apply (zenon_L211_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.91 apply (zenon_L239_); trivial. % 21.78/21.91 apply (zenon_L919_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.91 apply (zenon_L251_); trivial. % 21.78/21.91 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.91 apply (zenon_L892_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.92 apply (zenon_L184_); trivial. % 21.78/21.92 apply (zenon_L893_); trivial. % 21.78/21.92 apply (zenon_L870_); trivial. % 21.78/21.92 (* end of lemma zenon_L920_ *) % 21.78/21.92 assert (zenon_L921_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> False). % 21.78/21.92 do 0 intro. intros zenon_H240 zenon_H67 zenon_H31. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 21.78/21.92 exact (zenon_H237 zenon_H31). % 21.78/21.92 exact (zenon_H6c zenon_H67). % 21.78/21.92 (* end of lemma zenon_L921_ *) % 21.78/21.92 assert (zenon_L922_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> False). % 21.78/21.92 do 0 intro. intros zenon_H9b zenon_H67 zenon_H31. % 21.78/21.92 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.78/21.92 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 21.78/21.92 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.78/21.92 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.78/21.92 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.78/21.92 apply (zenon_L921_); trivial. % 21.78/21.92 (* end of lemma zenon_L922_ *) % 21.78/21.92 assert (zenon_L923_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 21.78/21.92 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H25 zenon_H1b3 zenon_H77 zenon_H4d zenon_Ha9 zenon_Ha5. % 21.78/21.92 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.92 apply (zenon_L171_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.92 exact (zenon_H1b3 zenon_Hef). % 21.78/21.92 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.92 apply (zenon_L59_); trivial. % 21.78/21.92 apply (zenon_L299_); trivial. % 21.78/21.92 (* end of lemma zenon_L923_ *) % 21.78/21.92 assert (zenon_L924_ : (((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)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> False). % 21.78/21.92 do 0 intro. intros zenon_H82 zenon_H7d zenon_Ha5 zenon_H5d zenon_Hb6 zenon_Hb2 zenon_H7a zenon_H2d zenon_H164 zenon_H48 zenon_Hac zenon_Ha0 zenon_H31 zenon_H177 zenon_H67. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.92 apply (zenon_L355_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.92 exact (zenon_H7a zenon_H3c). % 21.78/21.92 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.92 apply (zenon_L217_); trivial. % 21.78/21.92 apply (zenon_L718_); trivial. % 21.78/21.92 (* end of lemma zenon_L924_ *) % 21.78/21.92 assert (zenon_L925_ : (((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)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1c3 zenon_H68 zenon_H38 zenon_Ha5 zenon_Ha9 zenon_H189 zenon_H6d zenon_H77 zenon_H11f. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.78/21.92 apply (zenon_L165_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.78/21.92 apply (zenon_L299_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.78/21.92 apply (zenon_L439_); trivial. % 21.78/21.92 apply (zenon_L884_); trivial. % 21.78/21.92 (* end of lemma zenon_L925_ *) % 21.78/21.92 assert (zenon_L926_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1c3 zenon_H9f zenon_H11f zenon_Ha5 zenon_Ha9 zenon_H189 zenon_H6d zenon_H68 zenon_H167. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.78/21.92 apply (zenon_L673_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.78/21.92 apply (zenon_L299_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.78/21.92 apply (zenon_L439_); trivial. % 21.78/21.92 apply (zenon_L295_); trivial. % 21.78/21.92 (* end of lemma zenon_L926_ *) % 21.78/21.92 assert (zenon_L927_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H19a zenon_Ha0 zenon_H77 zenon_H1c3 zenon_H9f zenon_H11f zenon_Ha5 zenon_Ha9 zenon_H189 zenon_H6d zenon_H68. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.78/21.92 apply (zenon_L925_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.78/21.92 apply (zenon_L90_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.78/21.92 apply (zenon_L885_); trivial. % 21.78/21.92 apply (zenon_L926_); trivial. % 21.78/21.92 (* end of lemma zenon_L927_ *) % 21.78/21.92 assert (zenon_L928_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1a8 zenon_H3d zenon_H1b3 zenon_H68 zenon_H189 zenon_Ha5 zenon_H11f zenon_H9f zenon_H1c3 zenon_H77 zenon_Ha0 zenon_H19a zenon_Ha9 zenon_Hac. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.92 apply (zenon_L214_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.92 exact (zenon_H1b3 zenon_Hef). % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.92 apply (zenon_L927_); trivial. % 21.78/21.92 apply (zenon_L371_); trivial. % 21.78/21.92 (* end of lemma zenon_L928_ *) % 21.78/21.92 assert (zenon_L929_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 21.78/21.92 do 0 intro. intros zenon_Hf0 zenon_He7 zenon_Hdd. % 21.78/21.92 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 21.78/21.92 intro zenon_D_pnotp. % 21.78/21.92 apply zenon_Hf0. % 21.78/21.92 rewrite <- zenon_D_pnotp. % 21.78/21.92 exact zenon_He7. % 21.78/21.92 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H265]. % 21.78/21.92 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 21.78/21.92 congruence. % 21.78/21.92 apply zenon_H10f. apply refl_equal. % 21.78/21.92 apply zenon_H265. apply sym_equal. exact zenon_Hdd. % 21.78/21.92 (* end of lemma zenon_L929_ *) % 21.78/21.92 assert (zenon_L930_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1c3 zenon_H77 zenon_H155 zenon_Ha5 zenon_Ha9 zenon_H115 zenon_H68 zenon_H181. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.78/21.92 apply (zenon_L98_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.78/21.92 apply (zenon_L299_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.78/21.92 apply (zenon_L158_); trivial. % 21.78/21.92 exact (zenon_H181 zenon_H17c). % 21.78/21.92 (* end of lemma zenon_L930_ *) % 21.78/21.92 assert (zenon_L931_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> False). % 21.78/21.92 do 0 intro. intros zenon_H169 zenon_He3 zenon_H40 zenon_H11a zenon_Hac zenon_H158 zenon_H4d. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 21.78/21.92 exact (zenon_H1d4 zenon_H4d). % 21.78/21.92 apply (zenon_L373_); trivial. % 21.78/21.92 (* end of lemma zenon_L931_ *) % 21.78/21.92 assert (zenon_L932_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H3e zenon_H4d zenon_H158 zenon_Hac zenon_H11a zenon_He3 zenon_H169. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 21.78/21.92 apply (zenon_L931_); trivial. % 21.78/21.92 apply (zenon_L931_); trivial. % 21.78/21.92 (* end of lemma zenon_L932_ *) % 21.78/21.92 assert (zenon_L933_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H13c zenon_Ha0 zenon_H25 zenon_H173 zenon_Hdb zenon_Hb6 zenon_H4d zenon_Hb9 zenon_H195. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.92 apply (zenon_L116_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.92 apply (zenon_L120_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.92 apply (zenon_L124_); trivial. % 21.78/21.92 apply (zenon_L172_); trivial. % 21.78/21.92 (* end of lemma zenon_L933_ *) % 21.78/21.92 assert (zenon_L934_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H13a zenon_H47 zenon_H195 zenon_H4d zenon_Hb6 zenon_H173 zenon_H25 zenon_Ha0 zenon_H13c zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.92 apply (zenon_L253_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.92 apply (zenon_L933_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.92 apply (zenon_L178_); trivial. % 21.78/21.92 apply (zenon_L154_); trivial. % 21.78/21.92 (* end of lemma zenon_L934_ *) % 21.78/21.92 assert (zenon_L935_ : (((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)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((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)))) -> (~((e1) = (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)) = (e2)) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1cf zenon_H68 zenon_H31 zenon_H156 zenon_Hef zenon_H8b zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H77 zenon_H25e zenon_H195 zenon_H93 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H9f zenon_Hb9 zenon_H196. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.92 apply (zenon_L264_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.92 apply (zenon_L100_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.92 exact (zenon_H8b zenon_H8a). % 21.78/21.92 apply (zenon_L820_); trivial. % 21.78/21.92 (* end of lemma zenon_L935_ *) % 21.78/21.92 assert (zenon_L936_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (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 (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 (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H164 zenon_H9f zenon_H93 zenon_H192 zenon_H3d zenon_H48 zenon_H12e zenon_H31 zenon_H1cf zenon_H129 zenon_Hc0 zenon_H13a zenon_H68 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H19a zenon_H7e zenon_H7d zenon_H16a zenon_H7b zenon_H77 zenon_H8b zenon_H156 zenon_Hb6 zenon_He4 zenon_H177 zenon_H196 zenon_Hef zenon_H67 zenon_H1bb zenon_Hbb zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_Hb9 zenon_H195. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.78/21.92 apply (zenon_L935_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.78/21.92 apply (zenon_L669_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.78/21.92 apply (zenon_L80_); trivial. % 21.78/21.92 apply (zenon_L684_); trivial. % 21.78/21.92 (* end of lemma zenon_L936_ *) % 21.78/21.92 assert (zenon_L937_ : (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((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))))) -> (~((e0) = (e1))) -> ((op (e0) (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 (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1ba zenon_H1d5 zenon_H186 zenon_H1bb zenon_H67 zenon_Hef zenon_H177 zenon_He4 zenon_H156 zenon_H8b zenon_H7b zenon_H16a zenon_H19a zenon_H68 zenon_H13a zenon_Hc0 zenon_H129 zenon_H1cf zenon_H12e zenon_H48 zenon_H3d zenon_H192 zenon_H164 zenon_Hbc zenon_Hbb zenon_H7d zenon_H179 zenon_H212 zenon_H77 zenon_H25e zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H195 zenon_H4d zenon_Hb6 zenon_H173 zenon_H25 zenon_H13c zenon_Ha0 zenon_H31 zenon_Hb9 zenon_H196. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.92 apply (zenon_L116_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.78/21.92 exact (zenon_H7b zenon_H65). % 21.78/21.92 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.78/21.92 exact (zenon_H1ba zenon_H6d). % 21.78/21.92 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.78/21.92 exact (zenon_H8b zenon_H8a). % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.92 apply (zenon_L252_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.92 apply (zenon_L100_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.92 exact (zenon_H8b zenon_H8a). % 21.78/21.92 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.78/21.92 apply (zenon_L936_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.78/21.92 apply (zenon_L658_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.78/21.92 apply (zenon_L367_); trivial. % 21.78/21.92 apply (zenon_L674_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.92 apply (zenon_L124_); trivial. % 21.78/21.92 apply (zenon_L172_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.92 apply (zenon_L933_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.92 apply (zenon_L68_); trivial. % 21.78/21.92 apply (zenon_L154_); trivial. % 21.78/21.92 (* end of lemma zenon_L937_ *) % 21.78/21.92 assert (zenon_L938_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((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 (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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((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)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_Hfa zenon_H1a8 zenon_H196 zenon_Hb9 zenon_Ha0 zenon_H13c zenon_H25 zenon_H173 zenon_Hb6 zenon_H4d zenon_H195 zenon_H1b4 zenon_H25b zenon_Hf5 zenon_H20f zenon_H25e zenon_H77 zenon_H212 zenon_H179 zenon_H7d zenon_Hbb zenon_Hbc zenon_H164 zenon_H192 zenon_H3d zenon_H48 zenon_H12e zenon_H129 zenon_Hc0 zenon_H13a zenon_H19a zenon_H16a zenon_H7b zenon_H156 zenon_He4 zenon_H177 zenon_H67 zenon_H1bb zenon_H1d5 zenon_H1ba zenon_H1cf zenon_H68 zenon_H31 zenon_H186 zenon_H8b zenon_H1cd. % 21.78/21.92 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.92 apply (zenon_L171_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.92 apply (zenon_L937_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.92 apply (zenon_L59_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.92 apply (zenon_L214_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.92 apply (zenon_L937_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.92 exact (zenon_H1ba zenon_H6d). % 21.78/21.92 apply (zenon_L709_); trivial. % 21.78/21.92 (* end of lemma zenon_L938_ *) % 21.78/21.92 assert (zenon_L939_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hdd zenon_H68 zenon_H8b zenon_Hf7 zenon_H195. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.78/21.92 exact (zenon_H7b zenon_H65). % 21.78/21.92 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.78/21.92 apply (zenon_L54_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.78/21.92 exact (zenon_H8b zenon_H8a). % 21.78/21.92 apply (zenon_L228_); trivial. % 21.78/21.92 (* end of lemma zenon_L939_ *) % 21.78/21.92 assert (zenon_L940_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 21.78/21.92 do 0 intro. intros zenon_H13c zenon_Ha0 zenon_H25 zenon_H167 zenon_Hb6 zenon_H4d zenon_Ha9 zenon_Hf7. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.92 apply (zenon_L116_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.92 apply (zenon_L294_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.92 apply (zenon_L124_); trivial. % 21.78/21.92 apply (zenon_L299_); trivial. % 21.78/21.92 (* end of lemma zenon_L940_ *) % 21.78/21.92 assert (zenon_L941_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H25e zenon_H136 zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H11f zenon_H117 zenon_Hb6 zenon_H54 zenon_H10c zenon_Hf0 zenon_H14c zenon_Ha0 zenon_H196. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H38 | zenon_intro zenon_H25f ]. % 21.78/21.92 apply (zenon_L663_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H155 | zenon_intro zenon_H260 ]. % 21.78/21.92 apply (zenon_L187_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H9e ]. % 21.78/21.92 apply (zenon_L673_); trivial. % 21.78/21.92 apply (zenon_L581_); trivial. % 21.78/21.92 (* end of lemma zenon_L941_ *) % 21.78/21.92 assert (zenon_L942_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H13a zenon_H155 zenon_H7e zenon_H7d zenon_H16a zenon_H7b zenon_H77 zenon_H8b zenon_H17c zenon_H129 zenon_H4d zenon_H156 zenon_Hb6 zenon_He4 zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.92 apply (zenon_L444_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.92 apply (zenon_L667_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.92 apply (zenon_L178_); trivial. % 21.78/21.92 apply (zenon_L154_); trivial. % 21.78/21.92 (* end of lemma zenon_L942_ *) % 21.78/21.92 assert (zenon_L943_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1bb zenon_Hf7 zenon_Ha9 zenon_H25 zenon_H13c zenon_Ha0 zenon_H14c zenon_Hf0 zenon_H10c zenon_H54 zenon_H117 zenon_H9f zenon_H1b4 zenon_Hf5 zenon_H136 zenon_H25e zenon_H196 zenon_Hb9 zenon_H177 zenon_He4 zenon_Hb6 zenon_H156 zenon_H4d zenon_H129 zenon_H8b zenon_H77 zenon_H7b zenon_H16a zenon_H7d zenon_H7e zenon_H155 zenon_H13a zenon_Hbb zenon_H1cb. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.78/21.92 apply (zenon_L940_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.78/21.92 apply (zenon_L941_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.78/21.92 apply (zenon_L942_); trivial. % 21.78/21.92 apply (zenon_L622_); trivial. % 21.78/21.92 (* end of lemma zenon_L943_ *) % 21.78/21.92 assert (zenon_L944_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1d5 zenon_H67 zenon_H19a zenon_H26d zenon_H196 zenon_H14c zenon_Hf0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H9f zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H1cf zenon_H68 zenon_H31 zenon_Hf7 zenon_H8b zenon_H77 zenon_H212 zenon_H25 zenon_H179 zenon_H7d zenon_Hbb zenon_Hbc zenon_H1bb zenon_Ha9 zenon_H13c zenon_H177 zenon_He4 zenon_H156 zenon_H129 zenon_H7b zenon_H16a zenon_H155 zenon_H13a zenon_H1cb zenon_H12e zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_Hb9 zenon_H195. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.92 apply (zenon_L252_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.92 apply (zenon_L438_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.92 exact (zenon_H8b zenon_H8a). % 21.78/21.92 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.78/21.92 apply (zenon_L756_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.78/21.92 apply (zenon_L943_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.78/21.92 apply (zenon_L658_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.78/21.92 apply (zenon_L750_); trivial. % 21.78/21.92 apply (zenon_L941_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.78/21.92 apply (zenon_L77_); trivial. % 21.78/21.92 apply (zenon_L684_); trivial. % 21.78/21.92 (* end of lemma zenon_L944_ *) % 21.78/21.92 assert (zenon_L945_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> False). % 21.78/21.92 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_H156 zenon_H4d zenon_H7b zenon_H1a8 zenon_Ha9 zenon_Hdb zenon_H155 zenon_H31 zenon_H68 zenon_H173 zenon_H16a zenon_H2c zenon_Hf0 zenon_H8b zenon_H16b zenon_H139 zenon_H1ba zenon_H77. % 21.78/21.92 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.92 apply (zenon_L55_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.92 apply (zenon_L486_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.92 apply (zenon_L378_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.92 apply (zenon_L110_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.92 apply (zenon_L745_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.92 exact (zenon_H1ba zenon_H6d). % 21.78/21.92 apply (zenon_L169_); trivial. % 21.78/21.92 (* end of lemma zenon_L945_ *) % 21.78/21.92 assert (zenon_L946_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1bb zenon_H18a zenon_H34 zenon_H1b7 zenon_H7f zenon_H1cb zenon_H160 zenon_Hc0 zenon_H129. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.78/21.92 apply (zenon_L416_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.78/21.92 apply (zenon_L780_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.78/21.92 apply (zenon_L236_); trivial. % 21.78/21.92 apply (zenon_L190_); trivial. % 21.78/21.92 (* end of lemma zenon_L946_ *) % 21.78/21.92 assert (zenon_L947_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H12e zenon_H48 zenon_H129 zenon_Hc0 zenon_H1cb zenon_H1b7 zenon_H34 zenon_H18a zenon_H1bb zenon_H160 zenon_H77 zenon_H25e zenon_H136 zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_Hb6 zenon_H54 zenon_H10c zenon_Hf0 zenon_H14c zenon_Ha0 zenon_H196. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.78/21.92 apply (zenon_L456_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.78/21.92 apply (zenon_L946_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.78/21.92 apply (zenon_L367_); trivial. % 21.78/21.92 apply (zenon_L941_); trivial. % 21.78/21.92 (* end of lemma zenon_L947_ *) % 21.78/21.92 assert (zenon_L948_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((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) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H19a zenon_H26d zenon_H31 zenon_H196 zenon_H14c zenon_Hf0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H9f zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H77 zenon_H160 zenon_H1bb zenon_H18a zenon_H34 zenon_H1b7 zenon_H1cb zenon_Hc0 zenon_H129 zenon_H48 zenon_H12e zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_Hb9 zenon_H195. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.78/21.92 apply (zenon_L756_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.78/21.92 apply (zenon_L947_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.78/21.92 apply (zenon_L77_); trivial. % 21.78/21.92 apply (zenon_L684_); trivial. % 21.78/21.92 (* end of lemma zenon_L948_ *) % 21.78/21.92 assert (zenon_L949_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((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) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1cf zenon_H1d5 zenon_H67 zenon_H4e zenon_H76 zenon_H8b zenon_H19a zenon_H26d zenon_H31 zenon_H196 zenon_H14c zenon_Hf0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H9f zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H77 zenon_H1bb zenon_H18a zenon_H34 zenon_H1b7 zenon_H1cb zenon_Hc0 zenon_H129 zenon_H48 zenon_H12e zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_Hb9 zenon_H195. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.92 apply (zenon_L252_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.92 apply (zenon_L83_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.92 exact (zenon_H8b zenon_H8a). % 21.78/21.92 apply (zenon_L948_); trivial. % 21.78/21.92 (* end of lemma zenon_L949_ *) % 21.78/21.92 assert (zenon_L950_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((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) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1cf zenon_H68 zenon_Hf7 zenon_H8b zenon_H19a zenon_H26d zenon_H31 zenon_H196 zenon_H14c zenon_Hf0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H9f zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H77 zenon_H1bb zenon_H18a zenon_H34 zenon_H1b7 zenon_H1cb zenon_Hc0 zenon_H129 zenon_H48 zenon_H12e zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_Hb9 zenon_H195. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.92 apply (zenon_L264_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.92 apply (zenon_L438_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.92 exact (zenon_H8b zenon_H8a). % 21.78/21.92 apply (zenon_L948_); trivial. % 21.78/21.92 (* end of lemma zenon_L950_ *) % 21.78/21.92 assert (zenon_L951_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (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 (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((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))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 21.78/21.92 do 0 intro. intros zenon_H141 zenon_H7b zenon_H16a zenon_H195 zenon_H10c zenon_H4d zenon_H186 zenon_H20f zenon_H25b zenon_H12e zenon_H48 zenon_H129 zenon_Hc0 zenon_H1cb zenon_H1b7 zenon_H34 zenon_H18a zenon_H1bb zenon_H77 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_Hb6 zenon_H54 zenon_Hf0 zenon_H196 zenon_H31 zenon_H26d zenon_H19a zenon_H8b zenon_Hf7 zenon_H68 zenon_H1cf zenon_Ha0 zenon_Hb9. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.92 apply (zenon_L217_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.92 apply (zenon_L939_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.92 apply (zenon_L950_); trivial. % 21.78/21.92 apply (zenon_L77_); trivial. % 21.78/21.92 (* end of lemma zenon_L951_ *) % 21.78/21.92 assert (zenon_L952_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1cf zenon_H68 zenon_H31 zenon_H4d zenon_H8b zenon_H12e zenon_H48 zenon_H129 zenon_Hc0 zenon_H1cb zenon_H1b7 zenon_H34 zenon_H18a zenon_H1bb zenon_H77 zenon_H25e zenon_H136 zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_Hb6 zenon_H54 zenon_H10c zenon_Hf0 zenon_H14c zenon_Ha0 zenon_H196. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.92 apply (zenon_L264_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.92 apply (zenon_L59_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.92 exact (zenon_H8b zenon_H8a). % 21.78/21.92 apply (zenon_L947_); trivial. % 21.78/21.92 (* end of lemma zenon_L952_ *) % 21.78/21.92 assert (zenon_L953_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (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) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (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 (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (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 (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H13b zenon_H179 zenon_Ha9 zenon_Hbb zenon_H163 zenon_H186 zenon_H20f zenon_H25b zenon_H26d zenon_H19a zenon_H1d5 zenon_H67 zenon_H4e zenon_Hfa zenon_H13c zenon_H24 zenon_Ha0 zenon_H1cf zenon_H68 zenon_H31 zenon_H8b zenon_H12e zenon_H48 zenon_H129 zenon_Hc0 zenon_H1cb zenon_H1b7 zenon_H34 zenon_H18a zenon_H1bb zenon_H77 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_H54 zenon_Hf0 zenon_H196 zenon_H16a zenon_H7b zenon_H16b zenon_H109 zenon_H141 zenon_Hb6 zenon_H4d zenon_Hb9 zenon_H195. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.78/21.92 apply (zenon_L297_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.92 apply (zenon_L900_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.92 apply (zenon_L217_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.92 apply (zenon_L929_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.92 apply (zenon_L949_); trivial. % 21.78/21.92 apply (zenon_L77_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.92 apply (zenon_L124_); trivial. % 21.78/21.92 apply (zenon_L172_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.92 apply (zenon_L779_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.92 apply (zenon_L59_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.92 apply (zenon_L900_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.92 apply (zenon_L951_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.92 apply (zenon_L617_); trivial. % 21.78/21.92 apply (zenon_L299_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.78/21.92 apply (zenon_L117_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.92 apply (zenon_L900_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.92 apply (zenon_L359_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.92 apply (zenon_L682_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.92 apply (zenon_L952_); trivial. % 21.78/21.92 apply (zenon_L77_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.92 apply (zenon_L124_); trivial. % 21.78/21.92 apply (zenon_L172_); trivial. % 21.78/21.92 (* end of lemma zenon_L953_ *) % 21.78/21.92 assert (zenon_L954_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (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 (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))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (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) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (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 (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (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 (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> False). % 21.78/21.92 do 0 intro. intros zenon_H1fe zenon_H7d zenon_H212 zenon_Hbc zenon_H164 zenon_H192 zenon_H1cd zenon_H73 zenon_H131 zenon_H13f zenon_H15d zenon_H82 zenon_Hb6 zenon_Hbb zenon_H177 zenon_He4 zenon_H156 zenon_H4d zenon_H7b zenon_H1a8 zenon_Ha9 zenon_H31 zenon_H68 zenon_H173 zenon_H16a zenon_H2c zenon_Hf0 zenon_H8b zenon_H16b zenon_H139 zenon_H1ba zenon_H77 zenon_H13b zenon_H179 zenon_H163 zenon_H186 zenon_H20f zenon_H25b zenon_H26d zenon_H19a zenon_H1d5 zenon_H67 zenon_H4e zenon_Hfa zenon_H13c zenon_H24 zenon_Ha0 zenon_H1cf zenon_H12e zenon_H129 zenon_Hc0 zenon_H1cb zenon_H1b7 zenon_H18a zenon_H1bb zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H117 zenon_H196 zenon_H109 zenon_H141 zenon_Hb9 zenon_H195 zenon_H13a zenon_H48. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.92 apply (zenon_L20_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.92 apply (zenon_L934_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.92 apply (zenon_L938_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.92 apply (zenon_L184_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.92 apply (zenon_L934_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.92 apply (zenon_L25_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.92 apply (zenon_L171_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.92 apply (zenon_L779_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.92 apply (zenon_L59_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.92 apply (zenon_L900_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.92 apply (zenon_L217_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.92 apply (zenon_L939_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.92 apply (zenon_L944_); trivial. % 21.78/21.92 apply (zenon_L77_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.92 apply (zenon_L124_); trivial. % 21.78/21.92 apply (zenon_L299_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.92 apply (zenon_L945_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.92 apply (zenon_L178_); trivial. % 21.78/21.92 apply (zenon_L115_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.92 apply (zenon_L938_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.92 apply (zenon_L486_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.92 apply (zenon_L378_); trivial. % 21.78/21.92 apply (zenon_L31_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.78/21.92 apply (zenon_L217_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.78/21.92 apply (zenon_L378_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.78/21.92 apply (zenon_L128_); trivial. % 21.78/21.92 apply (zenon_L182_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.92 apply (zenon_L251_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.92 apply (zenon_L251_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.92 apply (zenon_L14_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.92 apply (zenon_L953_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.92 apply (zenon_L55_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.92 apply (zenon_L68_); trivial. % 21.78/21.92 apply (zenon_L154_); trivial. % 21.78/21.92 apply (zenon_L456_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.92 apply (zenon_L239_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.92 apply (zenon_L744_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.92 apply (zenon_L14_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.92 apply (zenon_L953_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.92 apply (zenon_L945_); trivial. % 21.78/21.92 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.92 apply (zenon_L178_); trivial. % 21.78/21.92 apply (zenon_L115_); trivial. % 21.78/21.92 apply (zenon_L456_); trivial. % 21.78/21.92 (* end of lemma zenon_L954_ *) % 21.78/21.92 assert (zenon_L955_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (((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)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.78/21.93 do 0 intro. intros zenon_H164 zenon_H155 zenon_H160 zenon_H18a zenon_H1b7 zenon_H1cf zenon_H271 zenon_H1d8 zenon_H139 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_H191 zenon_H1cb zenon_H48 zenon_H12e zenon_H129 zenon_Hc0 zenon_H13a zenon_H68 zenon_Ha0 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H25b zenon_H186 zenon_H20f zenon_H195 zenon_H19a zenon_H7d zenon_H16a zenon_H7b zenon_H77 zenon_H8b zenon_H4d zenon_H156 zenon_Hb6 zenon_He4 zenon_Hbb zenon_Hb9 zenon_H196 zenon_Hef zenon_H1bb zenon_H31 zenon_H177 zenon_H67 zenon_H7e. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.78/21.93 apply (zenon_L795_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.78/21.93 apply (zenon_L669_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.78/21.93 apply (zenon_L406_); trivial. % 21.78/21.93 apply (zenon_L547_); trivial. % 21.78/21.93 (* end of lemma zenon_L955_ *) % 21.78/21.93 assert (zenon_L956_ : (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((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)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.93 do 0 intro. intros zenon_H1ba zenon_H1d5 zenon_H67 zenon_H177 zenon_H31 zenon_H1bb zenon_Hef zenon_He4 zenon_Hb6 zenon_H156 zenon_H4d zenon_H8b zenon_H7b zenon_H16a zenon_H19a zenon_H186 zenon_Ha0 zenon_H68 zenon_H13a zenon_Hc0 zenon_H129 zenon_H12e zenon_H48 zenon_H1cb zenon_H191 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_H111 zenon_H139 zenon_H1d8 zenon_H271 zenon_H1cf zenon_H1b7 zenon_H18a zenon_H155 zenon_H164 zenon_Hbc zenon_Hbb zenon_H7d zenon_H179 zenon_H25 zenon_H212 zenon_H77 zenon_H25e zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H9f zenon_Hb9 zenon_H196. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.78/21.93 exact (zenon_H7b zenon_H65). % 21.78/21.93 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.78/21.93 exact (zenon_H1ba zenon_H6d). % 21.78/21.93 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.78/21.93 exact (zenon_H8b zenon_H8a). % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.93 apply (zenon_L252_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.93 apply (zenon_L59_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.93 exact (zenon_H8b zenon_H8a). % 21.78/21.93 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.78/21.93 apply (zenon_L955_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.78/21.93 apply (zenon_L658_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.78/21.93 apply (zenon_L367_); trivial. % 21.78/21.93 apply (zenon_L674_); trivial. % 21.78/21.93 (* end of lemma zenon_L956_ *) % 21.78/21.93 assert (zenon_L957_ : (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.78/21.93 do 0 intro. intros zenon_Hb6 zenon_Ha0 zenon_H13c zenon_H25 zenon_H4d zenon_Hb9 zenon_H195 zenon_H1ba zenon_H1d5 zenon_H177 zenon_H1bb zenon_He4 zenon_H156 zenon_H8b zenon_H7b zenon_H16a zenon_H19a zenon_H186 zenon_H13a zenon_Hc0 zenon_H129 zenon_H12e zenon_H48 zenon_H1cb zenon_H191 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_H111 zenon_H139 zenon_H1d8 zenon_H271 zenon_H1cf zenon_H1b7 zenon_H18a zenon_H164 zenon_Hbc zenon_Hbb zenon_H7d zenon_H179 zenon_H212 zenon_H25e zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H196 zenon_Hef zenon_H173 zenon_H68 zenon_H31 zenon_H155 zenon_H77. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.93 apply (zenon_L956_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.93 apply (zenon_L933_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.93 apply (zenon_L68_); trivial. % 21.78/21.93 apply (zenon_L115_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.93 apply (zenon_L226_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.93 apply (zenon_L264_); trivial. % 21.78/21.93 apply (zenon_L98_); trivial. % 21.78/21.93 (* end of lemma zenon_L957_ *) % 21.78/21.93 assert (zenon_L958_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((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 (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (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))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.78/21.93 do 0 intro. intros zenon_H1bb zenon_H14c zenon_Hf0 zenon_H10c zenon_H54 zenon_H117 zenon_H9f zenon_H136 zenon_H196 zenon_Hb9 zenon_Hbb zenon_H177 zenon_He4 zenon_H156 zenon_H129 zenon_H8b zenon_H77 zenon_H7b zenon_H16a zenon_H7d zenon_H7e zenon_H19a zenon_H195 zenon_H20f zenon_H186 zenon_H25b zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H68 zenon_H13a zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H191 zenon_H1cb. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.78/21.93 apply (zenon_L421_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.78/21.93 apply (zenon_L941_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.78/21.93 apply (zenon_L668_); trivial. % 21.78/21.93 apply (zenon_L762_); trivial. % 21.78/21.93 (* end of lemma zenon_L958_ *) % 21.78/21.93 assert (zenon_L959_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((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 (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.93 do 0 intro. intros zenon_H1d5 zenon_H67 zenon_H26d zenon_H196 zenon_H14c zenon_H9f zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H1cf zenon_H68 zenon_H31 zenon_Hf7 zenon_H8b zenon_H77 zenon_H212 zenon_H25 zenon_H179 zenon_H7d zenon_Hbb zenon_Hbc zenon_H1bb zenon_H177 zenon_He4 zenon_H156 zenon_H129 zenon_H7b zenon_H16a zenon_H19a zenon_H13a zenon_H1a2 zenon_H1cb zenon_H12e zenon_Ha0 zenon_H191 zenon_Hf0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_Hb9 zenon_H195. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.93 apply (zenon_L252_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.93 apply (zenon_L438_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.93 exact (zenon_H8b zenon_H8a). % 21.78/21.93 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.78/21.93 apply (zenon_L756_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.78/21.93 apply (zenon_L958_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.78/21.93 apply (zenon_L658_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.78/21.93 apply (zenon_L750_); trivial. % 21.78/21.93 apply (zenon_L941_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.78/21.93 apply (zenon_L648_); trivial. % 21.78/21.93 apply (zenon_L684_); trivial. % 21.78/21.93 (* end of lemma zenon_L959_ *) % 21.78/21.93 assert (zenon_L960_ : (~((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (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 (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 (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.93 do 0 intro. intros zenon_H1ba zenon_H164 zenon_H9f zenon_H192 zenon_H3d zenon_H48 zenon_H12e zenon_H31 zenon_H1cf zenon_H129 zenon_Hc0 zenon_H13a zenon_H68 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H19a zenon_H7e zenon_H7d zenon_H16a zenon_H7b zenon_H77 zenon_H8b zenon_H156 zenon_Hb6 zenon_He4 zenon_H177 zenon_H196 zenon_Hef zenon_H67 zenon_H1bb zenon_Hbb zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_Hb9 zenon_H195. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.78/21.93 exact (zenon_H7b zenon_H65). % 21.78/21.93 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.78/21.93 exact (zenon_H1ba zenon_H6d). % 21.78/21.93 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.78/21.93 exact (zenon_H8b zenon_H8a). % 21.78/21.93 apply (zenon_L936_); trivial. % 21.78/21.93 (* end of lemma zenon_L960_ *) % 21.78/21.93 assert (zenon_L961_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (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 (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 (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.93 do 0 intro. intros zenon_H13c zenon_H25 zenon_H4d zenon_H186 zenon_H20f zenon_H25b zenon_Ha0 zenon_H1bb zenon_H67 zenon_Hef zenon_H196 zenon_H177 zenon_He4 zenon_Hb6 zenon_H156 zenon_H8b zenon_H77 zenon_H7b zenon_H16a zenon_H7d zenon_H7e zenon_H19a zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H68 zenon_H13a zenon_Hc0 zenon_H129 zenon_H1cf zenon_H31 zenon_H12e zenon_H48 zenon_H3d zenon_H192 zenon_H9f zenon_H164 zenon_H1ba zenon_H163 zenon_Hbb zenon_Hb9 zenon_H195. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.93 apply (zenon_L116_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.93 apply (zenon_L960_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.93 apply (zenon_L617_); trivial. % 21.78/21.93 apply (zenon_L172_); trivial. % 21.78/21.93 (* end of lemma zenon_L961_ *) % 21.78/21.93 assert (zenon_L962_ : (((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 (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((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)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.93 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hf0 zenon_H1cf zenon_H68 zenon_H31 zenon_H156 zenon_Hef zenon_H8b zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H77 zenon_H25e zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H9f zenon_Hb9 zenon_H196. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.78/21.93 exact (zenon_H7b zenon_H65). % 21.78/21.93 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.78/21.93 apply (zenon_L61_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.78/21.93 exact (zenon_H8b zenon_H8a). % 21.78/21.93 apply (zenon_L935_); trivial. % 21.78/21.93 (* end of lemma zenon_L962_ *) % 21.78/21.93 assert (zenon_L963_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.93 do 0 intro. intros zenon_H12e zenon_H48 zenon_H1cb zenon_H191 zenon_H4d zenon_H31 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H139 zenon_H1d8 zenon_H271 zenon_H68 zenon_H1cf zenon_H1b7 zenon_H34 zenon_H18a zenon_H1bb zenon_H160 zenon_H77 zenon_H25e zenon_H136 zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_Hb6 zenon_H54 zenon_H10c zenon_Hf0 zenon_H14c zenon_Ha0 zenon_H196. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.78/21.93 apply (zenon_L456_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.78/21.93 apply (zenon_L794_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.78/21.93 apply (zenon_L367_); trivial. % 21.78/21.93 apply (zenon_L941_); trivial. % 21.78/21.93 (* end of lemma zenon_L963_ *) % 21.78/21.93 assert (zenon_L964_ : ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> False). % 21.78/21.93 do 0 intro. intros zenon_He7 zenon_H171 zenon_H11f. % 21.78/21.93 apply (zenon_notand_s _ _ ax7); [ zenon_intro zenon_H273 | zenon_intro zenon_H272 ]. % 21.78/21.93 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H24b ]. % 21.78/21.93 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (e3) (e3))))). % 21.78/21.93 intro zenon_D_pnotp. % 21.78/21.93 apply zenon_H273. % 21.78/21.93 rewrite <- zenon_D_pnotp. % 21.78/21.93 exact zenon_H24a. % 21.78/21.93 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 21.78/21.93 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H274]. % 21.78/21.93 congruence. % 21.78/21.93 cut (((op (e1) (e1)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 21.78/21.93 intro zenon_D_pnotp. % 21.78/21.93 apply zenon_H274. % 21.78/21.93 rewrite <- zenon_D_pnotp. % 21.78/21.93 exact zenon_He7. % 21.78/21.93 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.78/21.93 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 21.78/21.93 congruence. % 21.78/21.93 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H24b ]. % 21.78/21.93 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))))). % 21.78/21.93 intro zenon_D_pnotp. % 21.78/21.93 apply zenon_H259. % 21.78/21.93 rewrite <- zenon_D_pnotp. % 21.78/21.93 exact zenon_H24a. % 21.78/21.93 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 21.78/21.93 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 21.78/21.93 congruence. % 21.78/21.93 apply (zenon_L659_); trivial. % 21.78/21.93 apply zenon_H24b. apply refl_equal. % 21.78/21.93 apply zenon_H24b. apply refl_equal. % 21.78/21.93 apply zenon_H46. apply refl_equal. % 21.78/21.93 apply zenon_H24b. apply refl_equal. % 21.78/21.93 apply zenon_H24b. apply refl_equal. % 21.78/21.93 apply (zenon_notand_s _ _ zenon_H272); [ zenon_intro zenon_H25a | zenon_intro zenon_H275 ]. % 21.78/21.93 apply zenon_H25a. apply sym_equal. exact zenon_H11f. % 21.78/21.93 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H244 | zenon_intro zenon_H245 ]. % 21.78/21.93 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((e2) = (op (e3) (op (e3) (e3))))). % 21.78/21.93 intro zenon_D_pnotp. % 21.78/21.93 apply zenon_H275. % 21.78/21.93 rewrite <- zenon_D_pnotp. % 21.78/21.93 exact zenon_H244. % 21.78/21.93 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 21.78/21.93 cut (((op (e3) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H276]. % 21.78/21.93 congruence. % 21.78/21.93 cut (((op (e3) (e1)) = (e2)) = ((op (e3) (op (e3) (e3))) = (e2))). % 21.78/21.93 intro zenon_D_pnotp. % 21.78/21.93 apply zenon_H276. % 21.78/21.93 rewrite <- zenon_D_pnotp. % 21.78/21.93 exact zenon_H171. % 21.78/21.93 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 21.78/21.93 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 21.78/21.93 congruence. % 21.78/21.93 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H244 | zenon_intro zenon_H245 ]. % 21.78/21.93 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e1)) = (op (e3) (op (e3) (e3))))). % 21.78/21.93 intro zenon_D_pnotp. % 21.78/21.93 apply zenon_H257. % 21.78/21.93 rewrite <- zenon_D_pnotp. % 21.78/21.93 exact zenon_H244. % 21.78/21.93 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 21.78/21.93 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H254]. % 21.78/21.93 congruence. % 21.78/21.93 apply (zenon_L660_); trivial. % 21.78/21.93 apply zenon_H245. apply refl_equal. % 21.78/21.93 apply zenon_H245. apply refl_equal. % 21.78/21.93 apply zenon_H6a. apply refl_equal. % 21.78/21.93 apply zenon_H245. apply refl_equal. % 21.78/21.93 apply zenon_H245. apply refl_equal. % 21.78/21.93 (* end of lemma zenon_L964_ *) % 21.78/21.93 assert (zenon_L965_ : (((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 (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> False). % 21.78/21.93 do 0 intro. intros zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H4d zenon_H163 zenon_He7 zenon_H171. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.78/21.93 apply (zenon_L456_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.78/21.93 apply (zenon_L146_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.78/21.93 apply (zenon_L285_); trivial. % 21.78/21.93 apply (zenon_L964_); trivial. % 21.78/21.93 (* end of lemma zenon_L965_ *) % 21.78/21.93 assert (zenon_L966_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (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) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (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)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (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))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (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 (e1) (e1)) = (e0)) -> False). % 21.78/21.93 do 0 intro. intros zenon_H1a8 zenon_H156 zenon_H7b zenon_H16a zenon_H195 zenon_Hb9 zenon_Hb6 zenon_H141 zenon_H131 zenon_H1ef zenon_H13e zenon_H186 zenon_H20f zenon_H25b zenon_H1cb zenon_H31 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H139 zenon_H1d8 zenon_H271 zenon_H68 zenon_H1cf zenon_H1b7 zenon_H18a zenon_H1bb zenon_H77 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H196 zenon_H26d zenon_H19a zenon_H8b zenon_H76 zenon_H4e zenon_H67 zenon_H1d5 zenon_H117 zenon_H54 zenon_Hf0 zenon_H191 zenon_Ha0 zenon_H24 zenon_H13c zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H4d zenon_H163 zenon_He7. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.93 apply (zenon_L214_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.93 apply (zenon_L962_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.93 apply (zenon_L900_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.93 apply (zenon_L755_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.93 apply (zenon_L54_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.93 apply (zenon_L252_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.93 apply (zenon_L83_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.93 exact (zenon_H8b zenon_H8a). % 21.78/21.93 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.78/21.93 apply (zenon_L756_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.78/21.93 apply (zenon_L963_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.78/21.93 apply (zenon_L77_); trivial. % 21.78/21.93 apply (zenon_L684_); trivial. % 21.78/21.93 apply (zenon_L648_); trivial. % 21.78/21.93 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.93 apply (zenon_L124_); trivial. % 21.78/21.93 apply (zenon_L172_); trivial. % 21.78/21.93 apply (zenon_L965_); trivial. % 21.78/21.93 (* end of lemma zenon_L966_ *) % 21.78/21.93 assert (zenon_L967_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((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)) = (op (e3) (e3)))) -> (((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))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (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) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.78/21.94 do 0 intro. intros zenon_H1a8 zenon_H192 zenon_H3d zenon_H156 zenon_H7b zenon_H16a zenon_Ha9 zenon_H4d zenon_Hb6 zenon_H141 zenon_H195 zenon_H20f zenon_H25b zenon_H12e zenon_H48 zenon_H129 zenon_Hc0 zenon_H1cb zenon_H1b7 zenon_H34 zenon_H18a zenon_H1bb zenon_H77 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_H54 zenon_Hf0 zenon_H196 zenon_H26d zenon_H19a zenon_Ha0 zenon_Hb9 zenon_H24 zenon_H13c zenon_H1cf zenon_H68 zenon_H31 zenon_Hf7 zenon_H186 zenon_H8b zenon_H1cd. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.94 apply (zenon_L214_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.94 apply (zenon_L962_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.94 apply (zenon_L900_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.94 apply (zenon_L217_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.94 apply (zenon_L54_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.94 apply (zenon_L950_); trivial. % 21.78/21.94 apply (zenon_L77_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.94 apply (zenon_L124_); trivial. % 21.78/21.94 apply (zenon_L299_); trivial. % 21.78/21.94 apply (zenon_L709_); trivial. % 21.78/21.94 (* end of lemma zenon_L967_ *) % 21.78/21.94 assert (zenon_L968_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (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) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (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 (e1) (e1)) = (op (e2) (e1)))) -> ((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (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 (e1) (e1)) = (e0)) -> False). % 21.78/21.94 do 0 intro. intros zenon_H1a8 zenon_H25b zenon_H20f zenon_H156 zenon_H7b zenon_H16a zenon_H195 zenon_Hb9 zenon_Hb6 zenon_H141 zenon_H131 zenon_H1ef zenon_H13e zenon_H196 zenon_Hf0 zenon_H54 zenon_H117 zenon_H9f zenon_H1b4 zenon_Hf5 zenon_H136 zenon_H25e zenon_H77 zenon_H1bb zenon_H18a zenon_H1b7 zenon_H1cf zenon_H68 zenon_H271 zenon_H1d8 zenon_H139 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_H31 zenon_H191 zenon_H1cb zenon_H8b zenon_Ha0 zenon_H24 zenon_H13c zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H4d zenon_H163 zenon_He7. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.94 apply (zenon_L214_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.94 apply (zenon_L962_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.94 apply (zenon_L900_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.94 apply (zenon_L755_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.94 apply (zenon_L54_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.94 apply (zenon_L264_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.94 apply (zenon_L59_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.94 exact (zenon_H8b zenon_H8a). % 21.78/21.94 apply (zenon_L963_); trivial. % 21.78/21.94 apply (zenon_L77_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.94 apply (zenon_L124_); trivial. % 21.78/21.94 apply (zenon_L172_); trivial. % 21.78/21.94 apply (zenon_L965_); trivial. % 21.78/21.94 (* end of lemma zenon_L968_ *) % 21.78/21.94 assert (zenon_L969_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((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)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.94 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hdd zenon_H1cf zenon_H68 zenon_H31 zenon_H4e zenon_H76 zenon_H8b zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H77 zenon_H25e zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H9f zenon_Hb9 zenon_H196. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.78/21.94 exact (zenon_H7b zenon_H65). % 21.78/21.94 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.78/21.94 apply (zenon_L54_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.78/21.94 exact (zenon_H8b zenon_H8a). % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.94 apply (zenon_L264_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.94 apply (zenon_L83_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.94 exact (zenon_H8b zenon_H8a). % 21.78/21.94 apply (zenon_L820_); trivial. % 21.78/21.94 (* end of lemma zenon_L969_ *) % 21.78/21.94 assert (zenon_L970_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e0) (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 (e1) (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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (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 (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (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) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (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 (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.78/21.94 do 0 intro. intros zenon_He4 zenon_H196 zenon_Hb9 zenon_H9f zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H25e zenon_H192 zenon_H12e zenon_H8b zenon_Hef zenon_Hf0 zenon_H7b zenon_H16a zenon_H156 zenon_Hdd zenon_H48 zenon_H1bb zenon_H18a zenon_H34 zenon_H1b7 zenon_H1cf zenon_H77 zenon_H68 zenon_H271 zenon_H1d8 zenon_H139 zenon_H1b4 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H191 zenon_H1cb. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.94 apply (zenon_L962_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.94 apply (zenon_L486_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.94 apply (zenon_L111_); trivial. % 21.78/21.94 apply (zenon_L794_); trivial. % 21.78/21.94 (* end of lemma zenon_L970_ *) % 21.78/21.94 assert (zenon_L971_ : (((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) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (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)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (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))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((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)) = (op (e3) (e3)))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 21.78/21.94 do 0 intro. intros zenon_H13b zenon_H179 zenon_H1d5 zenon_H67 zenon_He2 zenon_H55 zenon_H131 zenon_H1ef zenon_H13e zenon_H163 zenon_H1cb zenon_H191 zenon_H4d zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H1b4 zenon_H139 zenon_H1d8 zenon_H271 zenon_H68 zenon_H77 zenon_H1cf zenon_H1b7 zenon_H18a zenon_H1bb zenon_H48 zenon_H156 zenon_Hfa zenon_H4e zenon_He4 zenon_H1a8 zenon_H192 zenon_H7b zenon_H16a zenon_Ha9 zenon_H141 zenon_H195 zenon_H20f zenon_H25b zenon_H12e zenon_H129 zenon_Hc0 zenon_H25e zenon_Hf5 zenon_H9f zenon_H117 zenon_H54 zenon_Hf0 zenon_H196 zenon_H26d zenon_H19a zenon_Hb9 zenon_H24 zenon_H13c zenon_H186 zenon_H8b zenon_H7d zenon_H34. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.78/21.94 apply (zenon_L297_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.94 apply (zenon_L966_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.94 apply (zenon_L962_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.94 apply (zenon_L59_); trivial. % 21.78/21.94 apply (zenon_L967_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.94 apply (zenon_L486_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.94 apply (zenon_L15_); trivial. % 21.78/21.94 apply (zenon_L794_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.78/21.94 apply (zenon_L117_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.78/21.94 apply (zenon_L254_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.94 apply (zenon_L968_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.94 apply (zenon_L486_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.94 apply (zenon_L15_); trivial. % 21.78/21.94 apply (zenon_L794_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.94 apply (zenon_L969_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.94 apply (zenon_L970_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.94 apply (zenon_L59_); trivial. % 21.78/21.94 apply (zenon_L967_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.94 apply (zenon_L486_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.94 apply (zenon_L111_); trivial. % 21.78/21.94 apply (zenon_L794_); trivial. % 21.78/21.94 apply (zenon_L802_); trivial. % 21.78/21.94 (* end of lemma zenon_L971_ *) % 21.78/21.94 assert (zenon_L972_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (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) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (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 (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.78/21.94 do 0 intro. intros zenon_He4 zenon_Hdb zenon_H156 zenon_H55 zenon_H54 zenon_H1bb zenon_H18a zenon_H34 zenon_H1b7 zenon_H1cf zenon_H77 zenon_H68 zenon_H271 zenon_H1d8 zenon_H139 zenon_H1b4 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H191 zenon_H1cb. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.94 apply (zenon_L55_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.94 apply (zenon_L486_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.94 apply (zenon_L15_); trivial. % 21.78/21.94 apply (zenon_L794_); trivial. % 21.78/21.94 (* end of lemma zenon_L972_ *) % 21.78/21.94 assert (zenon_L973_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((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))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 21.78/21.94 do 0 intro. intros zenon_H92 zenon_H1ef zenon_H131 zenon_H4d zenon_H13e zenon_H68 zenon_H2d zenon_Hf0 zenon_Hef zenon_H8b zenon_H16a. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.78/21.94 apply (zenon_L717_); trivial. % 21.78/21.94 apply (zenon_L755_); trivial. % 21.78/21.94 (* end of lemma zenon_L973_ *) % 21.78/21.94 assert (zenon_L974_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((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))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 21.78/21.94 do 0 intro. intros zenon_H2f zenon_H1ef zenon_H131 zenon_H4d zenon_H13e zenon_H68 zenon_Hf0 zenon_Hef zenon_H8b zenon_H16a. % 21.78/21.94 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.78/21.94 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 21.78/21.94 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.78/21.94 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.78/21.94 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.78/21.94 apply (zenon_L973_); trivial. % 21.78/21.94 (* end of lemma zenon_L974_ *) % 21.78/21.94 assert (zenon_L975_ : (((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)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.94 do 0 intro. intros zenon_H139 zenon_H77 zenon_H47 zenon_Hef zenon_H173 zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.94 apply (zenon_L251_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.94 apply (zenon_L226_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.94 apply (zenon_L122_); trivial. % 21.78/21.94 apply (zenon_L167_); trivial. % 21.78/21.94 (* end of lemma zenon_L975_ *) % 21.78/21.94 assert (zenon_L976_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.94 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H25 zenon_H6e zenon_H173 zenon_H77 zenon_H4d zenon_H93 zenon_H195. % 21.78/21.94 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.94 apply (zenon_L171_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.94 apply (zenon_L226_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.94 apply (zenon_L59_); trivial. % 21.78/21.94 apply (zenon_L228_); trivial. % 21.78/21.94 (* end of lemma zenon_L976_ *) % 21.78/21.94 assert (zenon_L977_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.78/21.94 do 0 intro. intros zenon_H139 zenon_H7e zenon_H177 zenon_H19a zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H120 zenon_H20f zenon_H1bb zenon_H93 zenon_H164 zenon_Hef zenon_H173 zenon_H68 zenon_H31 zenon_H155 zenon_H77. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.94 apply (zenon_L864_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.94 apply (zenon_L226_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.94 apply (zenon_L264_); trivial. % 21.78/21.94 apply (zenon_L98_); trivial. % 21.78/21.94 (* end of lemma zenon_L977_ *) % 21.78/21.94 assert (zenon_L978_ : (((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 (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (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) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.78/21.94 do 0 intro. intros zenon_H1fe zenon_He4 zenon_H156 zenon_H24e zenon_H141 zenon_H2c zenon_H1a2 zenon_H55 zenon_Hfa zenon_H195 zenon_H179 zenon_H1b7 zenon_H73 zenon_H31 zenon_H68 zenon_H173 zenon_Hef zenon_H164 zenon_H20f zenon_H181 zenon_H18d zenon_H1b4 zenon_H19a zenon_H177 zenon_H139 zenon_H4d zenon_H4e zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H196 zenon_H82 zenon_H1cd zenon_H189 zenon_H1a8 zenon_H15d zenon_H12e zenon_H48 zenon_Hc4 zenon_H93 zenon_H129 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H160 zenon_H77 zenon_H120. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.94 apply (zenon_L859_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.94 apply (zenon_L975_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.94 apply (zenon_L559_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.94 apply (zenon_L214_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.94 apply (zenon_L264_); trivial. % 21.78/21.94 apply (zenon_L167_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.94 apply (zenon_L184_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.94 apply (zenon_L559_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.94 apply (zenon_L976_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.94 apply (zenon_L122_); trivial. % 21.78/21.94 apply (zenon_L98_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.94 apply (zenon_L975_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.94 apply (zenon_L975_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.94 apply (zenon_L14_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.94 apply (zenon_L217_); trivial. % 21.78/21.94 apply (zenon_L866_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.94 apply (zenon_L239_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.94 apply (zenon_L888_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.94 apply (zenon_L14_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.94 apply (zenon_L217_); trivial. % 21.78/21.94 apply (zenon_L977_); trivial. % 21.78/21.94 apply (zenon_L528_); trivial. % 21.78/21.94 (* end of lemma zenon_L978_ *) % 21.78/21.94 assert (zenon_L979_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (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) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (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)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 21.78/21.94 do 0 intro. intros zenon_Hc2 zenon_H82 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H141 zenon_H2c zenon_H15d zenon_H24e zenon_H1cd zenon_H1b7 zenon_H1b4 zenon_H181 zenon_H1a2 zenon_H68 zenon_He4 zenon_H212 zenon_H209 zenon_H160 zenon_Hbc zenon_H7d zenon_H18a zenon_H120 zenon_H129 zenon_H93 zenon_H1bb zenon_H55 zenon_H156 zenon_H77 zenon_H177 zenon_H196 zenon_H139 zenon_H4d zenon_H4e zenon_H48 zenon_Hfa zenon_H195 zenon_H73 zenon_H164 zenon_H12e zenon_H18d zenon_H20f zenon_H19a zenon_H179 zenon_H173 zenon_Hef zenon_Ha9 zenon_H13a zenon_H189 zenon_H1a8 zenon_H1fe. % 21.78/21.94 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.78/21.94 apply (zenon_L978_); trivial. % 21.78/21.94 apply (zenon_L978_); trivial. % 21.78/21.94 (* end of lemma zenon_L979_ *) % 21.78/21.94 assert (zenon_L980_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (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) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (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))))) -> (~((e0) = (e2))) -> (((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) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.78/21.94 do 0 intro. intros zenon_H1fe zenon_Hbc zenon_H179 zenon_H212 zenon_H121 zenon_H33 zenon_H104 zenon_H1a2 zenon_H55 zenon_H156 zenon_H117 zenon_Hf0 zenon_H164 zenon_H1b4 zenon_H25b zenon_Hf5 zenon_H20f zenon_H25e zenon_H195 zenon_H12e zenon_H192 zenon_H163 zenon_Hfa zenon_H131 zenon_H13f zenon_H141 zenon_He4 zenon_H68 zenon_H19a zenon_H13c zenon_H73 zenon_H94 zenon_H125 zenon_Hb2 zenon_H1c6 zenon_H1c3 zenon_H129 zenon_H18d zenon_H18a zenon_H48 zenon_H4d zenon_H4e zenon_H139 zenon_H77 zenon_Hb6 zenon_H31 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H177 zenon_H93 zenon_H196 zenon_H82 zenon_Hef zenon_H173 zenon_H15d zenon_H1bb zenon_H162 zenon_H1c7 zenon_H160 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H181 zenon_Hc4. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.94 apply (zenon_L913_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.94 apply (zenon_L541_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.94 apply (zenon_L541_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.94 apply (zenon_L14_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.94 apply (zenon_L914_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.94 apply (zenon_L55_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.94 apply (zenon_L68_); trivial. % 21.78/21.94 apply (zenon_L917_); trivial. % 21.78/21.94 apply (zenon_L211_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.94 apply (zenon_L184_); trivial. % 21.78/21.94 apply (zenon_L919_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.94 apply (zenon_L975_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.94 apply (zenon_L892_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.94 apply (zenon_L239_); trivial. % 21.78/21.94 apply (zenon_L893_); trivial. % 21.78/21.94 apply (zenon_L870_); trivial. % 21.78/21.94 (* end of lemma zenon_L980_ *) % 21.78/21.94 assert (zenon_L981_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (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) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (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) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (((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 (e1) (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 21.78/21.94 do 0 intro. intros zenon_Hc2 zenon_H15d zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H4e zenon_H4d zenon_H156 zenon_H55 zenon_H164 zenon_Hbc zenon_H33 zenon_H212 zenon_H162 zenon_H24e zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H181 zenon_H1bb zenon_He4 zenon_H18a zenon_H82 zenon_H31 zenon_H68 zenon_H77 zenon_H177 zenon_H160 zenon_H196 zenon_H93 zenon_H139 zenon_H48 zenon_H173 zenon_H1a2 zenon_H179 zenon_H73 zenon_Hef zenon_Hb2 zenon_H141 zenon_Hf0 zenon_H13f zenon_H131 zenon_H121 zenon_H104 zenon_H163 zenon_Hfa zenon_H192 zenon_H25e zenon_H1b4 zenon_Hf5 zenon_H20f zenon_H195 zenon_H25b zenon_H12e zenon_H117 zenon_H1c6 zenon_H129 zenon_H18d zenon_H19a zenon_H1c3 zenon_H13c zenon_H94 zenon_H125 zenon_H1fe. % 21.78/21.94 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.78/21.94 apply (zenon_L980_); trivial. % 21.78/21.94 apply (zenon_L980_); trivial. % 21.78/21.94 (* end of lemma zenon_L981_ *) % 21.78/21.94 assert (zenon_L982_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((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) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (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 (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 (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (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 (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> False). % 21.78/21.94 do 0 intro. intros zenon_Hca zenon_H1fe zenon_H125 zenon_H94 zenon_H13c zenon_H1c3 zenon_H19a zenon_H18d zenon_H129 zenon_H1c6 zenon_H117 zenon_H12e zenon_H25b zenon_H195 zenon_H20f zenon_Hf5 zenon_H1b4 zenon_H25e zenon_H192 zenon_Hfa zenon_H163 zenon_H104 zenon_H121 zenon_H131 zenon_H13f zenon_Hf0 zenon_H141 zenon_Hb2 zenon_Hef zenon_H73 zenon_H179 zenon_H1a2 zenon_H173 zenon_H48 zenon_H139 zenon_H93 zenon_H196 zenon_H160 zenon_H177 zenon_H77 zenon_H68 zenon_H31 zenon_H82 zenon_H18a zenon_He4 zenon_H1bb zenon_H181 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H24e zenon_H162 zenon_H212 zenon_H33 zenon_Hbc zenon_H164 zenon_H55 zenon_H156 zenon_H4d zenon_H4e zenon_H13a zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H15d zenon_Hc2. % 21.78/21.94 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.78/21.94 apply (zenon_L981_); trivial. % 21.78/21.94 apply (zenon_L434_); trivial. % 21.78/21.94 (* end of lemma zenon_L982_ *) % 21.78/21.94 assert (zenon_L983_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 21.78/21.94 do 0 intro. intros zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_H68 zenon_H31 zenon_Ha9 zenon_H9e. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.94 exact (zenon_H6c zenon_H67). % 21.78/21.94 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.94 apply (zenon_L226_); trivial. % 21.78/21.94 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.94 apply (zenon_L264_); trivial. % 21.78/21.94 apply (zenon_L92_); trivial. % 21.78/21.94 (* end of lemma zenon_L983_ *) % 21.78/21.95 assert (zenon_L984_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 21.78/21.95 do 0 intro. intros zenon_H169 zenon_Hef zenon_H4d. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 21.78/21.95 exact (zenon_H1d4 zenon_H4d). % 21.78/21.95 exact (zenon_H1b3 zenon_Hef). % 21.78/21.95 (* end of lemma zenon_L984_ *) % 21.78/21.95 assert (zenon_L985_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 21.78/21.95 do 0 intro. intros zenon_Hb1 zenon_Hef zenon_H4d. % 21.78/21.95 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.78/21.95 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 21.78/21.95 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.78/21.95 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.78/21.95 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.78/21.95 apply (zenon_L984_); trivial. % 21.78/21.95 (* end of lemma zenon_L985_ *) % 21.78/21.95 assert (zenon_L986_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha9 zenon_H6e zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.95 apply (zenon_L253_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.95 apply (zenon_L110_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.95 apply (zenon_L178_); trivial. % 21.78/21.95 apply (zenon_L154_); trivial. % 21.78/21.95 (* end of lemma zenon_L986_ *) % 21.78/21.95 assert (zenon_L987_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((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) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H139 zenon_H77 zenon_Hb9 zenon_Hbb zenon_H177 zenon_Ha9 zenon_H47 zenon_Hb6 zenon_H13a zenon_H68 zenon_H31 zenon_H16a zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_H196. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.95 apply (zenon_L251_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.95 apply (zenon_L986_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.95 apply (zenon_L264_); trivial. % 21.78/21.95 apply (zenon_L621_); trivial. % 21.78/21.95 (* end of lemma zenon_L987_ *) % 21.78/21.95 assert (zenon_L988_ : ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H7e zenon_H177 zenon_H1bb zenon_H196 zenon_Hb9 zenon_Hbb zenon_He4 zenon_Hb6 zenon_H156 zenon_H4d zenon_H8b zenon_H7b zenon_H16a zenon_H7d zenon_H19a zenon_H195 zenon_H20f zenon_H186 zenon_H25b zenon_H1b4 zenon_Hf5 zenon_H25e zenon_Ha0 zenon_H13a zenon_Hc0 zenon_H129 zenon_H12e zenon_H48 zenon_H1cb zenon_H191 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H139 zenon_H1d8 zenon_H271 zenon_H1cf zenon_H1b7 zenon_H18a zenon_H164 zenon_Hef zenon_H173 zenon_H68 zenon_H31 zenon_H155 zenon_H77. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.95 apply (zenon_L264_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.95 apply (zenon_L100_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.95 exact (zenon_H8b zenon_H8a). % 21.78/21.95 apply (zenon_L955_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.95 apply (zenon_L226_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.95 apply (zenon_L264_); trivial. % 21.78/21.95 apply (zenon_L98_); trivial. % 21.78/21.95 (* end of lemma zenon_L988_ *) % 21.78/21.95 assert (zenon_L989_ : (((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) (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) (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 (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((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) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H13a zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H25e zenon_H192 zenon_H3d zenon_H48 zenon_H12e zenon_H8b zenon_Hef zenon_Hf0 zenon_H7b zenon_H16a zenon_H1cb zenon_H191 zenon_H4d zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H1b4 zenon_H139 zenon_H1d8 zenon_H271 zenon_H68 zenon_H77 zenon_H1cf zenon_H1b7 zenon_H34 zenon_H18a zenon_H1bb zenon_H54 zenon_H55 zenon_H156 zenon_He4 zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.95 apply (zenon_L962_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.95 apply (zenon_L972_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.95 apply (zenon_L178_); trivial. % 21.78/21.95 apply (zenon_L154_); trivial. % 21.78/21.95 (* end of lemma zenon_L989_ *) % 21.78/21.95 assert (zenon_L990_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (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 (e0) (e1)) = (op (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 (e2) (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 (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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((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) (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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H1fe zenon_H212 zenon_H179 zenon_H1d5 zenon_H13c zenon_H173 zenon_H164 zenon_H129 zenon_Hc0 zenon_H186 zenon_H19a zenon_H7d zenon_H73 zenon_H1c6 zenon_H266 zenon_H190 zenon_H6f zenon_H1ef zenon_H13e zenon_H1ba zenon_H131 zenon_H13f zenon_H15d zenon_H82 zenon_Ha9 zenon_H4e zenon_H1cb zenon_H191 zenon_H4d zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H1b4 zenon_H139 zenon_H1d8 zenon_H271 zenon_H68 zenon_H77 zenon_H1cf zenon_H1b7 zenon_H18a zenon_H1bb zenon_H55 zenon_H156 zenon_H13a zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H25e zenon_H192 zenon_H12e zenon_H8b zenon_Hef zenon_Hf0 zenon_H7b zenon_H16a zenon_He4 zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196 zenon_H48. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.95 apply (zenon_L774_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.95 apply (zenon_L987_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.95 apply (zenon_L937_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.95 apply (zenon_L226_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.95 apply (zenon_L264_); trivial. % 21.78/21.95 apply (zenon_L621_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.95 apply (zenon_L239_); trivial. % 21.78/21.95 apply (zenon_L957_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.95 apply (zenon_L987_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.95 apply (zenon_L987_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.95 apply (zenon_L14_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.95 apply (zenon_L217_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.78/21.95 apply (zenon_L730_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.78/21.95 apply (zenon_L960_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.78/21.95 apply (zenon_L217_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.78/21.95 apply (zenon_L113_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.78/21.95 apply (zenon_L128_); trivial. % 21.78/21.95 apply (zenon_L182_); trivial. % 21.78/21.95 apply (zenon_L388_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.95 apply (zenon_L55_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.95 apply (zenon_L178_); trivial. % 21.78/21.95 apply (zenon_L154_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.95 apply (zenon_L214_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.95 apply (zenon_L264_); trivial. % 21.78/21.95 apply (zenon_L621_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.95 apply (zenon_L184_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.95 apply (zenon_L987_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.95 apply (zenon_L14_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.95 apply (zenon_L217_); trivial. % 21.78/21.95 apply (zenon_L988_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.95 apply (zenon_L987_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.95 apply (zenon_L14_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.95 apply (zenon_L989_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.95 apply (zenon_L486_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.95 apply (zenon_L15_); trivial. % 21.78/21.95 apply (zenon_L794_); trivial. % 21.78/21.95 apply (zenon_L456_); trivial. % 21.78/21.95 (* end of lemma zenon_L990_ *) % 21.78/21.95 assert (zenon_L991_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (((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)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((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)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hdd zenon_H1cf zenon_H68 zenon_H31 zenon_H156 zenon_Hef zenon_H8b zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H77 zenon_H25e zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H9f zenon_Hb9 zenon_H196. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.78/21.95 exact (zenon_H7b zenon_H65). % 21.78/21.95 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.78/21.95 apply (zenon_L54_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.78/21.95 exact (zenon_H8b zenon_H8a). % 21.78/21.95 apply (zenon_L935_); trivial. % 21.78/21.95 (* end of lemma zenon_L991_ *) % 21.78/21.95 assert (zenon_L992_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (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 (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H164 zenon_H9f zenon_H192 zenon_H3d zenon_H48 zenon_H12e zenon_H31 zenon_H1cf zenon_Hdd zenon_H129 zenon_Hc0 zenon_H13a zenon_H68 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H19a zenon_H7e zenon_H7d zenon_H16a zenon_H7b zenon_H77 zenon_H8b zenon_H156 zenon_Hb6 zenon_He4 zenon_H177 zenon_H196 zenon_Hef zenon_H67 zenon_H1bb zenon_Hbb zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_Hb9 zenon_H195. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.78/21.95 apply (zenon_L991_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.78/21.95 apply (zenon_L669_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.78/21.95 apply (zenon_L80_); trivial. % 21.78/21.95 apply (zenon_L684_); trivial. % 21.78/21.95 (* end of lemma zenon_L992_ *) % 21.78/21.95 assert (zenon_L993_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((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) (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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H13c zenon_H25 zenon_Ha0 zenon_H164 zenon_H48 zenon_H129 zenon_Hc0 zenon_H13a zenon_H68 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H25b zenon_H186 zenon_H20f zenon_H19a zenon_H7d zenon_H16a zenon_H7b zenon_H77 zenon_H8b zenon_H156 zenon_He4 zenon_H177 zenon_Hbb zenon_H196 zenon_Hef zenon_H1bb zenon_H104 zenon_H67 zenon_H7e zenon_H9f zenon_H192 zenon_H3d zenon_H12e zenon_H31 zenon_H1cf zenon_H13e zenon_H1ef zenon_H1bf zenon_H191 zenon_H141 zenon_Hb6 zenon_H4d zenon_Hb9 zenon_H195. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.95 apply (zenon_L116_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.95 apply (zenon_L644_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.95 apply (zenon_L992_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.95 apply (zenon_L670_); trivial. % 21.78/21.95 apply (zenon_L77_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.95 apply (zenon_L124_); trivial. % 21.78/21.95 apply (zenon_L172_); trivial. % 21.78/21.95 (* end of lemma zenon_L993_ *) % 21.78/21.95 assert (zenon_L994_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e3)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e3) (e0)) = (op (e3) (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) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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))))) -> (((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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H139 zenon_Hb9 zenon_H31 zenon_Ha0 zenon_Hb6 zenon_H13c zenon_H164 zenon_H48 zenon_H129 zenon_Hc0 zenon_H13a zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H25b zenon_H186 zenon_H20f zenon_H19a zenon_H7d zenon_H156 zenon_He4 zenon_H177 zenon_Hbb zenon_H1bb zenon_H104 zenon_H192 zenon_H12e zenon_H1cf zenon_H13e zenon_H1ef zenon_H1bf zenon_H191 zenon_H141 zenon_H4d zenon_H195 zenon_H3d zenon_H77 zenon_H7e zenon_H25 zenon_H68 zenon_H1d5 zenon_H125 zenon_H16a zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_H196. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.95 apply (zenon_L993_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.95 apply (zenon_L55_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.95 apply (zenon_L68_); trivial. % 21.78/21.95 apply (zenon_L154_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.95 apply (zenon_L214_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.95 apply (zenon_L651_); trivial. % 21.78/21.95 apply (zenon_L621_); trivial. % 21.78/21.95 (* end of lemma zenon_L994_ *) % 21.78/21.95 assert (zenon_L995_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (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) (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)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H201 zenon_H8b zenon_Hef zenon_Hf0 zenon_H7b zenon_H16a zenon_H125 zenon_H1d5 zenon_H68 zenon_H3d zenon_H4d zenon_H141 zenon_H191 zenon_H1bf zenon_H1ef zenon_H13e zenon_H1cf zenon_H12e zenon_H192 zenon_H104 zenon_H1bb zenon_H177 zenon_He4 zenon_H156 zenon_H19a zenon_H186 zenon_H13a zenon_Hc0 zenon_H129 zenon_H48 zenon_H164 zenon_H13c zenon_Hb6 zenon_Ha0 zenon_H31 zenon_H139 zenon_Hbc zenon_Hbb zenon_H7d zenon_H179 zenon_H25 zenon_H212 zenon_H77 zenon_H25e zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H9f zenon_Hb9 zenon_H196. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.78/21.95 exact (zenon_H7b zenon_H65). % 21.78/21.95 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.78/21.95 apply (zenon_L61_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.78/21.95 exact (zenon_H8b zenon_H8a). % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.95 apply (zenon_L264_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.95 apply (zenon_L678_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.95 exact (zenon_H8b zenon_H8a). % 21.78/21.95 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.78/21.95 apply (zenon_L994_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.78/21.95 apply (zenon_L658_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.78/21.95 apply (zenon_L367_); trivial. % 21.78/21.95 apply (zenon_L674_); trivial. % 21.78/21.95 (* end of lemma zenon_L995_ *) % 21.78/21.95 assert (zenon_L996_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((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) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H164 zenon_H155 zenon_H160 zenon_H18a zenon_H1b7 zenon_H1cf zenon_H271 zenon_H1d8 zenon_H139 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_H31 zenon_H191 zenon_H1cb zenon_H48 zenon_H12e zenon_H129 zenon_Hc0 zenon_H13a zenon_H68 zenon_Ha0 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H19a zenon_H7e zenon_H7d zenon_H16a zenon_H7b zenon_H77 zenon_H8b zenon_H156 zenon_Hb6 zenon_He4 zenon_H177 zenon_Hbb zenon_H196 zenon_Hef zenon_H67 zenon_H1bb zenon_H14c zenon_H104 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_Hb9 zenon_H195. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.78/21.95 apply (zenon_L795_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.78/21.95 apply (zenon_L669_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.78/21.95 apply (zenon_L257_); trivial. % 21.78/21.95 apply (zenon_L684_); trivial. % 21.78/21.95 (* end of lemma zenon_L996_ *) % 21.78/21.95 assert (zenon_L997_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (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) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((~((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)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H13c zenon_H25 zenon_Ha0 zenon_H1d5 zenon_H1bf zenon_H201 zenon_H164 zenon_H155 zenon_H18a zenon_H1b7 zenon_H1cf zenon_H271 zenon_H1d8 zenon_H139 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_H31 zenon_H191 zenon_H1cb zenon_H48 zenon_H12e zenon_H129 zenon_Hc0 zenon_H13a zenon_H68 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H19a zenon_H7e zenon_H7d zenon_H16a zenon_H7b zenon_H77 zenon_H8b zenon_H156 zenon_He4 zenon_H177 zenon_Hbb zenon_H196 zenon_Hef zenon_H67 zenon_H1bb zenon_H104 zenon_H25b zenon_H20f zenon_H186 zenon_H9f zenon_H192 zenon_H3d zenon_H89 zenon_H1ef zenon_H13e zenon_H141 zenon_Hb6 zenon_H4d zenon_Hb9 zenon_H195. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.95 apply (zenon_L116_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.95 apply (zenon_L645_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.95 apply (zenon_L992_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.95 apply (zenon_L252_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.95 apply (zenon_L678_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.95 exact (zenon_H8b zenon_H8a). % 21.78/21.95 apply (zenon_L996_); trivial. % 21.78/21.95 apply (zenon_L77_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.95 apply (zenon_L124_); trivial. % 21.78/21.95 apply (zenon_L172_); trivial. % 21.78/21.95 (* end of lemma zenon_L997_ *) % 21.78/21.95 assert (zenon_L998_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H16a zenon_H77 zenon_H8b zenon_H22d zenon_H89 zenon_H1ef zenon_H1bf zenon_H13e zenon_H92 zenon_H55 zenon_H53 zenon_H7b zenon_Hb9 zenon_H94. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.78/21.95 exact (zenon_H7b zenon_H65). % 21.78/21.95 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.78/21.95 apply (zenon_L56_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.78/21.95 exact (zenon_H8b zenon_H8a). % 21.78/21.95 apply (zenon_L797_); trivial. % 21.78/21.95 (* end of lemma zenon_L998_ *) % 21.78/21.95 assert (zenon_L999_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (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)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H196 zenon_Hb9 zenon_Ha0 zenon_H13c zenon_H25 zenon_Hb6 zenon_H4d zenon_H195 zenon_H141 zenon_H192 zenon_H186 zenon_H20f zenon_H25b zenon_H104 zenon_H1bb zenon_Hbb zenon_H177 zenon_He4 zenon_H19a zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H13a zenon_Hc0 zenon_H129 zenon_H12e zenon_H48 zenon_H1cb zenon_H191 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H139 zenon_H1d8 zenon_H271 zenon_H1cf zenon_H1b7 zenon_H18a zenon_H164 zenon_H201 zenon_H1d5 zenon_H156 zenon_H94 zenon_H7b zenon_H55 zenon_H92 zenon_H13e zenon_H1bf zenon_H1ef zenon_H89 zenon_H22d zenon_H8b zenon_H16a zenon_H7d zenon_H7e zenon_Hef zenon_H173 zenon_H68 zenon_H31 zenon_H155 zenon_H77. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.95 apply (zenon_L997_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.95 apply (zenon_L486_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.95 apply (zenon_L998_); trivial. % 21.78/21.95 apply (zenon_L31_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.95 apply (zenon_L933_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.95 apply (zenon_L68_); trivial. % 21.78/21.95 apply (zenon_L154_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.95 apply (zenon_L226_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.95 apply (zenon_L264_); trivial. % 21.78/21.95 apply (zenon_L98_); trivial. % 21.78/21.95 (* end of lemma zenon_L999_ *) % 21.78/21.95 assert (zenon_L1000_ : (~((op (e0) (e3)) = (op (e2) (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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((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) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 21.78/21.95 do 0 intro. intros zenon_H196 zenon_H1b4 zenon_H25b zenon_Hf5 zenon_H20f zenon_H25e zenon_H77 zenon_H212 zenon_H179 zenon_H7d zenon_Hbc zenon_H141 zenon_H192 zenon_H186 zenon_H104 zenon_H1bb zenon_He4 zenon_H19a zenon_H13a zenon_Hc0 zenon_H129 zenon_H12e zenon_H48 zenon_H1cb zenon_H191 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_H111 zenon_H139 zenon_H1d8 zenon_H271 zenon_H1cf zenon_H1b7 zenon_H18a zenon_H164 zenon_H201 zenon_H1d5 zenon_H156 zenon_H94 zenon_H7b zenon_H55 zenon_H92 zenon_H13e zenon_H1bf zenon_H1ef zenon_H89 zenon_H22d zenon_H8b zenon_H16a zenon_Hef zenon_H68 zenon_H31 zenon_H67 zenon_Hf0 zenon_H195 zenon_Hb9 zenon_H4d zenon_H173 zenon_H25 zenon_Ha0 zenon_H13c zenon_H177 zenon_Hbb zenon_Hb6 zenon_H155. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.78/21.95 exact (zenon_H7b zenon_H65). % 21.78/21.95 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.78/21.95 apply (zenon_L61_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.78/21.95 exact (zenon_H8b zenon_H8a). % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.95 apply (zenon_L252_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.95 apply (zenon_L678_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.95 exact (zenon_H8b zenon_H8a). % 21.78/21.95 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.78/21.95 apply (zenon_L999_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.78/21.95 apply (zenon_L658_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.78/21.95 apply (zenon_L367_); trivial. % 21.78/21.95 apply (zenon_L674_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.95 apply (zenon_L933_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.95 apply (zenon_L178_); trivial. % 21.78/21.95 apply (zenon_L115_); trivial. % 21.78/21.95 (* end of lemma zenon_L1000_ *) % 21.78/21.95 assert (zenon_L1001_ : ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((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)) = (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 (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((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) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H155 zenon_Hb6 zenon_Hbb zenon_H177 zenon_H13c zenon_Ha0 zenon_H25 zenon_H4d zenon_Hb9 zenon_H195 zenon_H22d zenon_H89 zenon_H1ef zenon_H1bf zenon_H13e zenon_H92 zenon_H55 zenon_H94 zenon_H156 zenon_H1d5 zenon_H201 zenon_H164 zenon_H18a zenon_H1b7 zenon_H1cf zenon_H271 zenon_H1d8 zenon_H139 zenon_H111 zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_H191 zenon_H1cb zenon_H48 zenon_H12e zenon_H129 zenon_Hc0 zenon_H13a zenon_H19a zenon_He4 zenon_H1bb zenon_H104 zenon_H186 zenon_H192 zenon_H141 zenon_Hbc zenon_H7d zenon_H179 zenon_H212 zenon_H77 zenon_H25e zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H173 zenon_H68 zenon_H31 zenon_H16a zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_H196. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.95 apply (zenon_L1000_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.95 apply (zenon_L226_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.95 apply (zenon_L264_); trivial. % 21.78/21.95 apply (zenon_L621_); trivial. % 21.78/21.95 (* end of lemma zenon_L1001_ *) % 21.78/21.95 assert (zenon_L1002_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((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)) = (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 (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((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) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H15d zenon_Ha9 zenon_H125 zenon_H73 zenon_Hb6 zenon_Hbb zenon_H177 zenon_H13c zenon_Ha0 zenon_H25 zenon_H4d zenon_Hb9 zenon_H195 zenon_H22d zenon_H89 zenon_H1ef zenon_H1bf zenon_H13e zenon_H92 zenon_H55 zenon_H94 zenon_H156 zenon_H1d5 zenon_H201 zenon_H164 zenon_H18a zenon_H1b7 zenon_H1cf zenon_H271 zenon_H1d8 zenon_H139 zenon_H111 zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_H191 zenon_H1cb zenon_H48 zenon_H12e zenon_H129 zenon_Hc0 zenon_H13a zenon_H19a zenon_He4 zenon_H1bb zenon_H104 zenon_H186 zenon_H192 zenon_H141 zenon_Hbc zenon_H7d zenon_H179 zenon_H212 zenon_H77 zenon_H25e zenon_H20f zenon_Hf5 zenon_H25b zenon_H1b4 zenon_H173 zenon_H68 zenon_H31 zenon_H16a zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_H196. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.95 apply (zenon_L987_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.95 apply (zenon_L995_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.95 apply (zenon_L933_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.95 apply (zenon_L178_); trivial. % 21.78/21.95 apply (zenon_L154_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.95 apply (zenon_L184_); trivial. % 21.78/21.95 apply (zenon_L1001_); trivial. % 21.78/21.95 (* end of lemma zenon_L1002_ *) % 21.78/21.95 assert (zenon_L1003_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.78/21.95 do 0 intro. intros zenon_H1d5 zenon_H67 zenon_Hbb zenon_H1bf zenon_H201 zenon_H8b zenon_H12e zenon_H48 zenon_H1cb zenon_H191 zenon_H4d zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H139 zenon_H1d8 zenon_H271 zenon_H68 zenon_H1cf zenon_H1b7 zenon_H34 zenon_H18a zenon_H1bb zenon_H77 zenon_H155 zenon_H1b4. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.95 apply (zenon_L252_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.95 apply (zenon_L678_); trivial. % 21.78/21.95 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.95 exact (zenon_H8b zenon_H8a). % 21.78/21.95 apply (zenon_L795_); trivial. % 21.78/21.95 (* end of lemma zenon_L1003_ *) % 21.78/21.95 assert (zenon_L1004_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (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 (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.78/21.96 do 0 intro. intros zenon_H1b4 zenon_H1bb zenon_H18a zenon_H34 zenon_H1b7 zenon_H1cf zenon_H271 zenon_H1d8 zenon_H139 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_Ha0 zenon_Hb6 zenon_H4d zenon_H191 zenon_H1cb zenon_H48 zenon_H12e zenon_H8b zenon_H201 zenon_H1bf zenon_Hbb zenon_H1d5 zenon_Hef zenon_H173 zenon_H68 zenon_H31 zenon_H155 zenon_H77. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.96 apply (zenon_L1003_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.96 apply (zenon_L226_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.96 apply (zenon_L264_); trivial. % 21.78/21.96 apply (zenon_L98_); trivial. % 21.78/21.96 (* end of lemma zenon_L1004_ *) % 21.78/21.96 assert (zenon_L1005_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((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) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (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) (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 (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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) (e1)) = (op (e3) (e1)))) -> (~((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 (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) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((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)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (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 (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 21.78/21.96 do 0 intro. intros zenon_H1fe zenon_H212 zenon_H179 zenon_H7d zenon_H141 zenon_H186 zenon_H104 zenon_H19a zenon_Hc0 zenon_H129 zenon_H164 zenon_H94 zenon_H92 zenon_H22d zenon_H13c zenon_H73 zenon_H125 zenon_H13e zenon_H1ef zenon_H89 zenon_H15d zenon_H13a zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H25e zenon_H192 zenon_Hf0 zenon_H7b zenon_H16a zenon_H55 zenon_H156 zenon_He4 zenon_H177 zenon_Hb9 zenon_H196 zenon_H4e zenon_Ha9 zenon_H82 zenon_H1b4 zenon_H1bb zenon_H18a zenon_H1b7 zenon_H1cf zenon_H271 zenon_H1d8 zenon_H139 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_Ha0 zenon_Hb6 zenon_H4d zenon_H191 zenon_H1cb zenon_H48 zenon_H12e zenon_H8b zenon_H201 zenon_H1bf zenon_Hbb zenon_H1d5 zenon_Hef zenon_H173 zenon_H68 zenon_H31 zenon_H77. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.96 apply (zenon_L774_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.96 apply (zenon_L1002_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.96 apply (zenon_L645_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.96 apply (zenon_L987_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.96 apply (zenon_L987_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.96 apply (zenon_L14_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.96 apply (zenon_L989_); trivial. % 21.78/21.96 apply (zenon_L456_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.96 apply (zenon_L239_); trivial. % 21.78/21.96 apply (zenon_L1004_); trivial. % 21.78/21.96 (* end of lemma zenon_L1005_ *) % 21.78/21.96 assert (zenon_L1006_ : ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (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)) = (op (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) (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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> False). % 21.78/21.96 do 0 intro. intros zenon_H8f zenon_H92 zenon_H139 zenon_H196 zenon_H31 zenon_H173 zenon_H68 zenon_H15d zenon_H1a2 zenon_H1cb zenon_H271 zenon_H1d8 zenon_H111 zenon_H1cd zenon_Hcc zenon_H270 zenon_H1b7 zenon_H18a zenon_Ha0 zenon_H1d5 zenon_H156 zenon_H179 zenon_Hbc zenon_H212 zenon_H1cf zenon_H48 zenon_H192 zenon_H25e zenon_H1b4 zenon_Hf5 zenon_H20f zenon_H195 zenon_H25b zenon_H12e zenon_H1bb zenon_Hc0 zenon_H19a zenon_H186 zenon_H4d zenon_He4 zenon_H7d zenon_H129 zenon_H164 zenon_H13c zenon_H77 zenon_H13a zenon_Hb9 zenon_Hbb zenon_H177 zenon_Ha9 zenon_Hb6 zenon_H73 zenon_H4e zenon_H1c6 zenon_H131 zenon_H13f zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H82 zenon_H1fe zenon_Hf0 zenon_Hef zenon_H8b zenon_H16a zenon_H22d zenon_H94 zenon_H89 zenon_H201 zenon_H141 zenon_H104 zenon_H125 zenon_H91. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.78/21.96 apply (zenon_L779_); trivial. % 21.78/21.96 apply (zenon_L990_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.78/21.96 apply (zenon_L779_); trivial. % 21.78/21.96 apply (zenon_L1005_); trivial. % 21.78/21.96 apply (zenon_L130_); trivial. % 21.78/21.96 (* end of lemma zenon_L1006_ *) % 21.78/21.96 assert (zenon_L1007_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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 (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)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (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 (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (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))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 21.78/21.96 do 0 intro. intros zenon_H26a zenon_H5d zenon_H181 zenon_H2c zenon_H189 zenon_H1a8 zenon_H24e zenon_Hb2 zenon_H117 zenon_H18d zenon_H26d zenon_H11a zenon_H33 zenon_Hfa zenon_H163 zenon_H1f1 zenon_H1c3 zenon_H109 zenon_H121 zenon_H125 zenon_H104 zenon_H141 zenon_H201 zenon_H94 zenon_H22d zenon_H16a zenon_H8b zenon_Hef zenon_Hf0 zenon_H1fe zenon_H82 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13f zenon_H131 zenon_H1c6 zenon_H4e zenon_H73 zenon_Hb6 zenon_Ha9 zenon_H177 zenon_H13a zenon_H77 zenon_H13c zenon_H164 zenon_H129 zenon_H7d zenon_He4 zenon_H4d zenon_H186 zenon_H19a zenon_H1bb zenon_H12e zenon_H25b zenon_H195 zenon_H20f zenon_Hf5 zenon_H1b4 zenon_H25e zenon_H192 zenon_H48 zenon_H1cf zenon_H212 zenon_Hbc zenon_H179 zenon_H156 zenon_H1d5 zenon_Ha0 zenon_H18a zenon_H1b7 zenon_H270 zenon_Hcc zenon_H1cd zenon_H111 zenon_H1d8 zenon_H271 zenon_H1cb zenon_H1a2 zenon_H15d zenon_H68 zenon_H173 zenon_H31 zenon_H196 zenon_H139. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.78/21.96 apply (zenon_L2_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.78/21.96 apply (zenon_L700_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.78/21.96 apply (zenon_L974_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.78/21.96 apply (zenon_L757_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.78/21.96 apply (zenon_L758_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.78/21.96 apply (zenon_L11_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.78/21.96 apply (zenon_L810_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.78/21.96 apply (zenon_L335_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.78/21.96 apply (zenon_L814_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.78/21.96 apply (zenon_L343_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.78/21.96 apply (zenon_L37_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.78/21.96 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.78/21.96 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.78/21.96 apply (zenon_L899_); trivial. % 21.78/21.96 apply (zenon_L979_); trivial. % 21.78/21.96 apply (zenon_L982_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 21.78/21.96 exact (zenon_H237 zenon_H31). % 21.78/21.96 apply (zenon_L983_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.78/21.96 apply (zenon_L985_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.78/21.96 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.78/21.96 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.78/21.96 apply (zenon_L1006_); trivial. % 21.78/21.96 apply (zenon_L51_); trivial. % 21.78/21.96 (* end of lemma zenon_L1007_ *) % 21.78/21.96 assert (zenon_L1008_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (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) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 21.78/21.96 do 0 intro. intros zenon_H92 zenon_H1ef zenon_H2d zenon_H131 zenon_H4d zenon_H13e zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_H16a. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.78/21.96 apply (zenon_L779_); trivial. % 21.78/21.96 apply (zenon_L755_); trivial. % 21.78/21.96 (* end of lemma zenon_L1008_ *) % 21.78/21.96 assert (zenon_L1009_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((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)) = (op (e2) (e2)))) -> False). % 21.78/21.96 do 0 intro. intros zenon_H2f zenon_H104 zenon_Hbb zenon_H16a zenon_H8b zenon_Hef zenon_Hf0 zenon_H13e zenon_H4d zenon_H131 zenon_H1ef. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.78/21.96 apply (zenon_L1008_); trivial. % 21.78/21.96 apply (zenon_L130_); trivial. % 21.78/21.96 (* end of lemma zenon_L1009_ *) % 21.78/21.96 assert (zenon_L1010_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e3)) -> (((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 (e0) (e2)) = (op (e0) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.78/21.96 do 0 intro. intros zenon_H164 zenon_H1b7 zenon_H68 zenon_H93 zenon_H26a zenon_H195 zenon_H163 zenon_H160 zenon_H13f zenon_H189 zenon_H19a zenon_H48 zenon_H18d zenon_H131 zenon_H77 zenon_H25 zenon_Hfa zenon_H94 zenon_Ha8 zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H191 zenon_H1cb zenon_H26d zenon_H14c zenon_H104 zenon_H67 zenon_H7e. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.78/21.96 apply (zenon_L456_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.78/21.96 apply (zenon_L763_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.78/21.96 apply (zenon_L257_); trivial. % 21.78/21.96 apply (zenon_L547_); trivial. % 21.78/21.96 (* end of lemma zenon_L1010_ *) % 21.78/21.96 assert (zenon_L1011_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (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 (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (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))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 21.78/21.96 do 0 intro. intros zenon_H26a zenon_H2c zenon_H189 zenon_H1a8 zenon_H24e zenon_Hb2 zenon_H117 zenon_H18d zenon_H26d zenon_H11a zenon_H33 zenon_H121 zenon_Hfa zenon_H163 zenon_H1f1 zenon_H1c3 zenon_H109 zenon_Hbb zenon_H125 zenon_H104 zenon_H141 zenon_H201 zenon_H94 zenon_H22d zenon_H16a zenon_H8b zenon_Hef zenon_Hf0 zenon_H1fe zenon_H82 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13f zenon_H131 zenon_H1c6 zenon_H4e zenon_H73 zenon_Hb6 zenon_Ha9 zenon_H177 zenon_H13a zenon_H77 zenon_H13c zenon_H164 zenon_H129 zenon_H7d zenon_He4 zenon_H4d zenon_H186 zenon_H19a zenon_H1bb zenon_H12e zenon_H25b zenon_H195 zenon_H20f zenon_Hf5 zenon_H1b4 zenon_H25e zenon_H192 zenon_H48 zenon_H1cf zenon_H212 zenon_Hbc zenon_H179 zenon_H156 zenon_H1d5 zenon_Ha0 zenon_H18a zenon_H1b7 zenon_H270 zenon_Hcc zenon_H1cd zenon_H111 zenon_H1d8 zenon_H271 zenon_H1cb zenon_H1a2 zenon_H15d zenon_H68 zenon_H173 zenon_H31 zenon_H196 zenon_H139. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.78/21.96 apply (zenon_L2_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.78/21.96 apply (zenon_L700_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.78/21.96 apply (zenon_L1009_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.78/21.96 apply (zenon_L757_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.78/21.96 apply (zenon_L758_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.78/21.96 apply (zenon_L11_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.78/21.96 apply (zenon_L778_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.78/21.96 apply (zenon_L779_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.96 apply (zenon_L774_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.96 apply (zenon_L775_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.96 apply (zenon_L775_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.96 apply (zenon_L14_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.96 apply (zenon_L15_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.96 apply (zenon_L645_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.96 apply (zenon_L111_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.78/21.96 exact (zenon_H7b zenon_H65). % 21.78/21.96 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.78/21.96 apply (zenon_L61_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.78/21.96 exact (zenon_H8b zenon_H8a). % 21.78/21.96 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.96 apply (zenon_L264_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.96 apply (zenon_L678_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.96 exact (zenon_H8b zenon_H8a). % 21.78/21.96 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.78/21.96 apply (zenon_L1010_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.78/21.96 apply (zenon_L113_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.78/21.96 exact (zenon_H191 zenon_H110). % 21.78/21.96 apply (zenon_L797_); trivial. % 21.78/21.96 apply (zenon_L766_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.96 apply (zenon_L214_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.96 apply (zenon_L651_); trivial. % 21.78/21.96 apply (zenon_L621_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.96 apply (zenon_L239_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.96 apply (zenon_L775_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.96 apply (zenon_L25_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.96 apply (zenon_L15_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.96 apply (zenon_L116_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.96 apply (zenon_L798_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.96 apply (zenon_L617_); trivial. % 21.78/21.96 apply (zenon_L799_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.96 apply (zenon_L226_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.96 apply (zenon_L264_); trivial. % 21.78/21.96 apply (zenon_L98_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.96 apply (zenon_L645_); trivial. % 21.78/21.96 apply (zenon_L776_); trivial. % 21.78/21.96 apply (zenon_L130_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.78/21.96 apply (zenon_L335_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.78/21.96 apply (zenon_L814_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.78/21.96 apply (zenon_L343_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.78/21.96 apply (zenon_L37_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.78/21.96 apply (zenon_L901_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.78/21.96 apply (zenon_L791_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.78/21.96 apply (zenon_L361_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.78/21.96 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.78/21.96 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.78/21.96 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.78/21.96 apply (zenon_L1006_); trivial. % 21.78/21.96 apply (zenon_L51_); trivial. % 21.78/21.96 (* end of lemma zenon_L1011_ *) % 21.78/21.96 assert (zenon_L1012_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.96 do 0 intro. intros zenon_H139 zenon_H47 zenon_H195 zenon_H4d zenon_H77 zenon_H173 zenon_H25 zenon_H68 zenon_Hfa zenon_H8a zenon_H111 zenon_H93 zenon_H196. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.96 apply (zenon_L251_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.96 apply (zenon_L976_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.96 apply (zenon_L258_); trivial. % 21.78/21.96 apply (zenon_L167_); trivial. % 21.78/21.96 (* end of lemma zenon_L1012_ *) % 21.78/21.96 assert (zenon_L1013_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 21.78/21.96 do 0 intro. intros zenon_H20b zenon_H11d zenon_H73 zenon_H4d zenon_H8a zenon_H111 zenon_Hbb zenon_H177. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H31 | zenon_intro zenon_H20c ]. % 21.78/21.96 apply (zenon_L406_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H153 | zenon_intro zenon_H20d ]. % 21.78/21.96 apply (zenon_L184_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H66 | zenon_intro zenon_Hfe ]. % 21.78/21.96 apply (zenon_L258_); trivial. % 21.78/21.96 apply (zenon_L178_); trivial. % 21.78/21.96 (* end of lemma zenon_L1013_ *) % 21.78/21.96 assert (zenon_L1014_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((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) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.96 do 0 intro. intros zenon_H139 zenon_H77 zenon_H131 zenon_H4d zenon_H1f1 zenon_H2d zenon_H48 zenon_H13f zenon_H117 zenon_Ha0 zenon_Hb6 zenon_H104 zenon_Hbb zenon_H156 zenon_He4 zenon_H31 zenon_Ha9 zenon_H47 zenon_H13a zenon_H8a zenon_H111 zenon_H93 zenon_H196. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.96 apply (zenon_L251_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.96 apply (zenon_L842_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.96 apply (zenon_L258_); trivial. % 21.78/21.96 apply (zenon_L167_); trivial. % 21.78/21.96 (* end of lemma zenon_L1014_ *) % 21.78/21.96 assert (zenon_L1015_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.78/21.96 do 0 intro. intros zenon_H1bb zenon_H195 zenon_Hb9 zenon_H10c zenon_H4d zenon_H186 zenon_H20f zenon_H25b zenon_H1c7 zenon_H160 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H181 zenon_Hc4. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 21.78/21.96 apply (zenon_L684_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 21.78/21.96 apply (zenon_L848_); trivial. % 21.78/21.96 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 21.78/21.96 exact (zenon_H181 zenon_H17c). % 21.78/21.97 exact (zenon_Hc4 zenon_Hc3). % 21.78/21.97 (* end of lemma zenon_L1015_ *) % 21.78/21.97 assert (zenon_L1016_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 21.78/21.97 do 0 intro. intros zenon_H164 zenon_H1c7 zenon_H25b zenon_H20f zenon_H186 zenon_H10c zenon_H195 zenon_Hef zenon_Hb6 zenon_Hb9 zenon_H19a zenon_H26d zenon_H31 zenon_H48 zenon_H93 zenon_H68 zenon_H1b7 zenon_H1bb zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4 zenon_H18d zenon_H177 zenon_Hbb zenon_H111 zenon_H8a zenon_H4d zenon_H73 zenon_H20b zenon_H67 zenon_H7e. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.78/21.97 apply (zenon_L1015_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.78/21.97 apply (zenon_L822_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.78/21.97 apply (zenon_L1013_); trivial. % 21.78/21.97 apply (zenon_L547_); trivial. % 21.78/21.97 (* end of lemma zenon_L1016_ *) % 21.78/21.97 assert (zenon_L1017_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> ((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 (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (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)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.78/21.97 do 0 intro. intros zenon_H13f zenon_H7e zenon_H67 zenon_H20b zenon_H73 zenon_H8a zenon_H111 zenon_Hbb zenon_H177 zenon_H18d zenon_Hc4 zenon_H181 zenon_H1b4 zenon_H24e zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H160 zenon_H1cd zenon_H1bb zenon_H1b7 zenon_H68 zenon_H48 zenon_H31 zenon_H26d zenon_H19a zenon_Hb6 zenon_Hef zenon_H195 zenon_H10c zenon_H186 zenon_H20f zenon_H25b zenon_H1c7 zenon_H164 zenon_H121 zenon_H104 zenon_H2d zenon_Ha0 zenon_H117 zenon_H4d zenon_H131 zenon_H77 zenon_H93. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.78/21.97 apply (zenon_L217_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.78/21.97 apply (zenon_L67_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.78/21.97 apply (zenon_L113_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.78/21.97 apply (zenon_L815_); trivial. % 21.78/21.97 apply (zenon_L1016_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.78/21.97 apply (zenon_L128_); trivial. % 21.78/21.97 apply (zenon_L218_); trivial. % 21.78/21.97 (* end of lemma zenon_L1017_ *) % 21.78/21.97 assert (zenon_L1018_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((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)) = (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))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((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 (e3) (e0)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H1c6 zenon_H3d zenon_H117 zenon_Ha0 zenon_H104 zenon_H121 zenon_H164 zenon_H25b zenon_H20f zenon_H186 zenon_H195 zenon_Hef zenon_H19a zenon_H26d zenon_H31 zenon_H68 zenon_H1b7 zenon_H1bb zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4 zenon_H18d zenon_H177 zenon_Hbb zenon_H111 zenon_H8a zenon_H73 zenon_H20b zenon_H67 zenon_H7e zenon_H93 zenon_H77 zenon_H131 zenon_H4d zenon_Hb6 zenon_H2d zenon_H48 zenon_H13f zenon_H1c7. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.78/21.97 apply (zenon_L55_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.78/21.97 apply (zenon_L1017_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.78/21.97 apply (zenon_L825_); trivial. % 21.78/21.97 exact (zenon_H1c7 zenon_Hac). % 21.78/21.97 (* end of lemma zenon_L1018_ *) % 21.78/21.97 assert (zenon_L1019_ : (((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (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))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e2)) = (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 (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> (~((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) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H1fe zenon_H129 zenon_Hfa zenon_H173 zenon_H31 zenon_H82 zenon_H4e zenon_H189 zenon_H1c6 zenon_H117 zenon_H104 zenon_H121 zenon_H164 zenon_H25b zenon_H20f zenon_H186 zenon_H195 zenon_H26d zenon_H20b zenon_H131 zenon_H13f zenon_H1a8 zenon_H8a zenon_H111 zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_He4 zenon_H156 zenon_H1cb zenon_H1f1 zenon_H18d zenon_H13a zenon_Ha9 zenon_Hb6 zenon_H139 zenon_H68 zenon_Ha0 zenon_H19a zenon_H77 zenon_H1c7 zenon_H163 zenon_H192 zenon_H48 zenon_H12e zenon_H73 zenon_H4d zenon_H1bb zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.97 apply (zenon_L817_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.97 apply (zenon_L1012_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.97 apply (zenon_L171_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.78/21.97 apply (zenon_L853_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.78/21.97 apply (zenon_L837_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.78/21.97 apply (zenon_L1013_); trivial. % 21.78/21.97 apply (zenon_L560_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.97 apply (zenon_L227_); trivial. % 21.78/21.97 apply (zenon_L228_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.97 apply (zenon_L184_); trivial. % 21.78/21.97 apply (zenon_L816_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.97 apply (zenon_L1014_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.97 apply (zenon_L818_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.97 apply (zenon_L14_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.97 apply (zenon_L217_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.97 apply (zenon_L214_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.97 apply (zenon_L1018_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.97 apply (zenon_L439_); trivial. % 21.78/21.97 apply (zenon_L240_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.97 apply (zenon_L214_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.97 apply (zenon_L258_); trivial. % 21.78/21.97 apply (zenon_L167_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.97 apply (zenon_L239_); trivial. % 21.78/21.97 apply (zenon_L816_); trivial. % 21.78/21.97 apply (zenon_L854_); trivial. % 21.78/21.97 (* end of lemma zenon_L1019_ *) % 21.78/21.97 assert (zenon_L1020_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (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))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e2)) = (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 (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> (~((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) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H1a2 zenon_H1fe zenon_H129 zenon_Hfa zenon_H173 zenon_H31 zenon_H82 zenon_H4e zenon_H189 zenon_H1c6 zenon_H117 zenon_H104 zenon_H121 zenon_H164 zenon_H25b zenon_H20f zenon_H186 zenon_H195 zenon_H26d zenon_H20b zenon_H131 zenon_H13f zenon_H1a8 zenon_H8a zenon_H111 zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_He4 zenon_H156 zenon_H1cb zenon_H1f1 zenon_H18d zenon_H13a zenon_Ha9 zenon_Hb6 zenon_H139 zenon_H68 zenon_Ha0 zenon_H19a zenon_H77 zenon_H1c7 zenon_H163 zenon_H192 zenon_H48 zenon_H12e zenon_H73 zenon_H4d zenon_H1bb zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.78/21.97 apply (zenon_L68_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.78/21.97 apply (zenon_L124_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.78/21.97 apply (zenon_L815_); trivial. % 21.78/21.97 apply (zenon_L1019_); trivial. % 21.78/21.97 (* end of lemma zenon_L1020_ *) % 21.78/21.97 assert (zenon_L1021_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H164 zenon_H1b7 zenon_H68 zenon_H93 zenon_H1bb zenon_H20f zenon_H181 zenon_Hc4 zenon_H18d zenon_H48 zenon_H129 zenon_H1b4 zenon_H19a zenon_H177 zenon_Hbb zenon_H111 zenon_H8a zenon_H4d zenon_H73 zenon_H20b zenon_H12e zenon_H67 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H160 zenon_H77 zenon_H120. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.78/21.97 apply (zenon_L528_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.78/21.97 apply (zenon_L557_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.78/21.97 apply (zenon_L1013_); trivial. % 21.78/21.97 apply (zenon_L558_); trivial. % 21.78/21.97 (* end of lemma zenon_L1021_ *) % 21.78/21.97 assert (zenon_L1022_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H139 zenon_H120 zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H12e zenon_H20b zenon_H73 zenon_Hbb zenon_H177 zenon_H19a zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H20f zenon_H1bb zenon_H1b7 zenon_H164 zenon_H195 zenon_H4d zenon_H77 zenon_H173 zenon_H25 zenon_H68 zenon_Hfa zenon_H8a zenon_H111 zenon_H93 zenon_H196. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.97 apply (zenon_L1021_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.97 apply (zenon_L976_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.97 apply (zenon_L258_); trivial. % 21.78/21.97 apply (zenon_L167_); trivial. % 21.78/21.97 (* end of lemma zenon_L1022_ *) % 21.78/21.97 assert (zenon_L1023_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H117 zenon_Ha0 zenon_H93 zenon_H77 zenon_H131 zenon_H4d zenon_Hb6 zenon_H2d zenon_H48 zenon_H13f zenon_H8a zenon_Ha9 zenon_H9e zenon_H196. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.78/21.97 apply (zenon_L67_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.78/21.97 apply (zenon_L825_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.78/21.97 apply (zenon_L153_); trivial. % 21.78/21.97 apply (zenon_L154_); trivial. % 21.78/21.97 (* end of lemma zenon_L1023_ *) % 21.78/21.97 assert (zenon_L1024_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H139 zenon_Ha9 zenon_H8a zenon_H13f zenon_H48 zenon_H2d zenon_Hb6 zenon_H4d zenon_H131 zenon_H77 zenon_Ha0 zenon_H117 zenon_H47 zenon_H13a zenon_H68 zenon_H31 zenon_H93 zenon_H196. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.97 apply (zenon_L251_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.97 apply (zenon_L253_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.97 apply (zenon_L110_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.97 apply (zenon_L68_); trivial. % 21.78/21.97 apply (zenon_L1023_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.97 apply (zenon_L264_); trivial. % 21.78/21.97 apply (zenon_L167_); trivial. % 21.78/21.97 (* end of lemma zenon_L1024_ *) % 21.78/21.97 assert (zenon_L1025_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H117 zenon_H2d zenon_Hb6 zenon_H53 zenon_H8a zenon_Ha9 zenon_H19a zenon_H77 zenon_H93 zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H120 zenon_H1bb zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_H195. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.78/21.97 apply (zenon_L67_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.78/21.97 apply (zenon_L113_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.78/21.97 apply (zenon_L153_); trivial. % 21.78/21.97 apply (zenon_L860_); trivial. % 21.78/21.97 (* end of lemma zenon_L1025_ *) % 21.78/21.97 assert (zenon_L1026_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((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) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (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 (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H1c6 zenon_H6e zenon_H195 zenon_H186 zenon_H20f zenon_H25b zenon_H1bb zenon_H120 zenon_H181 zenon_Hc4 zenon_H18d zenon_H129 zenon_H1b4 zenon_H19a zenon_H53 zenon_H117 zenon_H93 zenon_H77 zenon_H131 zenon_H2d zenon_H48 zenon_H13f zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H8a zenon_Ha9 zenon_H1cd. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.78/21.97 apply (zenon_L110_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.78/21.97 apply (zenon_L1025_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.78/21.97 apply (zenon_L825_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.78/21.97 apply (zenon_L68_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.78/21.97 apply (zenon_L124_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.78/21.97 apply (zenon_L153_); trivial. % 21.78/21.97 apply (zenon_L360_); trivial. % 21.78/21.97 (* end of lemma zenon_L1026_ *) % 21.78/21.97 assert (zenon_L1027_ : (((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))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (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)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (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) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (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 (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (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))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H1fe zenon_H24e zenon_H141 zenon_H2c zenon_H55 zenon_H111 zenon_Hfa zenon_H173 zenon_H1b7 zenon_H20b zenon_H196 zenon_H31 zenon_H68 zenon_He4 zenon_H156 zenon_H1cd zenon_Ha9 zenon_H8a zenon_Hb6 zenon_Ha0 zenon_H1a2 zenon_H117 zenon_H19a zenon_H1b4 zenon_H18d zenon_H181 zenon_H25b zenon_H20f zenon_H186 zenon_H195 zenon_H1c6 zenon_H13f zenon_H1f1 zenon_H4d zenon_H131 zenon_H189 zenon_H164 zenon_H177 zenon_H1a8 zenon_H139 zenon_H4e zenon_H13a zenon_H82 zenon_H73 zenon_H15d zenon_H12e zenon_H48 zenon_Hc4 zenon_H93 zenon_H129 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H160 zenon_H77 zenon_H120. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.97 apply (zenon_L859_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.78/21.97 apply (zenon_L68_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.78/21.97 apply (zenon_L124_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.78/21.97 apply (zenon_L153_); trivial. % 21.78/21.97 apply (zenon_L1022_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.97 apply (zenon_L1024_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.97 apply (zenon_L1024_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.97 apply (zenon_L14_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.97 apply (zenon_L217_); trivial. % 21.78/21.97 apply (zenon_L866_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.97 apply (zenon_L184_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.97 apply (zenon_L888_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.97 apply (zenon_L14_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.97 apply (zenon_L217_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.97 apply (zenon_L865_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.97 apply (zenon_L486_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.97 apply (zenon_L1026_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.97 apply (zenon_L864_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.97 apply (zenon_L439_); trivial. % 21.78/21.97 apply (zenon_L240_); trivial. % 21.78/21.97 apply (zenon_L31_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.97 apply (zenon_L214_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.97 apply (zenon_L486_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.97 apply (zenon_L1026_); trivial. % 21.78/21.97 apply (zenon_L840_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.97 apply (zenon_L264_); trivial. % 21.78/21.97 apply (zenon_L167_); trivial. % 21.78/21.97 apply (zenon_L528_); trivial. % 21.78/21.97 (* end of lemma zenon_L1027_ *) % 21.78/21.97 assert (zenon_L1028_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H117 zenon_H2d zenon_Hb6 zenon_H53 zenon_H104 zenon_Hbb zenon_H19a zenon_H77 zenon_H93 zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H120 zenon_H1bb zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_H195. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.78/21.97 apply (zenon_L67_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.78/21.97 apply (zenon_L113_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.78/21.97 apply (zenon_L129_); trivial. % 21.78/21.97 apply (zenon_L860_); trivial. % 21.78/21.97 (* end of lemma zenon_L1028_ *) % 21.78/21.97 assert (zenon_L1029_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((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) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (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) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H1c6 zenon_Ha9 zenon_H6e zenon_H195 zenon_H4d zenon_H186 zenon_H20f zenon_H25b zenon_Ha0 zenon_H1bb zenon_H120 zenon_H181 zenon_Hc4 zenon_H18d zenon_H48 zenon_H129 zenon_H1b4 zenon_H93 zenon_H77 zenon_H19a zenon_H104 zenon_H2d zenon_H117 zenon_Hb6 zenon_H53 zenon_Hbb zenon_H1cd. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.78/21.97 apply (zenon_L110_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.78/21.97 apply (zenon_L1028_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.78/21.97 apply (zenon_L113_); trivial. % 21.78/21.97 apply (zenon_L360_); trivial. % 21.78/21.97 (* end of lemma zenon_L1029_ *) % 21.78/21.97 assert (zenon_L1030_ : (((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))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (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))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H1fe zenon_H24e zenon_H55 zenon_Hfa zenon_H173 zenon_H1b7 zenon_H73 zenon_H20b zenon_H196 zenon_H111 zenon_H8a zenon_He4 zenon_H156 zenon_H1cd zenon_Hbb zenon_Hb6 zenon_H117 zenon_H104 zenon_H19a zenon_H1b4 zenon_H18d zenon_H181 zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H195 zenon_Ha9 zenon_H1c6 zenon_H189 zenon_H164 zenon_H68 zenon_H31 zenon_H177 zenon_H1a8 zenon_H139 zenon_H4e zenon_H13a zenon_H82 zenon_H13f zenon_H1f1 zenon_H131 zenon_H15d zenon_H12e zenon_H48 zenon_Hc4 zenon_H93 zenon_H129 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H160 zenon_H77 zenon_H120. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.97 apply (zenon_L13_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.97 apply (zenon_L14_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.97 apply (zenon_L1021_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.97 apply (zenon_L856_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.97 apply (zenon_L258_); trivial. % 21.78/21.97 apply (zenon_L167_); trivial. % 21.78/21.97 apply (zenon_L867_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.97 apply (zenon_L1022_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.97 apply (zenon_L1014_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.97 apply (zenon_L1014_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.97 apply (zenon_L14_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.97 apply (zenon_L217_); trivial. % 21.78/21.97 apply (zenon_L866_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.97 apply (zenon_L239_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.97 apply (zenon_L850_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.97 apply (zenon_L14_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.97 apply (zenon_L217_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.97 apply (zenon_L865_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.97 apply (zenon_L486_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.97 apply (zenon_L1029_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.97 apply (zenon_L864_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.97 apply (zenon_L439_); trivial. % 21.78/21.97 apply (zenon_L240_); trivial. % 21.78/21.97 apply (zenon_L527_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.97 apply (zenon_L214_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.97 apply (zenon_L486_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.97 apply (zenon_L1029_); trivial. % 21.78/21.97 apply (zenon_L31_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.78/21.97 apply (zenon_L258_); trivial. % 21.78/21.97 apply (zenon_L167_); trivial. % 21.78/21.97 apply (zenon_L528_); trivial. % 21.78/21.97 (* end of lemma zenon_L1030_ *) % 21.78/21.97 assert (zenon_L1031_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.97 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H25 zenon_H162 zenon_H20b zenon_H73 zenon_H4d zenon_H8a zenon_H111 zenon_Hbb zenon_H177 zenon_H12e zenon_Hc4 zenon_H181 zenon_H18a zenon_H1bb zenon_H3d zenon_H192 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H164 zenon_H160 zenon_H163 zenon_H93 zenon_H195. % 21.78/21.97 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.97 apply (zenon_L171_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.78/21.97 apply (zenon_L870_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.78/21.97 apply (zenon_L878_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.78/21.97 apply (zenon_L1013_); trivial. % 21.78/21.97 exact (zenon_H162 zenon_H167). % 21.78/21.97 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.97 apply (zenon_L227_); trivial. % 21.78/21.97 apply (zenon_L228_); trivial. % 21.78/21.97 (* end of lemma zenon_L1031_ *) % 21.78/21.97 assert (zenon_L1032_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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 (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (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 (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((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)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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) (e3)) = (e3))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H82 zenon_H196 zenon_H13a zenon_Ha9 zenon_Hb6 zenon_H155 zenon_H77 zenon_H139 zenon_H48 zenon_Hbc zenon_Hbb zenon_H160 zenon_H7d zenon_H179 zenon_H25 zenon_H212 zenon_H55 zenon_H4d zenon_H156 zenon_Hfa zenon_H68 zenon_H20b zenon_H73 zenon_H8a zenon_H111 zenon_H177 zenon_H12e zenon_H192 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H24e zenon_H164 zenon_H163 zenon_H93 zenon_H195 zenon_He4 zenon_H1bb zenon_H162 zenon_H18a zenon_H181 zenon_Hc4. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.97 apply (zenon_L850_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.97 apply (zenon_L25_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.97 apply (zenon_L1031_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.97 apply (zenon_L486_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.97 apply (zenon_L15_); trivial. % 21.78/21.97 apply (zenon_L658_); trivial. % 21.78/21.97 apply (zenon_L211_); trivial. % 21.78/21.97 (* end of lemma zenon_L1032_ *) % 21.78/21.97 assert (zenon_L1033_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (((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) (e3)) = (e3))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H82 zenon_H196 zenon_H93 zenon_H177 zenon_H160 zenon_H13a zenon_Ha9 zenon_Hbb zenon_Hb6 zenon_H155 zenon_H77 zenon_H139 zenon_H4e zenon_H4d zenon_H48 zenon_H2d zenon_H1bb zenon_H162 zenon_H18a zenon_H181 zenon_Hc4. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.97 apply (zenon_L850_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.97 apply (zenon_L14_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.97 apply (zenon_L217_); trivial. % 21.78/21.97 apply (zenon_L211_); trivial. % 21.78/21.97 (* end of lemma zenon_L1033_ *) % 21.78/21.97 assert (zenon_L1034_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((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 (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (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)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.78/21.97 do 0 intro. intros zenon_H1fe zenon_H33 zenon_H195 zenon_H163 zenon_H164 zenon_H192 zenon_H12e zenon_H20b zenon_H68 zenon_Hfa zenon_H55 zenon_H212 zenon_H179 zenon_Hbc zenon_H173 zenon_H18a zenon_H48 zenon_H4d zenon_H4e zenon_H139 zenon_H77 zenon_Hb6 zenon_Hbb zenon_Ha9 zenon_H13a zenon_H177 zenon_H93 zenon_H196 zenon_H82 zenon_H73 zenon_H131 zenon_H1f1 zenon_H13f zenon_H117 zenon_Ha0 zenon_H104 zenon_H156 zenon_He4 zenon_H31 zenon_H8a zenon_H111 zenon_H15d zenon_H1bb zenon_H162 zenon_H1c7 zenon_H160 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H181 zenon_Hc4. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.97 apply (zenon_L13_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.97 apply (zenon_L215_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.97 apply (zenon_L184_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.97 apply (zenon_L850_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.97 apply (zenon_L14_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.97 apply (zenon_L912_); trivial. % 21.78/21.97 apply (zenon_L211_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.97 apply (zenon_L1012_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.97 apply (zenon_L1031_); trivial. % 21.78/21.97 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.97 apply (zenon_L239_); trivial. % 21.78/21.98 apply (zenon_L1032_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.98 apply (zenon_L1014_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.98 apply (zenon_L892_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.98 apply (zenon_L184_); trivial. % 21.78/21.98 apply (zenon_L1033_); trivial. % 21.78/21.98 apply (zenon_L870_); trivial. % 21.78/21.98 (* end of lemma zenon_L1034_ *) % 21.78/21.98 assert (zenon_L1035_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (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 (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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 (e1) (e3)) = (op (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 21.78/21.98 do 0 intro. intros zenon_H99 zenon_H179 zenon_H33 zenon_H1fe zenon_H1cb zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_He4 zenon_H1f1 zenon_H131 zenon_H13f zenon_H104 zenon_H117 zenon_H156 zenon_H13a zenon_H82 zenon_H1a8 zenon_H189 zenon_H121 zenon_H26d zenon_H25b zenon_H186 zenon_H1c6 zenon_H4e zenon_H8a zenon_H111 zenon_H173 zenon_H4d zenon_H195 zenon_Hfa zenon_H12e zenon_H163 zenon_H192 zenon_H19a zenon_H18d zenon_H20f zenon_H129 zenon_H20b zenon_H73 zenon_H164 zenon_H48 zenon_H139 zenon_H196 zenon_H177 zenon_H77 zenon_H68 zenon_H31 zenon_H1bb zenon_H1b4 zenon_H1b7 zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H1cd zenon_H24e zenon_H15d zenon_Hbb zenon_H55. % 21.78/21.98 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.78/21.98 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.78/21.98 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.78/21.98 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.78/21.98 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.78/21.98 exact (zenon_H1a3 zenon_Hbb). % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.78/21.98 apply (zenon_L1019_); trivial. % 21.78/21.98 apply (zenon_L1019_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.78/21.98 exact (zenon_H1a3 zenon_Hbb). % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.78/21.98 apply (zenon_L1030_); trivial. % 21.78/21.98 apply (zenon_L1030_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.78/21.98 exact (zenon_H1a3 zenon_Hbb). % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.78/21.98 apply (zenon_L1034_); trivial. % 21.78/21.98 apply (zenon_L1034_); trivial. % 21.78/21.98 apply (zenon_L895_); trivial. % 21.78/21.98 (* end of lemma zenon_L1035_ *) % 21.78/21.98 assert (zenon_L1036_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (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 (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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 (e1) (e3)) = (op (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 21.78/21.98 do 0 intro. intros zenon_H1a2 zenon_Hc4 zenon_H1c7 zenon_H9f zenon_H99 zenon_H179 zenon_H33 zenon_H1fe zenon_H1cb zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_He4 zenon_H1f1 zenon_H131 zenon_H13f zenon_H104 zenon_H117 zenon_H156 zenon_H13a zenon_H82 zenon_H1a8 zenon_H189 zenon_H121 zenon_H26d zenon_H25b zenon_H186 zenon_H1c6 zenon_H4e zenon_H8a zenon_H111 zenon_H173 zenon_H4d zenon_H195 zenon_Hfa zenon_H12e zenon_H163 zenon_H192 zenon_H19a zenon_H18d zenon_H20f zenon_H129 zenon_H20b zenon_H73 zenon_H164 zenon_H48 zenon_H139 zenon_H196 zenon_H177 zenon_H77 zenon_H68 zenon_H31 zenon_H1bb zenon_H1b4 zenon_H1b7 zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H1cd zenon_H24e zenon_H15d zenon_H55. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.78/21.98 apply (zenon_L68_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.78/21.98 apply (zenon_L124_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.78/21.98 apply (zenon_L819_); trivial. % 21.78/21.98 apply (zenon_L1035_); trivial. % 21.78/21.98 (* end of lemma zenon_L1036_ *) % 21.78/21.98 assert (zenon_L1037_ : (((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) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.78/21.98 do 0 intro. intros zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H8a zenon_Ha9 zenon_H9d zenon_Hbc. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.78/21.98 apply (zenon_L68_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.78/21.98 apply (zenon_L124_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.78/21.98 apply (zenon_L153_); trivial. % 21.78/21.98 apply (zenon_L48_); trivial. % 21.78/21.98 (* end of lemma zenon_L1037_ *) % 21.78/21.98 assert (zenon_L1038_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (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 (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 (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e0)) = (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))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.78/21.98 do 0 intro. intros zenon_Hb2 zenon_H55 zenon_H15d zenon_H24e zenon_H1cd zenon_H18a zenon_H7d zenon_H212 zenon_H1b7 zenon_H1b4 zenon_H1bb zenon_H68 zenon_H77 zenon_H177 zenon_H196 zenon_H139 zenon_H48 zenon_H164 zenon_H73 zenon_H20b zenon_H129 zenon_H20f zenon_H18d zenon_H19a zenon_H192 zenon_H163 zenon_H12e zenon_Hfa zenon_H195 zenon_H173 zenon_H111 zenon_H4e zenon_H1c6 zenon_H186 zenon_H25b zenon_H26d zenon_H121 zenon_H189 zenon_H1a8 zenon_H82 zenon_H13a zenon_H156 zenon_H117 zenon_H104 zenon_H13f zenon_H131 zenon_H1f1 zenon_He4 zenon_H1cb zenon_H1fe zenon_H33 zenon_H179 zenon_H99 zenon_H1c7 zenon_Hc4 zenon_H25 zenon_H54 zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H8a zenon_Ha9 zenon_Hbc. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.78/21.98 apply (zenon_L1036_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.78/21.98 apply (zenon_L116_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.78/21.98 apply (zenon_L151_); trivial. % 21.78/21.98 apply (zenon_L1037_); trivial. % 21.78/21.98 (* end of lemma zenon_L1038_ *) % 21.78/21.98 assert (zenon_L1039_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (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 (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((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 (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.78/21.98 do 0 intro. intros zenon_Hb2 zenon_H55 zenon_H212 zenon_H1b4 zenon_H164 zenon_H73 zenon_H20b zenon_H129 zenon_H20f zenon_H18d zenon_H19a zenon_H192 zenon_H163 zenon_H12e zenon_Hfa zenon_H195 zenon_H173 zenon_H111 zenon_H1c6 zenon_H186 zenon_H25b zenon_H26d zenon_H121 zenon_H189 zenon_H1a8 zenon_H156 zenon_H104 zenon_H1f1 zenon_He4 zenon_H1cb zenon_H1fe zenon_H33 zenon_H179 zenon_H99 zenon_H1a2 zenon_Hbc zenon_H18a zenon_H48 zenon_H4d zenon_H4e zenon_H139 zenon_H77 zenon_Hb6 zenon_H31 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H177 zenon_H93 zenon_H196 zenon_H82 zenon_H8a zenon_H13f zenon_H131 zenon_H117 zenon_H68 zenon_H15d zenon_H1bb zenon_H162 zenon_H1c7 zenon_H160 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H181 zenon_Hc4. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.98 apply (zenon_L913_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.98 apply (zenon_L1012_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.98 apply (zenon_L14_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.98 apply (zenon_L1038_); trivial. % 21.78/21.98 apply (zenon_L211_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.98 apply (zenon_L1024_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.98 apply (zenon_L892_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.98 apply (zenon_L239_); trivial. % 21.78/21.98 apply (zenon_L893_); trivial. % 21.78/21.98 apply (zenon_L870_); trivial. % 21.78/21.98 (* end of lemma zenon_L1039_ *) % 21.78/21.98 assert (zenon_L1040_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((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) (e0)) = (op (e3) (e2)))) -> False). % 21.78/21.98 do 0 intro. intros zenon_H9b zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H8a zenon_Ha9 zenon_Hbc. % 21.78/21.98 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.78/21.98 apply (zenon_L1037_); trivial. % 21.78/21.98 (* end of lemma zenon_L1040_ *) % 21.78/21.98 assert (zenon_L1041_ : (((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)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.78/21.98 do 0 intro. intros zenon_H1a2 zenon_Ha0 zenon_H31 zenon_H186 zenon_Ha5 zenon_H8a zenon_Ha9 zenon_Hac zenon_H1cd. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.78/21.98 apply (zenon_L68_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.78/21.98 apply (zenon_L308_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.78/21.98 apply (zenon_L153_); trivial. % 21.78/21.98 apply (zenon_L360_); trivial. % 21.78/21.98 (* end of lemma zenon_L1041_ *) % 21.78/21.98 assert (zenon_L1042_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (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)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.78/21.98 do 0 intro. intros zenon_Hb1 zenon_H1a2 zenon_Ha0 zenon_H31 zenon_H186 zenon_H8a zenon_Ha9 zenon_H1cd. % 21.78/21.98 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.78/21.98 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 21.78/21.98 apply (zenon_L1041_); trivial. % 21.78/21.98 (* end of lemma zenon_L1042_ *) % 21.78/21.98 assert (zenon_L1043_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e0) (e2)) = (op (e0) (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) (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 (e1) (e1)) = (op (e1) (e2)))) -> (((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 (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (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) (e2)) = (e2)) -> False). % 21.78/21.98 do 0 intro. intros zenon_Hcc zenon_H1d8 zenon_H55 zenon_H2c zenon_H141 zenon_H15d zenon_H24e zenon_H18a zenon_H7d zenon_H212 zenon_H1b7 zenon_H1b4 zenon_H181 zenon_H1bb zenon_H68 zenon_H77 zenon_H177 zenon_H196 zenon_H139 zenon_H48 zenon_H164 zenon_H73 zenon_H20b zenon_H129 zenon_H20f zenon_H18d zenon_H19a zenon_H192 zenon_H163 zenon_H12e zenon_Hfa zenon_H195 zenon_H173 zenon_H111 zenon_H4e zenon_H1c6 zenon_H25b zenon_H26d zenon_H189 zenon_H1a8 zenon_H82 zenon_H13a zenon_H156 zenon_H117 zenon_H13f zenon_H131 zenon_H1f1 zenon_He4 zenon_H1cb zenon_H1fe zenon_H104 zenon_H121 zenon_Hb2 zenon_H179 zenon_H33 zenon_Hbc zenon_H4d zenon_Hb6 zenon_H1cd zenon_Ha9 zenon_H186 zenon_H31 zenon_Ha0 zenon_H1a2 zenon_H8a. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.78/21.98 apply (zenon_L2_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.78/21.98 apply (zenon_L700_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.78/21.98 apply (zenon_L782_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.78/21.98 apply (zenon_L757_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.78/21.98 apply (zenon_L758_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.78/21.98 apply (zenon_L11_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.78/21.98 apply (zenon_L787_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.78/21.98 apply (zenon_L335_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.78/21.98 apply (zenon_L814_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.78/21.98 apply (zenon_L88_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.78/21.98 apply (zenon_L37_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.78/21.98 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.78/21.98 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.78/21.98 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.78/21.98 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.78/21.98 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.78/21.98 apply (zenon_L1020_); trivial. % 21.78/21.98 apply (zenon_L1020_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.78/21.98 apply (zenon_L1027_); trivial. % 21.78/21.98 apply (zenon_L1027_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.78/21.98 apply (zenon_L1039_); trivial. % 21.78/21.98 apply (zenon_L1039_); trivial. % 21.78/21.98 apply (zenon_L434_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.78/21.98 apply (zenon_L1040_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.78/21.98 apply (zenon_L1042_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.78/21.98 apply (zenon_L792_); trivial. % 21.78/21.98 apply (zenon_L51_); trivial. % 21.78/21.98 (* end of lemma zenon_L1043_ *) % 21.78/21.98 assert (zenon_L1044_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((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)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((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)) = (op (e3) (e0)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> False). % 21.78/21.98 do 0 intro. intros zenon_H271 zenon_H31 zenon_H1d8 zenon_H8a zenon_H26d zenon_H4d zenon_H4e zenon_H186 zenon_H68 zenon_H131 zenon_H55 zenon_H2c zenon_H141 zenon_H1a2 zenon_H15d zenon_H24e zenon_H1cd zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1b7 zenon_H1b4 zenon_H1bb zenon_H77 zenon_H177 zenon_H196 zenon_H139 zenon_H48 zenon_H164 zenon_H73 zenon_H20b zenon_H129 zenon_H20f zenon_H18d zenon_H19a zenon_H192 zenon_H163 zenon_H12e zenon_Hfa zenon_H195 zenon_H173 zenon_H111 zenon_H1c6 zenon_H25b zenon_H189 zenon_H1a8 zenon_H82 zenon_H13a zenon_H156 zenon_H117 zenon_H13f zenon_H1f1 zenon_He4 zenon_Ha9 zenon_H1cb zenon_H1fe zenon_H104 zenon_H121 zenon_Hb6 zenon_Ha0 zenon_Hb2 zenon_H179 zenon_H33 zenon_Hcc. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 21.78/21.98 apply (zenon_L1043_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.78/21.98 apply (zenon_L2_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.78/21.98 apply (zenon_L700_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.78/21.98 apply (zenon_L782_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.78/21.98 apply (zenon_L757_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.78/21.98 apply (zenon_L758_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.78/21.98 apply (zenon_L11_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.78/21.98 apply (zenon_L787_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.78/21.98 apply (zenon_L335_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.78/21.98 apply (zenon_L789_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.78/21.98 apply (zenon_L343_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.78/21.98 apply (zenon_L37_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.78/21.98 apply (zenon_L1035_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.78/21.98 apply (zenon_L791_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.78/21.98 apply (zenon_L361_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.78/21.98 apply (zenon_L792_); trivial. % 21.78/21.98 apply (zenon_L51_); trivial. % 21.78/21.98 (* end of lemma zenon_L1044_ *) % 21.78/21.98 assert (zenon_L1045_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (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) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (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 (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 (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) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((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) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (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) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> False). % 21.78/21.98 do 0 intro. intros zenon_H277 zenon_H31 zenon_H1d8 zenon_H16a zenon_Hf0 zenon_H68 zenon_H13e zenon_H131 zenon_H1ef zenon_H26d zenon_H4e zenon_H73 zenon_H13c zenon_H156 zenon_H117 zenon_H12e zenon_H18a zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H1b4 zenon_H271 zenon_H1bb zenon_H13a zenon_Ha9 zenon_H15d zenon_H77 zenon_H1fe zenon_H48 zenon_H55 zenon_H125 zenon_H1d5 zenon_H164 zenon_H104 zenon_Hfa zenon_H195 zenon_H163 zenon_Hb6 zenon_H18d zenon_H189 zenon_Ha0 zenon_H1b7 zenon_H19a zenon_H13f zenon_H94 zenon_H1a2 zenon_H1cb zenon_H26a zenon_H22d zenon_H179 zenon_H1cf zenon_H141 zenon_H82 zenon_H173 zenon_H196 zenon_H139 zenon_H190 zenon_H186 zenon_H2c zenon_H129 zenon_H177 zenon_H7d zenon_H24e zenon_H5d zenon_Hb2 zenon_H121 zenon_H1f1 zenon_H1a8 zenon_H212 zenon_He4 zenon_H25b zenon_H20f zenon_Hf5 zenon_H25e zenon_H192 zenon_H11a zenon_H33 zenon_H1c6 zenon_H1c3 zenon_H109 zenon_H201 zenon_H6f zenon_H266 zenon_H20b zenon_Hef. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H4d ]. % 21.78/21.98 exact (zenon_H1b3 zenon_Hef). % 21.78/21.98 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ]. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 21.78/21.98 apply (zenon_L1007_); trivial. % 21.78/21.98 apply (zenon_L1011_); trivial. % 21.78/21.98 apply (zenon_L1044_); trivial. % 21.78/21.98 (* end of lemma zenon_L1045_ *) % 21.78/21.98 assert (zenon_L1046_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (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) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.98 do 0 intro. intros zenon_H18d zenon_H1cb zenon_Hbb zenon_H13a zenon_H7e zenon_H7d zenon_H16a zenon_H7b zenon_H8b zenon_H129 zenon_H4d zenon_H156 zenon_He4 zenon_H177 zenon_H13c zenon_H25 zenon_Ha9 zenon_H1bb zenon_H77 zenon_Hf7 zenon_Hb9 zenon_H25e zenon_H136 zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_Hb6 zenon_H54 zenon_H10c zenon_Hf0 zenon_H14c zenon_Ha0 zenon_H196. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.78/21.98 apply (zenon_L943_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.78/21.98 apply (zenon_L206_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.78/21.98 apply (zenon_L182_); trivial. % 21.78/21.98 apply (zenon_L941_); trivial. % 21.78/21.98 (* end of lemma zenon_L1046_ *) % 21.78/21.98 assert (zenon_L1047_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> False). % 21.78/21.98 do 0 intro. intros zenon_H201 zenon_H48 zenon_Hb6 zenon_H1bf zenon_H1cf zenon_H68 zenon_H31 zenon_Ha9 zenon_H133 zenon_H8b zenon_H77. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.78/21.98 apply (zenon_L239_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.78/21.98 apply (zenon_L124_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.78/21.98 exact (zenon_H1bf zenon_H105). % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.98 apply (zenon_L264_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.98 apply (zenon_L436_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.98 exact (zenon_H8b zenon_H8a). % 21.78/21.98 apply (zenon_L367_); trivial. % 21.78/21.98 (* end of lemma zenon_L1047_ *) % 21.78/21.98 assert (zenon_L1048_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 21.78/21.98 do 0 intro. intros zenon_H24 zenon_Hb9 zenon_Ha0 zenon_H13f zenon_H7e zenon_H67 zenon_H18d zenon_H1cb zenon_Hbb zenon_H13a zenon_H7d zenon_H16a zenon_H7b zenon_H8b zenon_H129 zenon_H156 zenon_He4 zenon_H177 zenon_H13c zenon_H25 zenon_H1bb zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_Hf0 zenon_H196 zenon_H31 zenon_H26d zenon_H19a zenon_H6d zenon_H77 zenon_H1bf zenon_H68 zenon_H48 zenon_H16b zenon_H141 zenon_Hb6 zenon_H4d zenon_Ha9 zenon_Hf7. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.98 apply (zenon_L900_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.98 apply (zenon_L627_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.98 apply (zenon_L54_); trivial. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.98 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.78/21.99 apply (zenon_L756_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.78/21.99 apply (zenon_L1046_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_L547_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.78/21.99 apply (zenon_L56_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.78/21.99 exact (zenon_H1bf zenon_H105). % 21.78/21.99 apply (zenon_L182_); trivial. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.99 apply (zenon_L124_); trivial. % 21.78/21.99 apply (zenon_L299_); trivial. % 21.78/21.99 (* end of lemma zenon_L1048_ *) % 21.78/21.99 assert (zenon_L1049_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 21.78/21.99 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_Hdb zenon_H156 zenon_H4d zenon_H94 zenon_Hb9 zenon_H7b zenon_H55 zenon_H92 zenon_H13e zenon_H1bf zenon_H1ef zenon_H89 zenon_H22d zenon_H8b zenon_H77 zenon_H16a zenon_H7d zenon_H7e. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.99 apply (zenon_L55_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.99 apply (zenon_L486_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.99 apply (zenon_L998_); trivial. % 21.78/21.99 apply (zenon_L31_); trivial. % 21.78/21.99 (* end of lemma zenon_L1049_ *) % 21.78/21.99 assert (zenon_L1050_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 21.78/21.99 do 0 intro. intros zenon_H24 zenon_Hb9 zenon_Ha0 zenon_H1d5 zenon_H67 zenon_H19a zenon_H26d zenon_H196 zenon_Hf0 zenon_H54 zenon_H117 zenon_H9f zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H1cf zenon_H68 zenon_H31 zenon_H8b zenon_H77 zenon_H212 zenon_H25 zenon_H179 zenon_H7d zenon_Hbb zenon_Hbc zenon_H1bb zenon_H13c zenon_H177 zenon_He4 zenon_H156 zenon_H129 zenon_H7b zenon_H16a zenon_H155 zenon_H13a zenon_H1cb zenon_H12e zenon_H25b zenon_H20f zenon_H186 zenon_H195 zenon_H6d zenon_H48 zenon_H141 zenon_Hb6 zenon_H4d zenon_Ha9 zenon_Hf7. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.99 apply (zenon_L900_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.99 apply (zenon_L217_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.99 apply (zenon_L54_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.99 apply (zenon_L944_); trivial. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.99 apply (zenon_L124_); trivial. % 21.78/21.99 apply (zenon_L299_); trivial. % 21.78/21.99 (* end of lemma zenon_L1050_ *) % 21.78/21.99 assert (zenon_L1051_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((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 (e2) (e0)) = (op (e2) (e1)))) -> (((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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (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) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.78/21.99 do 0 intro. intros zenon_H20b zenon_H266 zenon_H6f zenon_H109 zenon_H1c3 zenon_H1c6 zenon_H33 zenon_H11a zenon_H192 zenon_H1f1 zenon_H121 zenon_Hb2 zenon_H5d zenon_H24e zenon_H190 zenon_H82 zenon_H22d zenon_H26a zenon_H1a2 zenon_H94 zenon_H13f zenon_H1b7 zenon_H189 zenon_H18d zenon_H163 zenon_Hfa zenon_H104 zenon_H164 zenon_H125 zenon_H55 zenon_H1fe zenon_H15d zenon_H271 zenon_H111 zenon_Hcc zenon_H270 zenon_H18a zenon_H73 zenon_H4e zenon_H1ef zenon_H131 zenon_H13e zenon_H1d8 zenon_H277 zenon_H1bf zenon_H201 zenon_H1a8 zenon_H3d zenon_H173 zenon_H2c zenon_H16b zenon_H139 zenon_Ha9 zenon_H4d zenon_Hb6 zenon_H141 zenon_H48 zenon_H195 zenon_H20f zenon_H25b zenon_H12e zenon_H1cb zenon_H13a zenon_H155 zenon_H16a zenon_H7b zenon_H129 zenon_H156 zenon_He4 zenon_H177 zenon_H13c zenon_H1bb zenon_Hbc zenon_Hbb zenon_H7d zenon_H179 zenon_H25 zenon_H212 zenon_H77 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_H54 zenon_Hf0 zenon_H196 zenon_H26d zenon_H19a zenon_H67 zenon_H1d5 zenon_Ha0 zenon_Hb9 zenon_H24 zenon_H1cf zenon_H68 zenon_H31 zenon_H186 zenon_H8b zenon_H1cd. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.99 apply (zenon_L171_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.99 apply (zenon_L1045_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.99 apply (zenon_L678_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.99 apply (zenon_L214_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.99 apply (zenon_L745_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.99 apply (zenon_L1050_); trivial. % 21.78/21.99 apply (zenon_L709_); trivial. % 21.78/21.99 (* end of lemma zenon_L1051_ *) % 21.78/21.99 assert (zenon_L1052_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 21.78/21.99 do 0 intro. intros zenon_H201 zenon_H48 zenon_H31 zenon_H156 zenon_H3f zenon_H1bf zenon_Hb6 zenon_Hbb. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.78/21.99 apply (zenon_L239_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.78/21.99 apply (zenon_L486_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.78/21.99 exact (zenon_H1bf zenon_H105). % 21.78/21.99 apply (zenon_L363_); trivial. % 21.78/21.99 (* end of lemma zenon_L1052_ *) % 21.78/21.99 assert (zenon_L1053_ : (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> ((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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.99 do 0 intro. intros zenon_Ha0 zenon_H13f zenon_H4d zenon_H186 zenon_H20f zenon_H25b zenon_H1bb zenon_Hf7 zenon_H25 zenon_H13c zenon_Hf0 zenon_H117 zenon_H9f zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H196 zenon_H177 zenon_He4 zenon_H156 zenon_H129 zenon_H7b zenon_H16a zenon_H7d zenon_H7e zenon_H155 zenon_H13a zenon_Hbb zenon_H1cb zenon_H19a zenon_H6d zenon_H16b zenon_H141 zenon_H77 zenon_H8b zenon_Ha9 zenon_H31 zenon_H68 zenon_H1cf zenon_H1bf zenon_Hb6 zenon_H48 zenon_H201 zenon_Hb9 zenon_H195. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.99 apply (zenon_L116_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.99 apply (zenon_L627_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.99 apply (zenon_L54_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.78/21.99 apply (zenon_L246_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.78/21.99 apply (zenon_L943_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_L684_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.78/21.99 apply (zenon_L56_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.78/21.99 exact (zenon_H1bf zenon_H105). % 21.78/21.99 apply (zenon_L182_); trivial. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.99 apply (zenon_L1047_); trivial. % 21.78/21.99 apply (zenon_L172_); trivial. % 21.78/21.99 (* end of lemma zenon_L1053_ *) % 21.78/21.99 assert (zenon_L1054_ : (((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 (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.99 do 0 intro. intros zenon_H13c zenon_H24 zenon_Ha0 zenon_H1d5 zenon_H67 zenon_H4e zenon_H76 zenon_H19a zenon_H26d zenon_H196 zenon_Hf0 zenon_H54 zenon_H117 zenon_H9f zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H1bb zenon_H18a zenon_H34 zenon_H1b7 zenon_H1cb zenon_Hc0 zenon_H129 zenon_H12e zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H6d zenon_H141 zenon_H77 zenon_H8b zenon_Ha9 zenon_H31 zenon_H68 zenon_H1cf zenon_H1bf zenon_Hb6 zenon_H48 zenon_H201 zenon_Hb9 zenon_H195. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.99 apply (zenon_L900_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.99 apply (zenon_L217_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.99 apply (zenon_L54_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.99 apply (zenon_L949_); trivial. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.99 apply (zenon_L1047_); trivial. % 21.78/21.99 apply (zenon_L172_); trivial. % 21.78/21.99 (* end of lemma zenon_L1054_ *) % 21.78/21.99 assert (zenon_L1055_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((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 (e2) (e0)) = (op (e2) (e1)))) -> (((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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (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 (e1) (e1)) = (e0)) -> False). % 21.78/21.99 do 0 intro. intros zenon_H20b zenon_H266 zenon_H6f zenon_H109 zenon_H1c3 zenon_H1c6 zenon_H33 zenon_H11a zenon_He4 zenon_H212 zenon_H1a8 zenon_H1f1 zenon_H121 zenon_Hb2 zenon_H5d zenon_H24e zenon_H7d zenon_H177 zenon_H2c zenon_H190 zenon_H139 zenon_H173 zenon_H82 zenon_H179 zenon_H22d zenon_H26a zenon_H1a2 zenon_H94 zenon_H13f zenon_H189 zenon_H18d zenon_Hfa zenon_H104 zenon_H164 zenon_H125 zenon_H55 zenon_H1fe zenon_H15d zenon_H13a zenon_H271 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H156 zenon_H73 zenon_H1ef zenon_H131 zenon_H13e zenon_H16a zenon_H1d8 zenon_H277 zenon_H195 zenon_Hb9 zenon_H201 zenon_Hb6 zenon_H1bf zenon_H1cf zenon_H68 zenon_H31 zenon_Ha9 zenon_H8b zenon_H77 zenon_H141 zenon_H186 zenon_H20f zenon_H25b zenon_H129 zenon_Hc0 zenon_H1cb zenon_H1b7 zenon_H18a zenon_H1bb zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_H54 zenon_Hf0 zenon_H196 zenon_H26d zenon_H19a zenon_H76 zenon_H4e zenon_H67 zenon_H1d5 zenon_Ha0 zenon_H24 zenon_H13c zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H4d zenon_H163 zenon_He7. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.99 apply (zenon_L214_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.99 apply (zenon_L1045_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.99 apply (zenon_L1054_); trivial. % 21.78/21.99 apply (zenon_L965_); trivial. % 21.78/21.99 (* end of lemma zenon_L1055_ *) % 21.78/21.99 assert (zenon_L1056_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.99 do 0 intro. intros zenon_H1cf zenon_H1d5 zenon_H67 zenon_Hf7 zenon_H186 zenon_H8b zenon_H12e zenon_H48 zenon_H129 zenon_Hc0 zenon_H1cb zenon_H1b7 zenon_H34 zenon_H18a zenon_H1bb zenon_H77 zenon_H25e zenon_H136 zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_Hb6 zenon_H54 zenon_H10c zenon_Hf0 zenon_H14c zenon_Ha0 zenon_H196. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.99 apply (zenon_L252_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.99 apply (zenon_L438_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.99 exact (zenon_H8b zenon_H8a). % 21.78/21.99 apply (zenon_L947_); trivial. % 21.78/21.99 (* end of lemma zenon_L1056_ *) % 21.78/21.99 assert (zenon_L1057_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e0)) -> False). % 21.78/21.99 do 0 intro. intros zenon_H13c zenon_H24 zenon_Hb9 zenon_H1cf zenon_H1d5 zenon_H67 zenon_Hf7 zenon_H186 zenon_H8b zenon_H12e zenon_H48 zenon_H129 zenon_Hc0 zenon_H1cb zenon_H1b7 zenon_H34 zenon_H18a zenon_H1bb zenon_H77 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_H54 zenon_Hf0 zenon_H196 zenon_H68 zenon_H6d zenon_H109 zenon_H141 zenon_Hb6 zenon_H4d zenon_Ha0 zenon_H136. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.99 apply (zenon_L900_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.99 apply (zenon_L359_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.99 apply (zenon_L54_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.99 apply (zenon_L1056_); trivial. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.99 apply (zenon_L124_); trivial. % 21.78/21.99 apply (zenon_L90_); trivial. % 21.78/21.99 (* end of lemma zenon_L1057_ *) % 21.78/21.99 assert (zenon_L1058_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.78/21.99 do 0 intro. intros zenon_H1cf zenon_H68 zenon_H1cd zenon_H1bf zenon_H77 zenon_H31 zenon_H48 zenon_H201 zenon_H8b zenon_H1bb zenon_H18a zenon_H34 zenon_H1b7 zenon_H7f zenon_H1cb zenon_Hc0 zenon_H129. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.99 apply (zenon_L264_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.99 apply (zenon_L746_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.99 exact (zenon_H8b zenon_H8a). % 21.78/21.99 apply (zenon_L946_); trivial. % 21.78/21.99 (* end of lemma zenon_L1058_ *) % 21.78/21.99 assert (zenon_L1059_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (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))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.78/21.99 do 0 intro. intros zenon_He4 zenon_Hdb zenon_Hbb zenon_Hb6 zenon_H156 zenon_H16b zenon_H7b zenon_H16a zenon_H1cf zenon_H68 zenon_H1cd zenon_H1bf zenon_H77 zenon_H31 zenon_H48 zenon_H201 zenon_H8b zenon_H1bb zenon_H18a zenon_H34 zenon_H1b7 zenon_H1cb zenon_Hc0 zenon_H129. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.99 apply (zenon_L55_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.99 apply (zenon_L1052_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.99 apply (zenon_L378_); trivial. % 21.78/21.99 apply (zenon_L1058_); trivial. % 21.78/21.99 (* end of lemma zenon_L1059_ *) % 21.78/21.99 assert (zenon_L1060_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (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 (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 21.78/21.99 do 0 intro. intros zenon_H13c zenon_Hb9 zenon_Ha0 zenon_H1d5 zenon_H67 zenon_H26d zenon_H196 zenon_H9f zenon_H1b4 zenon_Hf5 zenon_H25e zenon_H212 zenon_H25 zenon_H179 zenon_H7d zenon_Hbb zenon_Hbc zenon_H1bb zenon_H177 zenon_He4 zenon_H156 zenon_H129 zenon_H7b zenon_H16a zenon_H19a zenon_H13a zenon_H1a2 zenon_H1cb zenon_H12e zenon_H191 zenon_Hf0 zenon_H54 zenon_H117 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H195 zenon_H6d zenon_H141 zenon_H77 zenon_H8b zenon_H31 zenon_H68 zenon_H1cf zenon_H1bf zenon_Hb6 zenon_H48 zenon_H201 zenon_Ha9 zenon_Hf7. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.99 apply (zenon_L116_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.99 apply (zenon_L217_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.99 apply (zenon_L54_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.99 apply (zenon_L959_); trivial. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.99 apply (zenon_L1047_); trivial. % 21.78/21.99 apply (zenon_L299_); trivial. % 21.78/21.99 (* end of lemma zenon_L1060_ *) % 21.78/21.99 assert (zenon_L1061_ : (((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) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e2)) = (op (e3) (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) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (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 (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (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 (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((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) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (((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))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.78/21.99 do 0 intro. intros zenon_H1a8 zenon_H139 zenon_H164 zenon_Hc0 zenon_H104 zenon_H192 zenon_H13e zenon_H1ef zenon_H3d zenon_H125 zenon_Ha9 zenon_H201 zenon_H48 zenon_Hb6 zenon_H1bf zenon_H77 zenon_H141 zenon_H195 zenon_H4d zenon_H20f zenon_H25b zenon_H117 zenon_H54 zenon_Hf0 zenon_H191 zenon_H12e zenon_H1cb zenon_H1a2 zenon_H13a zenon_H19a zenon_H16a zenon_H7b zenon_H129 zenon_H156 zenon_He4 zenon_H177 zenon_H1bb zenon_Hbc zenon_Hbb zenon_H7d zenon_H179 zenon_H25 zenon_H212 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H196 zenon_H26d zenon_H67 zenon_H1d5 zenon_Ha0 zenon_Hb9 zenon_H13c zenon_H1cf zenon_H68 zenon_H31 zenon_Hf7 zenon_H186 zenon_H8b zenon_H1cd. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.99 apply (zenon_L214_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.99 apply (zenon_L995_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.99 apply (zenon_L1060_); trivial. % 21.78/21.99 apply (zenon_L709_); trivial. % 21.78/21.99 (* end of lemma zenon_L1061_ *) % 21.78/21.99 assert (zenon_L1062_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((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) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 21.78/21.99 do 0 intro. intros zenon_H141 zenon_H13e zenon_H1bf zenon_H1ef zenon_H89 zenon_H195 zenon_H10c zenon_H4d zenon_H186 zenon_H20f zenon_H25b zenon_H117 zenon_Hb6 zenon_H54 zenon_Hf0 zenon_H191 zenon_H12e zenon_H1cb zenon_H1a2 zenon_H13a zenon_H19a zenon_H16a zenon_H7b zenon_H129 zenon_H156 zenon_He4 zenon_H177 zenon_H1bb zenon_Hbc zenon_Hbb zenon_H7d zenon_H179 zenon_H25 zenon_H212 zenon_H77 zenon_H8b zenon_Hf7 zenon_H31 zenon_H68 zenon_H1cf zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H196 zenon_H26d zenon_H67 zenon_H1d5 zenon_Ha0 zenon_Hb9. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.99 apply (zenon_L645_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.99 apply (zenon_L939_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.99 apply (zenon_L959_); trivial. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 (* end of lemma zenon_L1062_ *) % 21.78/21.99 assert (zenon_L1063_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((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) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 21.78/21.99 do 0 intro. intros zenon_H13c zenon_H24 zenon_Hb9 zenon_H6d zenon_H141 zenon_H13e zenon_H1ef zenon_H89 zenon_H195 zenon_H4d zenon_H186 zenon_H20f zenon_H25b zenon_H117 zenon_Hf0 zenon_H191 zenon_H12e zenon_H1cb zenon_H1a2 zenon_H13a zenon_H19a zenon_H16a zenon_H7b zenon_H129 zenon_H156 zenon_He4 zenon_H177 zenon_H1bb zenon_Hbc zenon_Hbb zenon_H7d zenon_H179 zenon_H25 zenon_H212 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H196 zenon_H26d zenon_H67 zenon_H1d5 zenon_Ha0 zenon_H13f zenon_H77 zenon_H8b zenon_H31 zenon_H68 zenon_H1cf zenon_H1bf zenon_Hb6 zenon_H48 zenon_H201 zenon_Ha9 zenon_Hf7. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.99 apply (zenon_L900_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.78/21.99 apply (zenon_L1062_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.78/21.99 apply (zenon_L56_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.78/21.99 exact (zenon_H1bf zenon_H105). % 21.78/21.99 apply (zenon_L182_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.99 apply (zenon_L1047_); trivial. % 21.78/21.99 apply (zenon_L299_); trivial. % 21.78/21.99 (* end of lemma zenon_L1063_ *) % 21.78/21.99 assert (zenon_L1064_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e2)) = (op (e3) (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) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (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 (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (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 (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((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) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (((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))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.78/21.99 do 0 intro. intros zenon_Hfa zenon_H155 zenon_H173 zenon_H22d zenon_H89 zenon_H92 zenon_H55 zenon_H94 zenon_H18a zenon_H1b7 zenon_H271 zenon_H1d8 zenon_H111 zenon_Hcc zenon_H270 zenon_H1a8 zenon_H139 zenon_H164 zenon_Hc0 zenon_H104 zenon_H192 zenon_H13e zenon_H1ef zenon_H3d zenon_H125 zenon_Ha9 zenon_H201 zenon_H48 zenon_Hb6 zenon_H1bf zenon_H77 zenon_H141 zenon_H195 zenon_H4d zenon_H20f zenon_H25b zenon_H117 zenon_H54 zenon_Hf0 zenon_H191 zenon_H12e zenon_H1cb zenon_H1a2 zenon_H13a zenon_H19a zenon_H16a zenon_H7b zenon_H129 zenon_H156 zenon_He4 zenon_H177 zenon_H1bb zenon_Hbc zenon_Hbb zenon_H7d zenon_H179 zenon_H25 zenon_H212 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H196 zenon_H26d zenon_H67 zenon_H1d5 zenon_Ha0 zenon_Hb9 zenon_H13c zenon_H1cf zenon_H68 zenon_H31 zenon_H186 zenon_H8b zenon_H1cd. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.99 apply (zenon_L171_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.99 apply (zenon_L1000_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.99 apply (zenon_L678_); trivial. % 21.78/21.99 apply (zenon_L1061_); trivial. % 21.78/21.99 (* end of lemma zenon_L1064_ *) % 21.78/21.99 assert (zenon_L1065_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 21.78/21.99 do 0 intro. intros zenon_H2c zenon_H9f zenon_Ha8. % 21.78/21.99 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 21.78/21.99 intro zenon_D_pnotp. % 21.78/21.99 apply zenon_H2c. % 21.78/21.99 rewrite <- zenon_D_pnotp. % 21.78/21.99 exact zenon_H9f. % 21.78/21.99 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 21.78/21.99 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 21.78/21.99 congruence. % 21.78/21.99 apply zenon_H27. apply refl_equal. % 21.78/21.99 apply zenon_Hba. apply sym_equal. exact zenon_Ha8. % 21.78/21.99 (* end of lemma zenon_L1065_ *) % 21.78/21.99 assert (zenon_L1066_ : (((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) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e1)) -> False). % 21.78/21.99 do 0 intro. intros zenon_H117 zenon_H9f zenon_H2c zenon_Ha9 zenon_H6d zenon_H191 zenon_Hb6 zenon_H128. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.78/21.99 apply (zenon_L1065_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.78/21.99 apply (zenon_L289_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.78/21.99 exact (zenon_H191 zenon_H110). % 21.78/21.99 apply (zenon_L182_); trivial. % 21.78/21.99 (* end of lemma zenon_L1066_ *) % 21.78/21.99 assert (zenon_L1067_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((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)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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 (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.78/21.99 do 0 intro. intros zenon_Hfa zenon_H1a8 zenon_H3d zenon_H192 zenon_H104 zenon_H67 zenon_Hc0 zenon_H12e zenon_H270 zenon_Hcc zenon_Hbc zenon_H111 zenon_H139 zenon_H1d8 zenon_H271 zenon_H1b7 zenon_H18a zenon_H164 zenon_H201 zenon_H1d5 zenon_H25 zenon_H195 zenon_Hb9 zenon_H4d zenon_Hb6 zenon_H141 zenon_H13e zenon_H1ef zenon_H89 zenon_H191 zenon_Ha9 zenon_H2c zenon_H9f zenon_H117 zenon_H1bf zenon_H77 zenon_H48 zenon_H155 zenon_H1cb zenon_H1a2 zenon_H13a zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H19a zenon_H7e zenon_H7d zenon_H16a zenon_H7b zenon_H129 zenon_H156 zenon_He4 zenon_H177 zenon_Hbb zenon_H196 zenon_H1bb zenon_Hf0 zenon_H25b zenon_H20f zenon_H13f zenon_Ha0 zenon_H24 zenon_H13c zenon_H1cf zenon_H68 zenon_H31 zenon_H186 zenon_H8b zenon_H1cd. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.99 apply (zenon_L171_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.99 apply (zenon_L997_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.99 apply (zenon_L59_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.99 apply (zenon_L214_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.99 apply (zenon_L997_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.99 apply (zenon_L900_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.99 apply (zenon_L645_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.99 apply (zenon_L54_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.78/21.99 apply (zenon_L246_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.78/21.99 apply (zenon_L958_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.78/21.99 apply (zenon_L648_); trivial. % 21.78/21.99 apply (zenon_L684_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.78/21.99 apply (zenon_L56_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.78/21.99 exact (zenon_H1bf zenon_H105). % 21.78/21.99 apply (zenon_L1066_); trivial. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.99 apply (zenon_L124_); trivial. % 21.78/21.99 apply (zenon_L172_); trivial. % 21.78/21.99 apply (zenon_L709_); trivial. % 21.78/21.99 (* end of lemma zenon_L1067_ *) % 21.78/21.99 assert (zenon_L1068_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.78/21.99 do 0 intro. intros zenon_H1d5 zenon_H67 zenon_Hf7 zenon_H186 zenon_H8b zenon_H12e zenon_H48 zenon_H1cb zenon_H191 zenon_H4d zenon_H31 zenon_H1a2 zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H139 zenon_H1d8 zenon_H271 zenon_H68 zenon_H1cf zenon_H1b7 zenon_H34 zenon_H18a zenon_H1bb zenon_H77 zenon_H25e zenon_H136 zenon_Hf5 zenon_H1b4 zenon_H9f zenon_H117 zenon_Hb6 zenon_H54 zenon_H10c zenon_Hf0 zenon_H14c zenon_Ha0 zenon_H196. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.99 apply (zenon_L252_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.99 apply (zenon_L438_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.99 exact (zenon_H8b zenon_H8a). % 21.78/21.99 apply (zenon_L963_); trivial. % 21.78/21.99 (* end of lemma zenon_L1068_ *) % 21.78/21.99 assert (zenon_L1069_ : ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (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)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((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 (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (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 (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (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) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> False). % 21.78/21.99 do 0 intro. intros zenon_H8f zenon_H92 zenon_H270 zenon_Hcc zenon_H111 zenon_H1d8 zenon_H271 zenon_H1a2 zenon_H22d zenon_H26a zenon_H94 zenon_H189 zenon_H18d zenon_H55 zenon_H104 zenon_H125 zenon_H1ef zenon_H13e zenon_He2 zenon_H68 zenon_H67 zenon_H15d zenon_H2c zenon_H139 zenon_Hf0 zenon_H26d zenon_Ha9 zenon_H117 zenon_H1cb zenon_H141 zenon_H24 zenon_H82 zenon_H73 zenon_H1d5 zenon_H156 zenon_H179 zenon_Hbc zenon_H212 zenon_H1cf zenon_H48 zenon_H192 zenon_H77 zenon_H25e zenon_H1b4 zenon_Hf5 zenon_H20f zenon_H25b zenon_H12e zenon_H31 zenon_H1bb zenon_Hc0 zenon_H19a zenon_H186 zenon_He4 zenon_H7d zenon_H129 zenon_H16a zenon_H164 zenon_H8b zenon_H1a8 zenon_H1cd zenon_Hfa zenon_Hb6 zenon_H13c zenon_Hb9 zenon_H195 zenon_H4d zenon_H173 zenon_Ha0 zenon_H177 zenon_Hbb zenon_H196 zenon_H13a zenon_H13f zenon_H131 zenon_H4e zenon_H163 zenon_H1b7 zenon_H18a zenon_H109 zenon_H13b zenon_H1fe zenon_H277 zenon_H190 zenon_H24e zenon_H5d zenon_Hb2 zenon_H121 zenon_H1f1 zenon_H11a zenon_H33 zenon_H1c6 zenon_H1c3 zenon_H201 zenon_H6f zenon_H266 zenon_H20b zenon_H89 zenon_H91. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.78/21.99 apply (zenon_L954_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.99 apply (zenon_L20_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.99 apply (zenon_L251_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.99 apply (zenon_L938_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.99 apply (zenon_L184_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.99 apply (zenon_L744_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.99 apply (zenon_L14_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.99 apply (zenon_L171_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.99 apply (zenon_L957_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.99 apply (zenon_L59_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.99 apply (zenon_L900_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.99 apply (zenon_L217_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.99 apply (zenon_L939_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.99 apply (zenon_L959_); trivial. % 21.78/21.99 apply (zenon_L648_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.99 apply (zenon_L124_); trivial. % 21.78/21.99 apply (zenon_L299_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.99 apply (zenon_L933_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.99 apply (zenon_L68_); trivial. % 21.78/21.99 apply (zenon_L154_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.99 apply (zenon_L171_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.99 apply (zenon_L961_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.99 apply (zenon_L59_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.99 apply (zenon_L214_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.99 apply (zenon_L961_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.99 exact (zenon_H1ba zenon_H6d). % 21.78/21.99 apply (zenon_L709_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.99 apply (zenon_L486_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.99 apply (zenon_L767_); trivial. % 21.78/21.99 apply (zenon_L31_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.99 apply (zenon_L933_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.99 apply (zenon_L178_); trivial. % 21.78/21.99 apply (zenon_L115_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.99 apply (zenon_L755_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.99 apply (zenon_L251_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.99 apply (zenon_L251_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.99 apply (zenon_L14_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.99 apply (zenon_L971_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.99 apply (zenon_L55_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.99 apply (zenon_L68_); trivial. % 21.78/21.99 apply (zenon_L154_); trivial. % 21.78/21.99 apply (zenon_L456_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.99 apply (zenon_L239_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.99 apply (zenon_L744_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.99 apply (zenon_L14_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.99 apply (zenon_L971_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.99 apply (zenon_L972_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.99 apply (zenon_L178_); trivial. % 21.78/21.99 apply (zenon_L115_); trivial. % 21.78/21.99 apply (zenon_L456_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/21.99 apply (zenon_L20_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.99 apply (zenon_L934_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.99 apply (zenon_L934_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.99 apply (zenon_L25_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.99 apply (zenon_L171_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.99 apply (zenon_L1045_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.99 apply (zenon_L678_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.99 apply (zenon_L214_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.99 apply (zenon_L779_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.99 apply (zenon_L116_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.99 apply (zenon_L217_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.99 apply (zenon_L54_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.78/21.99 apply (zenon_L264_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.78/21.99 apply (zenon_L438_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.78/21.99 exact (zenon_H8b zenon_H8a). % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.78/21.99 apply (zenon_L756_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.78/21.99 apply (zenon_L1046_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.78/21.99 apply (zenon_L658_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.78/21.99 apply (zenon_L367_); trivial. % 21.78/21.99 apply (zenon_L941_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_L684_); trivial. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.99 apply (zenon_L1047_); trivial. % 21.78/21.99 apply (zenon_L172_); trivial. % 21.78/21.99 apply (zenon_L709_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.99 apply (zenon_L933_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.99 apply (zenon_L68_); trivial. % 21.78/21.99 apply (zenon_L154_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.99 apply (zenon_L171_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.99 apply (zenon_L1045_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.99 apply (zenon_L59_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.99 apply (zenon_L214_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.99 apply (zenon_L1045_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.99 apply (zenon_L1048_); trivial. % 21.78/21.99 apply (zenon_L709_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.99 apply (zenon_L1049_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.99 apply (zenon_L178_); trivial. % 21.78/21.99 apply (zenon_L154_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.99 apply (zenon_L184_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.99 apply (zenon_L744_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.99 apply (zenon_L14_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.99 apply (zenon_L1051_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.99 apply (zenon_L1052_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.99 apply (zenon_L998_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.99 apply (zenon_L171_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.99 apply (zenon_L1045_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.99 apply (zenon_L746_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.99 apply (zenon_L116_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.99 apply (zenon_L627_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.99 apply (zenon_L939_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.99 apply (zenon_L944_); trivial. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.99 apply (zenon_L1047_); trivial. % 21.78/21.99 apply (zenon_L172_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.99 apply (zenon_L933_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.99 apply (zenon_L68_); trivial. % 21.78/21.99 apply (zenon_L154_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.99 apply (zenon_L171_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.99 apply (zenon_L1045_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.99 apply (zenon_L59_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.99 apply (zenon_L214_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.99 apply (zenon_L1045_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.99 apply (zenon_L1053_); trivial. % 21.78/21.99 apply (zenon_L709_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.99 apply (zenon_L1052_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.99 apply (zenon_L998_); trivial. % 21.78/21.99 apply (zenon_L31_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.99 apply (zenon_L1049_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.99 apply (zenon_L178_); trivial. % 21.78/21.99 apply (zenon_L115_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/21.99 apply (zenon_L627_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/21.99 apply (zenon_L251_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.99 apply (zenon_L251_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.99 apply (zenon_L14_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.78/21.99 apply (zenon_L297_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.99 apply (zenon_L1055_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.99 apply (zenon_L1045_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.99 apply (zenon_L59_); trivial. % 21.78/21.99 apply (zenon_L967_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.78/21.99 apply (zenon_L117_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.78/21.99 apply (zenon_L65_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.99 apply (zenon_L1055_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.99 apply (zenon_L962_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.99 apply (zenon_L678_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.99 apply (zenon_L214_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.99 apply (zenon_L962_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.99 apply (zenon_L1057_); trivial. % 21.78/21.99 apply (zenon_L709_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.78/21.99 apply (zenon_L682_); trivial. % 21.78/21.99 apply (zenon_L802_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/21.99 apply (zenon_L55_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/21.99 apply (zenon_L68_); trivial. % 21.78/21.99 apply (zenon_L154_); trivial. % 21.78/21.99 apply (zenon_L456_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/21.99 apply (zenon_L239_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/21.99 apply (zenon_L744_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/21.99 apply (zenon_L14_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.78/21.99 apply (zenon_L297_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.99 apply (zenon_L214_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.99 apply (zenon_L745_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.99 apply (zenon_L1054_); trivial. % 21.78/21.99 apply (zenon_L965_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/21.99 apply (zenon_L962_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/21.99 apply (zenon_L678_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/21.99 apply (zenon_L214_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/21.99 apply (zenon_L962_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/21.99 apply (zenon_L900_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/21.99 apply (zenon_L359_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/21.99 apply (zenon_L54_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.78/21.99 apply (zenon_L246_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.78/21.99 apply (zenon_L1056_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_L684_); trivial. % 21.78/21.99 apply (zenon_L77_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/21.99 apply (zenon_L124_); trivial. % 21.78/21.99 apply (zenon_L299_); trivial. % 21.78/21.99 apply (zenon_L709_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/21.99 apply (zenon_L1052_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/21.99 apply (zenon_L378_); trivial. % 21.78/21.99 apply (zenon_L1058_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.78/21.99 apply (zenon_L117_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.78/21.99 apply (zenon_L254_); trivial. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.78/21.99 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/22.00 apply (zenon_L214_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/22.00 apply (zenon_L745_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/22.00 apply (zenon_L900_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/22.00 apply (zenon_L217_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/22.00 apply (zenon_L54_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/22.00 apply (zenon_L952_); trivial. % 21.78/22.00 apply (zenon_L77_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/22.00 apply (zenon_L1047_); trivial. % 21.78/22.00 apply (zenon_L172_); trivial. % 21.78/22.00 apply (zenon_L965_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/22.00 apply (zenon_L486_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/22.00 apply (zenon_L15_); trivial. % 21.78/22.00 apply (zenon_L1058_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.78/22.00 apply (zenon_L682_); trivial. % 21.78/22.00 apply (zenon_L802_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/22.00 apply (zenon_L1059_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/22.00 apply (zenon_L178_); trivial. % 21.78/22.00 apply (zenon_L115_); trivial. % 21.78/22.00 apply (zenon_L456_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.78/22.00 apply (zenon_L20_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/22.00 apply (zenon_L251_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/22.00 apply (zenon_L251_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/22.00 apply (zenon_L14_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/22.00 apply (zenon_L171_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/22.00 apply (zenon_L995_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/22.00 apply (zenon_L678_); trivial. % 21.78/22.00 apply (zenon_L1061_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/22.00 apply (zenon_L933_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/22.00 apply (zenon_L68_); trivial. % 21.78/22.00 apply (zenon_L154_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/22.00 apply (zenon_L171_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/22.00 apply (zenon_L993_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/22.00 apply (zenon_L59_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/22.00 apply (zenon_L214_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/22.00 apply (zenon_L993_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/22.00 apply (zenon_L1063_); trivial. % 21.78/22.00 apply (zenon_L709_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/22.00 apply (zenon_L1049_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/22.00 apply (zenon_L178_); trivial. % 21.78/22.00 apply (zenon_L154_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/22.00 apply (zenon_L184_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/22.00 apply (zenon_L744_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/22.00 apply (zenon_L25_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/22.00 apply (zenon_L1064_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/22.00 apply (zenon_L486_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/22.00 apply (zenon_L998_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/22.00 apply (zenon_L171_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/22.00 apply (zenon_L1002_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/22.00 apply (zenon_L746_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/22.00 apply (zenon_L900_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/22.00 apply (zenon_L1062_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/22.00 apply (zenon_L124_); trivial. % 21.78/22.00 apply (zenon_L172_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/22.00 apply (zenon_L933_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/22.00 apply (zenon_L68_); trivial. % 21.78/22.00 apply (zenon_L115_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.78/22.00 apply (zenon_L1067_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.78/22.00 apply (zenon_L1052_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.78/22.00 apply (zenon_L998_); trivial. % 21.78/22.00 apply (zenon_L31_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/22.00 apply (zenon_L933_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/22.00 apply (zenon_L178_); trivial. % 21.78/22.00 apply (zenon_L154_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.78/22.00 apply (zenon_L755_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.78/22.00 apply (zenon_L251_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.78/22.00 apply (zenon_L251_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.78/22.00 apply (zenon_L14_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.78/22.00 apply (zenon_L297_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/22.00 apply (zenon_L966_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/22.00 apply (zenon_L1045_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/22.00 apply (zenon_L678_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.78/22.00 apply (zenon_L214_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.78/22.00 apply (zenon_L1045_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.78/22.00 apply (zenon_L900_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.78/22.00 apply (zenon_L217_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.78/22.00 apply (zenon_L54_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.78/22.00 apply (zenon_L756_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.78/22.00 apply (zenon_L1068_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.78/22.00 apply (zenon_L77_); trivial. % 21.78/22.00 apply (zenon_L294_); trivial. % 21.78/22.00 apply (zenon_L648_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.78/22.00 apply (zenon_L1047_); trivial. % 21.78/22.00 apply (zenon_L299_); trivial. % 21.78/22.00 apply (zenon_L965_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.78/22.00 apply (zenon_L117_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.78/22.00 apply (zenon_L254_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.78/22.00 apply (zenon_L968_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.78/22.00 apply (zenon_L969_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.78/22.00 apply (zenon_L970_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.78/22.00 apply (zenon_L678_); trivial. % 21.78/22.00 apply (zenon_L939_); trivial. % 21.78/22.00 apply (zenon_L802_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.78/22.00 apply (zenon_L972_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.78/22.00 apply (zenon_L68_); trivial. % 21.78/22.00 apply (zenon_L154_); trivial. % 21.78/22.00 apply (zenon_L456_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.78/22.00 apply (zenon_L239_); trivial. % 21.78/22.00 apply (zenon_L1003_); trivial. % 21.78/22.00 apply (zenon_L130_); trivial. % 21.78/22.00 (* end of lemma zenon_L1069_ *) % 21.78/22.00 assert (zenon_L1070_ : (~((op (e3) (e3)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((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) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((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 (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((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)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 21.78/22.00 do 0 intro. intros zenon_H181 zenon_H158 zenon_H20b zenon_H266 zenon_H6f zenon_H201 zenon_H1c3 zenon_H1c6 zenon_H33 zenon_H11a zenon_H1f1 zenon_H121 zenon_Hb2 zenon_H5d zenon_H24e zenon_H190 zenon_H277 zenon_H1fe zenon_H13b zenon_H109 zenon_H18a zenon_H1b7 zenon_H163 zenon_H4e zenon_H131 zenon_H13f zenon_H13a zenon_H196 zenon_H177 zenon_Ha0 zenon_H173 zenon_H4d zenon_H195 zenon_H13c zenon_Hb6 zenon_Hfa zenon_H1cd zenon_H1a8 zenon_H8b zenon_H164 zenon_H16a zenon_H129 zenon_H7d zenon_He4 zenon_H186 zenon_H19a zenon_H1bb zenon_H31 zenon_H12e zenon_H25b zenon_H20f zenon_Hf5 zenon_H1b4 zenon_H25e zenon_H77 zenon_H192 zenon_H48 zenon_H1cf zenon_H212 zenon_Hbc zenon_H179 zenon_H156 zenon_H1d5 zenon_H73 zenon_H82 zenon_H24 zenon_H141 zenon_H1cb zenon_H117 zenon_Ha9 zenon_H26d zenon_Hf0 zenon_H139 zenon_H2c zenon_H15d zenon_H67 zenon_H68 zenon_He2 zenon_H13e zenon_H1ef zenon_H125 zenon_H104 zenon_H55 zenon_H18d zenon_H189 zenon_H94 zenon_H26a zenon_H22d zenon_H1a2 zenon_H271 zenon_H1d8 zenon_H111 zenon_Hcc zenon_H270. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.78/22.00 apply (zenon_L2_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.78/22.00 apply (zenon_L700_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.78/22.00 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.78/22.00 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 21.78/22.00 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.78/22.00 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.78/22.00 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.78/22.00 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.78/22.00 apply (zenon_L754_); trivial. % 21.78/22.00 apply (zenon_L755_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.78/22.00 apply (zenon_L757_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.78/22.00 apply (zenon_L758_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.78/22.00 apply (zenon_L11_); trivial. % 21.78/22.00 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.78/22.00 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.78/22.00 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.78/22.00 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.78/22.00 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.78/22.00 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.88/22.00 apply (zenon_L813_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.88/22.00 apply (zenon_L335_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.88/22.00 apply (zenon_L814_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.88/22.00 apply (zenon_L343_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.88/22.00 apply (zenon_L37_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.88/22.00 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.88/22.00 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.88/22.00 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.88/22.00 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.88/22.00 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.88/22.00 apply (zenon_L908_); trivial. % 21.88/22.00 apply (zenon_L908_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.88/22.00 apply (zenon_L910_); trivial. % 21.88/22.00 apply (zenon_L910_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.88/22.00 apply (zenon_L920_); trivial. % 21.88/22.00 apply (zenon_L920_); trivial. % 21.88/22.00 apply (zenon_L238_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.88/22.00 apply (zenon_L922_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.88/22.00 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.88/22.00 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 21.88/22.00 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.88/22.00 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.88/22.00 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 21.88/22.00 exact (zenon_H1d4 zenon_H4d). % 21.88/22.00 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.00 apply (zenon_L20_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.00 apply (zenon_L923_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.00 apply (zenon_L924_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.00 apply (zenon_L251_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.88/22.00 apply (zenon_L252_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.88/22.00 apply (zenon_L83_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.88/22.00 exact (zenon_H8b zenon_H8a). % 21.88/22.00 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.88/22.00 apply (zenon_L456_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.88/22.00 apply (zenon_L146_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.88/22.00 apply (zenon_L367_); trivial. % 21.88/22.00 apply (zenon_L928_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.88/22.00 exact (zenon_H1b3 zenon_Hef). % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.88/22.00 apply (zenon_L59_); trivial. % 21.88/22.00 apply (zenon_L299_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.00 apply (zenon_L55_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.00 apply (zenon_L68_); trivial. % 21.88/22.00 apply (zenon_L262_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.00 apply (zenon_L184_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.88/22.00 apply (zenon_L297_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.88/22.00 apply (zenon_L359_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.88/22.00 apply (zenon_L929_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.88/22.00 apply (zenon_L68_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.88/22.00 apply (zenon_L308_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.88/22.00 apply (zenon_L278_); trivial. % 21.88/22.00 apply (zenon_L360_); trivial. % 21.88/22.00 apply (zenon_L930_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.88/22.00 apply (zenon_L117_); trivial. % 21.88/22.00 apply (zenon_L90_); trivial. % 21.88/22.00 apply (zenon_L932_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.88/22.00 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.88/22.00 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.88/22.00 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.88/22.00 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.88/22.00 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.88/22.00 apply (zenon_L1069_); trivial. % 21.88/22.00 apply (zenon_L51_); trivial. % 21.88/22.00 (* end of lemma zenon_L1070_ *) % 21.88/22.00 assert (zenon_L1071_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (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 (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((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))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e0)) = (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) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 21.88/22.00 do 0 intro. intros zenon_H92 zenon_H77 zenon_H67 zenon_H82 zenon_H1c6 zenon_H164 zenon_H177 zenon_H156 zenon_H2f zenon_H125 zenon_H24 zenon_Hf0 zenon_H121 zenon_H1b4 zenon_H104 zenon_H179 zenon_H2c zenon_H6f zenon_Hfa zenon_H195 zenon_Heb zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H31 zenon_Hb2 zenon_H1b3 zenon_H13f zenon_H1d8 zenon_H4e zenon_H117 zenon_H196 zenon_H183 zenon_H13a zenon_H33 zenon_H1cf zenon_H1cd zenon_H186 zenon_H181 zenon_H1c3 zenon_H201 zenon_H1bf zenon_H68 zenon_H8b zenon_H16a zenon_H48 zenon_H100 zenon_H1a8 zenon_H2d zenon_H15d zenon_H7d zenon_H13e zenon_H131 zenon_H1ef zenon_H26d zenon_H1fe zenon_H55 zenon_H141 zenon_H22d zenon_H1cb zenon_H1a2 zenon_H94 zenon_H19a zenon_H1b7 zenon_H189 zenon_H18d zenon_H163 zenon_H1d5 zenon_H5d zenon_H24e zenon_H129 zenon_H190 zenon_H1bb zenon_H271 zenon_H111 zenon_Hbc zenon_Hcc zenon_H270 zenon_H12e zenon_H13c zenon_H73 zenon_H212 zenon_H25b zenon_H20f zenon_Hf5 zenon_H25e zenon_H192 zenon_H11a zenon_H109 zenon_H13b zenon_H158 zenon_H20b zenon_H266 zenon_H277 zenon_He2 zenon_H23c zenon_H1f1 zenon_H26a zenon_H18a zenon_H173 zenon_He4 zenon_H139. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.00 apply (zenon_L251_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.00 apply (zenon_L251_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.00 apply (zenon_L701_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.00 apply (zenon_L55_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.00 apply (zenon_L68_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.00 apply (zenon_L701_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.00 apply (zenon_L46_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.00 apply (zenon_L67_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.88/22.00 apply (zenon_L214_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.88/22.00 exact (zenon_H1b3 zenon_Hef). % 21.88/22.00 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.88/22.00 apply (zenon_L217_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.88/22.00 apply (zenon_L327_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.88/22.00 exact (zenon_H1bf zenon_H105). % 21.88/22.00 apply (zenon_L739_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.88/22.00 apply (zenon_L69_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.88/22.00 apply (zenon_L327_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.88/22.00 exact (zenon_H1bf zenon_H105). % 21.88/22.00 apply (zenon_L710_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.00 apply (zenon_L217_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.00 apply (zenon_L701_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.00 apply (zenon_L55_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.00 apply (zenon_L68_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.00 apply (zenon_L701_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.00 apply (zenon_L46_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.00 apply (zenon_L742_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.00 apply (zenon_L722_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.88/22.00 apply (zenon_L217_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.88/22.00 apply (zenon_L327_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.88/22.00 exact (zenon_H1bf zenon_H105). % 21.88/22.00 apply (zenon_L149_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.00 apply (zenon_L67_); trivial. % 21.88/22.00 apply (zenon_L134_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.00 apply (zenon_L239_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.00 apply (zenon_L744_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.00 apply (zenon_L701_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.00 apply (zenon_L46_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.00 apply (zenon_L67_); trivial. % 21.88/22.00 apply (zenon_L749_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.00 apply (zenon_L217_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.00 apply (zenon_L701_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.00 apply (zenon_L46_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.00 apply (zenon_L752_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.00 apply (zenon_L1070_); trivial. % 21.88/22.00 apply (zenon_L192_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.00 apply (zenon_L67_); trivial. % 21.88/22.00 apply (zenon_L134_); trivial. % 21.88/22.00 apply (zenon_L644_); trivial. % 21.88/22.00 (* end of lemma zenon_L1071_ *) % 21.88/22.00 assert (zenon_L1072_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.88/22.00 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H13d zenon_H68 zenon_H93. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.88/22.00 apply (zenon_L359_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.88/22.00 apply (zenon_L929_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.88/22.00 exact (zenon_H13d zenon_H14c). % 21.88/22.00 apply (zenon_L158_); trivial. % 21.88/22.00 (* end of lemma zenon_L1072_ *) % 21.88/22.00 assert (zenon_L1073_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.88/22.00 do 0 intro. intros zenon_H16a zenon_H2c zenon_H67 zenon_H1ba zenon_H8b zenon_H18d zenon_Hb6 zenon_H1b7 zenon_He0 zenon_H68 zenon_H48 zenon_H9e zenon_Ha0 zenon_H19a zenon_H77 zenon_H7e zenon_H18a. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.88/22.00 apply (zenon_L180_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.88/22.00 exact (zenon_H1ba zenon_H6d). % 21.88/22.00 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.88/22.00 exact (zenon_H8b zenon_H8a). % 21.88/22.00 apply (zenon_L725_); trivial. % 21.88/22.00 (* end of lemma zenon_L1073_ *) % 21.88/22.00 assert (zenon_L1074_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.88/22.00 do 0 intro. intros zenon_He2 zenon_H1d8 zenon_H2f zenon_H177 zenon_H31 zenon_H141 zenon_H109 zenon_Hf0 zenon_H13d zenon_H164 zenon_H2d zenon_H55 zenon_H16a zenon_H2c zenon_H67 zenon_H1ba zenon_H8b zenon_H18d zenon_Hb6 zenon_H1b7 zenon_H68 zenon_H48 zenon_H9e zenon_Ha0 zenon_H19a zenon_H77 zenon_H7e zenon_H18a. % 21.88/22.00 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.88/22.00 apply (zenon_L315_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.88/22.00 apply (zenon_L27_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.88/22.00 exact (zenon_H1ba zenon_H6d). % 21.88/22.00 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.88/22.00 exact (zenon_H8b zenon_H8a). % 21.88/22.00 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.88/22.00 apply (zenon_L1072_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.88/22.00 apply (zenon_L725_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.88/22.00 apply (zenon_L406_); trivial. % 21.88/22.00 apply (zenon_L547_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.88/22.00 apply (zenon_L702_); trivial. % 21.88/22.00 apply (zenon_L1073_); trivial. % 21.88/22.00 (* end of lemma zenon_L1074_ *) % 21.88/22.00 assert (zenon_L1075_ : (((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) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.88/22.00 do 0 intro. intros zenon_H13a zenon_Ha9 zenon_H6f zenon_H1f1 zenon_H266 zenon_H16b zenon_He4 zenon_He2 zenon_H1d8 zenon_H2f zenon_H177 zenon_H31 zenon_H141 zenon_H109 zenon_Hf0 zenon_H13d zenon_H164 zenon_H2d zenon_H55 zenon_H16a zenon_H2c zenon_H67 zenon_H1ba zenon_H8b zenon_H18d zenon_Hb6 zenon_H1b7 zenon_H68 zenon_H48 zenon_Ha0 zenon_H19a zenon_H77 zenon_H7e zenon_H18a. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.00 apply (zenon_L701_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.00 apply (zenon_L705_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.00 apply (zenon_L68_); trivial. % 21.88/22.00 apply (zenon_L1074_); trivial. % 21.88/22.00 (* end of lemma zenon_L1075_ *) % 21.88/22.00 assert (zenon_L1076_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((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)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> False). % 21.88/22.00 do 0 intro. intros zenon_H266 zenon_H2d zenon_H55 zenon_H13e zenon_H191 zenon_H190 zenon_H13d zenon_H89 zenon_H1ba zenon_H6f zenon_Hdb. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_Hdd | zenon_intro zenon_H267 ]. % 21.88/22.00 apply (zenon_L702_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H53 | zenon_intro zenon_H268 ]. % 21.88/22.00 apply (zenon_L176_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H6d | zenon_intro zenon_H10d ]. % 21.88/22.00 exact (zenon_H1ba zenon_H6d). % 21.88/22.00 apply (zenon_L205_); trivial. % 21.88/22.00 (* end of lemma zenon_L1076_ *) % 21.88/22.00 assert (zenon_L1077_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (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 (e0) (e1)) = (op (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.88/22.00 do 0 intro. intros zenon_H13a zenon_Ha9 zenon_H191 zenon_H266 zenon_H190 zenon_H6f zenon_H1ef zenon_H13e zenon_He2 zenon_H1d8 zenon_H2f zenon_H177 zenon_H31 zenon_H141 zenon_H109 zenon_Hf0 zenon_H13d zenon_H164 zenon_H2d zenon_H55 zenon_H16a zenon_H2c zenon_H67 zenon_H1ba zenon_H8b zenon_H18d zenon_Hb6 zenon_H1b7 zenon_H68 zenon_H48 zenon_Ha0 zenon_H19a zenon_H77 zenon_H7e zenon_H18a. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.00 apply (zenon_L701_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.00 apply (zenon_L730_); trivial. % 21.88/22.00 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.00 apply (zenon_L68_); trivial. % 21.88/22.00 apply (zenon_L1074_); trivial. % 21.88/22.00 (* end of lemma zenon_L1077_ *) % 21.88/22.00 assert (zenon_L1078_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> False). % 21.88/22.01 do 0 intro. intros zenon_H3a zenon_H67 zenon_H31. % 21.88/22.01 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 21.88/22.01 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 21.88/22.01 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.88/22.01 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.88/22.01 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.88/22.01 apply (zenon_L921_); trivial. % 21.88/22.01 (* end of lemma zenon_L1078_ *) % 21.88/22.01 assert (zenon_L1079_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (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))))) -> (~((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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H6f zenon_H73 zenon_H13c zenon_H156 zenon_H117 zenon_H12e zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H1b4 zenon_H1d8 zenon_H271 zenon_H1bb zenon_H15d zenon_H196 zenon_H190 zenon_H129 zenon_H177 zenon_H7d zenon_H24e zenon_H5d zenon_Hb2 zenon_H121 zenon_H1f1 zenon_H1a8 zenon_H139 zenon_Ha9 zenon_H13a zenon_H173 zenon_H18a zenon_H186 zenon_Hf0 zenon_H2c zenon_H68 zenon_H67 zenon_H82 zenon_H13e zenon_H131 zenon_H1ef zenon_H48 zenon_H125 zenon_H1d5 zenon_H164 zenon_H104 zenon_Hfa zenon_H195 zenon_H163 zenon_Hb6 zenon_H18d zenon_H189 zenon_Ha0 zenon_H1b7 zenon_H19a zenon_H13f zenon_H94 zenon_H1a2 zenon_H1cb zenon_H26a zenon_H31 zenon_H26d zenon_H22d zenon_H179 zenon_H1cf zenon_H141 zenon_H55 zenon_H4e zenon_H5a zenon_H1fe zenon_H77 zenon_H8b zenon_H16a. % 21.88/22.01 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.88/22.01 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.88/22.01 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.88/22.01 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.88/22.01 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.88/22.01 apply (zenon_L813_); trivial. % 21.88/22.01 (* end of lemma zenon_L1079_ *) % 21.88/22.01 assert (zenon_L1080_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H61 zenon_H15d zenon_H77 zenon_H67 zenon_H192 zenon_H48 zenon_H31 zenon_Hf5. % 21.88/22.01 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.88/22.01 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.01 apply (zenon_L251_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.01 apply (zenon_L146_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.01 apply (zenon_L239_); trivial. % 21.88/22.01 apply (zenon_L192_); trivial. % 21.88/22.01 (* end of lemma zenon_L1080_ *) % 21.88/22.01 assert (zenon_L1081_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H13c zenon_Ha0 zenon_H25 zenon_H159 zenon_Ha9 zenon_H72 zenon_H9e zenon_Hf5. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.88/22.01 apply (zenon_L116_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.88/22.01 exact (zenon_H159 zenon_H10c). % 21.88/22.01 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.88/22.01 apply (zenon_L436_); trivial. % 21.88/22.01 apply (zenon_L262_); trivial. % 21.88/22.01 (* end of lemma zenon_L1081_ *) % 21.88/22.01 assert (zenon_L1082_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.88/22.01 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_H77 zenon_H87 zenon_H155 zenon_Hf5. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.01 exact (zenon_H7a zenon_H3c). % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.01 exact (zenon_H40 zenon_H3f). % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.01 apply (zenon_L343_); trivial. % 21.88/22.01 apply (zenon_L192_); trivial. % 21.88/22.01 (* end of lemma zenon_L1082_ *) % 21.88/22.01 assert (zenon_L1083_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 21.88/22.01 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_Hdb zenon_H40 zenon_H6d zenon_H77 zenon_H7d zenon_H7e. % 21.88/22.01 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.88/22.01 apply (zenon_L55_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.88/22.01 exact (zenon_H40 zenon_H3f). % 21.88/22.01 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.88/22.01 apply (zenon_L56_); trivial. % 21.88/22.01 apply (zenon_L31_); trivial. % 21.88/22.01 (* end of lemma zenon_L1083_ *) % 21.88/22.01 assert (zenon_L1084_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((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) (e3)) = (op (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) (e0)) = (e2)) -> (~((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 (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 21.88/22.01 do 0 intro. intros zenon_H13a zenon_H7d zenon_H77 zenon_H40 zenon_He4 zenon_Hb2 zenon_H196 zenon_H121 zenon_H179 zenon_H67 zenon_H177 zenon_H31 zenon_H48 zenon_H164 zenon_H104 zenon_H1b4 zenon_H6d zenon_Ha9 zenon_H117 zenon_Ha0 zenon_H2d zenon_Hb6 zenon_H7e. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.01 apply (zenon_L1083_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.01 apply (zenon_L68_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.01 apply (zenon_L719_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.01 apply (zenon_L67_); trivial. % 21.88/22.01 apply (zenon_L134_); trivial. % 21.88/22.01 (* end of lemma zenon_L1084_ *) % 21.88/22.01 assert (zenon_L1085_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 21.88/22.01 do 0 intro. intros zenon_H1a8 zenon_H77 zenon_H3d zenon_H1b3 zenon_Hdd zenon_H68 zenon_Ha9 zenon_Hac. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.88/22.01 apply (zenon_L214_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.88/22.01 exact (zenon_H1b3 zenon_Hef). % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.88/22.01 apply (zenon_L54_); trivial. % 21.88/22.01 apply (zenon_L371_); trivial. % 21.88/22.01 (* end of lemma zenon_L1085_ *) % 21.88/22.01 assert (zenon_L1086_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((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 (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (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) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((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 (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((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 (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H15c zenon_H68 zenon_H67 zenon_H15d zenon_H48 zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H31 zenon_H13c zenon_Hf5 zenon_H72 zenon_H13a zenon_H82 zenon_He4 zenon_H7d zenon_H6d zenon_Hb2 zenon_H121 zenon_H1b4 zenon_H104 zenon_H177 zenon_H164 zenon_H179 zenon_H196 zenon_H117 zenon_He2 zenon_H277 zenon_H201 zenon_H266 zenon_H20b zenon_H158 zenon_H13b zenon_H109 zenon_H1c3 zenon_H1c6 zenon_H33 zenon_H11a zenon_H192 zenon_H25e zenon_H20f zenon_H25b zenon_H212 zenon_H181 zenon_H73 zenon_H12e zenon_H270 zenon_Hcc zenon_Hbc zenon_H111 zenon_H271 zenon_H1bb zenon_H190 zenon_H129 zenon_H24e zenon_H5d zenon_H1f1 zenon_H173 zenon_H18a zenon_H125 zenon_H1d5 zenon_H195 zenon_H163 zenon_H18d zenon_H189 zenon_H1b7 zenon_H19a zenon_H13f zenon_H94 zenon_H1a2 zenon_H1cb zenon_H26a zenon_H22d zenon_H141 zenon_H55 zenon_H1fe zenon_H26d zenon_H1ef zenon_H131 zenon_H13e zenon_H24 zenon_H16a zenon_H8b zenon_Hf0 zenon_H1a8 zenon_H186 zenon_H1cd zenon_H1cf zenon_H2c zenon_H6f zenon_Hfa zenon_H4e zenon_H156 zenon_H139 zenon_H1d8 zenon_H1b3 zenon_H7a zenon_H40 zenon_H87 zenon_H77 zenon_Heb. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.88/22.01 apply (zenon_L344_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.01 apply (zenon_L20_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.01 apply (zenon_L251_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.01 apply (zenon_L55_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.01 apply (zenon_L68_); trivial. % 21.88/22.01 apply (zenon_L1081_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.01 apply (zenon_L239_); trivial. % 21.88/22.01 apply (zenon_L1082_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.01 apply (zenon_L251_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.01 exact (zenon_H7a zenon_H3c). % 21.88/22.01 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.01 apply (zenon_L217_); trivial. % 21.88/22.01 apply (zenon_L1084_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.01 apply (zenon_L251_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.01 apply (zenon_L251_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.01 exact (zenon_H7a zenon_H3c). % 21.88/22.01 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.01 apply (zenon_L55_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.01 apply (zenon_L68_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.01 exact (zenon_H7a zenon_H3c). % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.01 exact (zenon_H40 zenon_H3f). % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.01 apply (zenon_L1070_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.88/22.01 apply (zenon_L55_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.88/22.01 exact (zenon_H159 zenon_H10c). % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.88/22.01 apply (zenon_L289_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.88/22.01 apply (zenon_L359_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.88/22.01 apply (zenon_L1085_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.88/22.01 apply (zenon_L290_); trivial. % 21.88/22.01 apply (zenon_L209_); trivial. % 21.88/22.01 apply (zenon_L456_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.01 apply (zenon_L239_); trivial. % 21.88/22.01 apply (zenon_L1082_); trivial. % 21.88/22.01 (* end of lemma zenon_L1086_ *) % 21.88/22.01 assert (zenon_L1087_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 21.88/22.01 do 0 intro. intros zenon_He2 zenon_H1d8 zenon_H31 zenon_He3 zenon_H6d zenon_H68 zenon_H7d zenon_H34. % 21.88/22.01 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.88/22.01 apply (zenon_L254_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.88/22.01 exact (zenon_He3 zenon_He7). % 21.88/22.01 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.88/22.01 apply (zenon_L54_); trivial. % 21.88/22.01 apply (zenon_L802_); trivial. % 21.88/22.01 (* end of lemma zenon_L1087_ *) % 21.88/22.01 assert (zenon_L1088_ : ((~((op (e1) (e3)) = (e1)))\/(~((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))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((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))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (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)) = (op (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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H15c zenon_H156 zenon_H158 zenon_H68 zenon_H67 zenon_Heb zenon_H72 zenon_H77 zenon_H40 zenon_H48 zenon_H15d zenon_H13f zenon_H1d8 zenon_H183 zenon_H13a zenon_H33 zenon_H1cf zenon_H1cd zenon_H8b zenon_H186 zenon_H181 zenon_H1c3 zenon_H201 zenon_H196 zenon_H117 zenon_H100 zenon_H31 zenon_He3 zenon_H6d zenon_He4 zenon_He2 zenon_H179 zenon_H164 zenon_H177 zenon_H104 zenon_H1b4 zenon_H121 zenon_H7d zenon_H82 zenon_H4e zenon_Hb2 zenon_Ha9 zenon_Ha0 zenon_Hb6 zenon_H125 zenon_H1fe. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.01 apply (zenon_L20_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.01 apply (zenon_L60_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.01 apply (zenon_L346_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.01 apply (zenon_L346_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.01 apply (zenon_L58_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.01 apply (zenon_L68_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.01 apply (zenon_L66_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.01 apply (zenon_L67_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.88/22.01 apply (zenon_L70_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.88/22.01 apply (zenon_L56_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.88/22.01 apply (zenon_L404_); trivial. % 21.88/22.01 apply (zenon_L739_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.01 apply (zenon_L217_); trivial. % 21.88/22.01 apply (zenon_L1084_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.01 apply (zenon_L239_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.01 apply (zenon_L58_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.01 apply (zenon_L68_); trivial. % 21.88/22.01 apply (zenon_L115_); trivial. % 21.88/22.01 apply (zenon_L1087_); trivial. % 21.88/22.01 apply (zenon_L101_); trivial. % 21.88/22.01 (* end of lemma zenon_L1088_ *) % 21.88/22.01 assert (zenon_L1089_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H1a8 zenon_Ha9 zenon_Hdb zenon_H1b3 zenon_Hdd zenon_H68 zenon_H7f zenon_H77. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.88/22.01 apply (zenon_L110_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.88/22.01 exact (zenon_H1b3 zenon_Hef). % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.88/22.01 apply (zenon_L54_); trivial. % 21.88/22.01 apply (zenon_L169_); trivial. % 21.88/22.01 (* end of lemma zenon_L1089_ *) % 21.88/22.01 assert (zenon_L1090_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_H6d zenon_H14c zenon_Ha0 zenon_Ha5 zenon_H195. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.88/22.01 apply (zenon_L151_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.88/22.01 apply (zenon_L289_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.88/22.01 apply (zenon_L278_); trivial. % 21.88/22.01 apply (zenon_L172_); trivial. % 21.88/22.01 (* end of lemma zenon_L1090_ *) % 21.88/22.01 assert (zenon_L1091_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (((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))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((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 (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> False). % 21.88/22.01 do 0 intro. intros zenon_He4 zenon_H40 zenon_H55 zenon_H181 zenon_H68 zenon_Ha9 zenon_Ha5 zenon_H155 zenon_H1c3 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha0 zenon_H195 zenon_H1a8 zenon_Hdb zenon_H1b3 zenon_H109 zenon_H34 zenon_H141 zenon_H77. % 21.88/22.01 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.88/22.01 apply (zenon_L55_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.88/22.01 exact (zenon_H40 zenon_H3f). % 21.88/22.01 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.88/22.01 apply (zenon_L15_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.88/22.01 apply (zenon_L110_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.88/22.01 exact (zenon_H1b3 zenon_Hef). % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.88/22.01 apply (zenon_L359_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.88/22.01 apply (zenon_L1089_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.88/22.01 apply (zenon_L1090_); trivial. % 21.88/22.01 apply (zenon_L930_); trivial. % 21.88/22.01 apply (zenon_L169_); trivial. % 21.88/22.01 (* end of lemma zenon_L1091_ *) % 21.88/22.01 assert (zenon_L1092_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (((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 (e1) (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) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H15d zenon_Hf5 zenon_H82 zenon_H139 zenon_H7a zenon_Hb6 zenon_H31 zenon_Ha0 zenon_He4 zenon_H40 zenon_H55 zenon_H181 zenon_H68 zenon_Ha9 zenon_Ha5 zenon_H1c3 zenon_H117 zenon_H195 zenon_H1a8 zenon_H1b3 zenon_H109 zenon_H141 zenon_H77 zenon_H67 zenon_H13a zenon_H34 zenon_H48. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.01 apply (zenon_L251_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.01 apply (zenon_L732_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.01 apply (zenon_L239_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.01 apply (zenon_L744_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.01 exact (zenon_H7a zenon_H3c). % 21.88/22.01 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.01 apply (zenon_L1091_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.01 apply (zenon_L68_); trivial. % 21.88/22.01 apply (zenon_L115_); trivial. % 21.88/22.01 apply (zenon_L456_); trivial. % 21.88/22.01 (* end of lemma zenon_L1092_ *) % 21.88/22.01 assert (zenon_L1093_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (((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 (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (((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 (e1) (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) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H1fe zenon_Hb1 zenon_H177 zenon_Hac zenon_H164 zenon_Hb2 zenon_H5d zenon_H7d zenon_H15d zenon_Hf5 zenon_H82 zenon_H139 zenon_H7a zenon_Hb6 zenon_H31 zenon_Ha0 zenon_He4 zenon_H40 zenon_H55 zenon_H181 zenon_H68 zenon_Ha9 zenon_Ha5 zenon_H1c3 zenon_H117 zenon_H195 zenon_H1a8 zenon_H1b3 zenon_H109 zenon_H141 zenon_H77 zenon_H67 zenon_H13a zenon_H48. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.01 apply (zenon_L20_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.01 apply (zenon_L251_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.01 apply (zenon_L732_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.01 apply (zenon_L239_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.01 apply (zenon_L744_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.01 exact (zenon_H7a zenon_H3c). % 21.88/22.01 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.01 apply (zenon_L116_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.01 apply (zenon_L151_); trivial. % 21.88/22.01 apply (zenon_L221_); trivial. % 21.88/22.01 apply (zenon_L718_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.01 apply (zenon_L924_); trivial. % 21.88/22.01 apply (zenon_L1092_); trivial. % 21.88/22.01 (* end of lemma zenon_L1093_ *) % 21.88/22.01 assert (zenon_L1094_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.88/22.01 do 0 intro. intros zenon_Hb2 zenon_Ha9 zenon_H67 zenon_Ha0 zenon_H25 zenon_H94 zenon_Hb9 zenon_Hbb zenon_Hbc. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.01 apply (zenon_L116_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.01 apply (zenon_L47_); trivial. % 21.88/22.01 apply (zenon_L48_); trivial. % 21.88/22.01 (* end of lemma zenon_L1094_ *) % 21.88/22.01 assert (zenon_L1095_ : (((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 (e2) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (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))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H13a zenon_Ha9 zenon_H67 zenon_H6f zenon_H1ba zenon_H1f1 zenon_H55 zenon_H2d zenon_H266 zenon_H16a zenon_H68 zenon_H77 zenon_H8b zenon_H16b zenon_Hf0 zenon_Hb6 zenon_He4 zenon_Ha0 zenon_H31 zenon_Hb9 zenon_H196. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.01 apply (zenon_L705_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.01 apply (zenon_L68_); trivial. % 21.88/22.01 apply (zenon_L154_); trivial. % 21.88/22.01 (* end of lemma zenon_L1095_ *) % 21.88/22.01 assert (zenon_L1096_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H13a zenon_Ha9 zenon_H67 zenon_Hb6 zenon_H3d zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.01 apply (zenon_L55_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.01 apply (zenon_L178_); trivial. % 21.88/22.01 apply (zenon_L154_); trivial. % 21.88/22.01 (* end of lemma zenon_L1096_ *) % 21.88/22.01 assert (zenon_L1097_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.88/22.01 do 0 intro. intros zenon_Hb2 zenon_Ha9 zenon_H67 zenon_Hb6 zenon_H3c zenon_H94 zenon_Hb9 zenon_Hbb zenon_Hbc. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.01 apply (zenon_L46_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.01 apply (zenon_L47_); trivial. % 21.88/22.01 apply (zenon_L48_); trivial. % 21.88/22.01 (* end of lemma zenon_L1097_ *) % 21.88/22.01 assert (zenon_L1098_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H12e zenon_H48 zenon_H34 zenon_H3f zenon_H11a zenon_Hbb zenon_Hb6 zenon_H155 zenon_H1b4. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.88/22.01 apply (zenon_L456_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.88/22.01 apply (zenon_L552_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.88/22.01 apply (zenon_L363_); trivial. % 21.88/22.01 apply (zenon_L187_); trivial. % 21.88/22.01 (* end of lemma zenon_L1098_ *) % 21.88/22.01 assert (zenon_L1099_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H15d zenon_H77 zenon_H196 zenon_Hb9 zenon_Hbb zenon_H177 zenon_H48 zenon_H13a zenon_Ha9 zenon_H67 zenon_H191 zenon_H8b zenon_H266 zenon_H2d zenon_H55 zenon_H190 zenon_H1ba zenon_H6f zenon_H1ef zenon_H13e zenon_Ha0 zenon_H31 zenon_Hb6. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.01 apply (zenon_L251_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.01 apply (zenon_L1096_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.01 apply (zenon_L239_); trivial. % 21.88/22.01 apply (zenon_L737_); trivial. % 21.88/22.01 (* end of lemma zenon_L1099_ *) % 21.88/22.01 assert (zenon_L1100_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (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 (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (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) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (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)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (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 (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.88/22.01 do 0 intro. intros zenon_H15d zenon_H196 zenon_H82 zenon_Hb6 zenon_Hbb zenon_H177 zenon_Hb2 zenon_Ha9 zenon_H67 zenon_Hf5 zenon_He4 zenon_H156 zenon_H55 zenon_H1bb zenon_H18a zenon_H1b7 zenon_H1cf zenon_H77 zenon_H68 zenon_H271 zenon_H1d8 zenon_H139 zenon_H1b4 zenon_H111 zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_Ha0 zenon_H31 zenon_H191 zenon_H1cb zenon_H12e zenon_H11a zenon_Heb zenon_H94 zenon_Hb9 zenon_Hbc zenon_H13a zenon_H34 zenon_H48. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.01 apply (zenon_L251_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.01 apply (zenon_L1096_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.01 apply (zenon_L239_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.01 apply (zenon_L744_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.01 apply (zenon_L1097_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.01 apply (zenon_L701_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.01 apply (zenon_L46_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.01 apply (zenon_L1098_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.01 apply (zenon_L972_); trivial. % 21.88/22.01 apply (zenon_L192_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.01 apply (zenon_L47_); trivial. % 21.88/22.01 apply (zenon_L48_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.01 apply (zenon_L178_); trivial. % 21.88/22.01 apply (zenon_L115_); trivial. % 21.88/22.01 apply (zenon_L456_); trivial. % 21.88/22.01 (* end of lemma zenon_L1100_ *) % 21.88/22.01 assert (zenon_L1101_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e1)) -> False). % 21.88/22.01 do 0 intro. intros zenon_H117 zenon_Ha0 zenon_H2d zenon_Ha9 zenon_H6d zenon_H104 zenon_Hbb zenon_Hb6 zenon_H128. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.88/22.01 apply (zenon_L67_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.88/22.01 apply (zenon_L289_); trivial. % 21.88/22.01 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.88/22.01 apply (zenon_L129_); trivial. % 21.88/22.01 apply (zenon_L182_); trivial. % 21.88/22.01 (* end of lemma zenon_L1101_ *) % 21.88/22.01 assert (zenon_L1102_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H16a zenon_H7b zenon_H128 zenon_Hb6 zenon_Hbb zenon_H104 zenon_Ha9 zenon_H2d zenon_Ha0 zenon_H117 zenon_H8b zenon_H16b. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.88/22.02 exact (zenon_H7b zenon_H65). % 21.88/22.02 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.88/22.02 apply (zenon_L1101_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.88/22.02 exact (zenon_H8b zenon_H8a). % 21.88/22.02 exact (zenon_H16b zenon_H93). % 21.88/22.02 (* end of lemma zenon_L1102_ *) % 21.88/22.02 assert (zenon_L1103_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((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)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H92 zenon_H1ef zenon_H13e zenon_H48 zenon_H2d zenon_H16a zenon_H8b zenon_H77 zenon_H68 zenon_H1bf zenon_Ha0 zenon_Ha9 zenon_H104 zenon_Hbb zenon_Hb6 zenon_H117 zenon_H7b zenon_H13f. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.88/22.02 apply (zenon_L217_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.88/22.02 apply (zenon_L327_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.88/22.02 exact (zenon_H1bf zenon_H105). % 21.88/22.02 apply (zenon_L1102_); trivial. % 21.88/22.02 apply (zenon_L644_); trivial. % 21.88/22.02 (* end of lemma zenon_L1103_ *) % 21.88/22.02 assert (zenon_L1104_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 21.88/22.02 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H13d zenon_Ha0 zenon_Hb9. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.88/22.02 apply (zenon_L359_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.88/22.02 apply (zenon_L929_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.88/22.02 exact (zenon_H13d zenon_H14c). % 21.88/22.02 apply (zenon_L77_); trivial. % 21.88/22.02 (* end of lemma zenon_L1104_ *) % 21.88/22.02 assert (zenon_L1105_ : (((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 (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (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 (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_Heb zenon_H54 zenon_H100 zenon_H1b4 zenon_Hb6 zenon_Hbb zenon_H11a zenon_H34 zenon_H12e zenon_Hf3 zenon_H48 zenon_H155 zenon_Hf5. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.02 apply (zenon_L69_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.02 apply (zenon_L1098_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.02 apply (zenon_L117_); trivial. % 21.88/22.02 apply (zenon_L192_); trivial. % 21.88/22.02 (* end of lemma zenon_L1105_ *) % 21.88/22.02 assert (zenon_L1106_ : (((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)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((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) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((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 (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((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)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 21.88/22.02 do 0 intro. intros zenon_Heb zenon_H54 zenon_H100 zenon_H155 zenon_H34 zenon_H91 zenon_H89 zenon_H20b zenon_H266 zenon_H6f zenon_H201 zenon_H1c3 zenon_H1c6 zenon_H33 zenon_H11a zenon_H1f1 zenon_H121 zenon_Hb2 zenon_H5d zenon_H24e zenon_H190 zenon_H277 zenon_H1fe zenon_H13b zenon_H109 zenon_H18a zenon_H1b7 zenon_H163 zenon_H4e zenon_H131 zenon_H13f zenon_H13a zenon_H196 zenon_Hbb zenon_H177 zenon_Ha0 zenon_H173 zenon_H195 zenon_Hb9 zenon_H13c zenon_Hb6 zenon_Hfa zenon_H1cd zenon_H1a8 zenon_H8b zenon_H164 zenon_H16a zenon_H129 zenon_H7d zenon_He4 zenon_H186 zenon_H19a zenon_Hc0 zenon_H1bb zenon_H31 zenon_H12e zenon_H25b zenon_H20f zenon_Hf5 zenon_H1b4 zenon_H25e zenon_H77 zenon_H192 zenon_H1cf zenon_H212 zenon_Hbc zenon_H179 zenon_H156 zenon_H1d5 zenon_H73 zenon_H82 zenon_H24 zenon_H141 zenon_H1cb zenon_H117 zenon_Ha9 zenon_H26d zenon_Hf0 zenon_H139 zenon_H2c zenon_H15d zenon_H67 zenon_H68 zenon_He2 zenon_H13e zenon_H1ef zenon_H125 zenon_H104 zenon_H55 zenon_H18d zenon_H189 zenon_H94 zenon_H26a zenon_H22d zenon_H1a2 zenon_H271 zenon_H1d8 zenon_H111 zenon_Hcc zenon_H270 zenon_H92 zenon_H8f zenon_H48 zenon_H136. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.02 apply (zenon_L69_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.02 apply (zenon_L1098_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.02 apply (zenon_L1069_); trivial. % 21.88/22.02 apply (zenon_L157_); trivial. % 21.88/22.02 (* end of lemma zenon_L1106_ *) % 21.88/22.02 assert (zenon_L1107_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (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) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (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 (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_He4 zenon_Hdb zenon_H156 zenon_Hdd zenon_H48 zenon_H1bb zenon_H18a zenon_H34 zenon_H1b7 zenon_H1cf zenon_H77 zenon_H68 zenon_H271 zenon_H1d8 zenon_H139 zenon_H1b4 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H4d zenon_H191 zenon_H1cb. % 21.88/22.02 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.88/22.02 apply (zenon_L55_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.88/22.02 apply (zenon_L486_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.88/22.02 apply (zenon_L111_); trivial. % 21.88/22.02 apply (zenon_L794_); trivial. % 21.88/22.02 (* end of lemma zenon_L1107_ *) % 21.88/22.02 assert (zenon_L1108_ : ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (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 (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (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) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((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))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((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) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((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)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (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) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H8f zenon_H22d zenon_H26a zenon_H189 zenon_H18d zenon_H125 zenon_He2 zenon_H277 zenon_H24e zenon_H5d zenon_H121 zenon_H33 zenon_H1c6 zenon_H1c3 zenon_H20b zenon_H100 zenon_H92 zenon_H13e zenon_H190 zenon_H1ef zenon_H1a2 zenon_H271 zenon_H1d8 zenon_H111 zenon_Hcc zenon_H270 zenon_H68 zenon_H67 zenon_Hb2 zenon_Hbb zenon_Hbc zenon_Hb9 zenon_H94 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H196 zenon_H31 zenon_Hb6 zenon_H266 zenon_H6f zenon_Hf0 zenon_H55 zenon_H16a zenon_H8b zenon_H77 zenon_H1f1 zenon_He4 zenon_H139 zenon_H12e zenon_H1b4 zenon_H11a zenon_H1fe zenon_H13b zenon_H109 zenon_H18a zenon_H1b7 zenon_H163 zenon_H4e zenon_H131 zenon_H13f zenon_H173 zenon_H195 zenon_H13c zenon_Hfa zenon_H1cd zenon_H1a8 zenon_H164 zenon_H129 zenon_H7d zenon_H186 zenon_H19a zenon_Hc0 zenon_H1bb zenon_H25b zenon_H20f zenon_Hf5 zenon_H25e zenon_H192 zenon_H1cf zenon_H212 zenon_H179 zenon_H156 zenon_H1d5 zenon_H73 zenon_H82 zenon_H24 zenon_H141 zenon_H1cb zenon_H117 zenon_H26d zenon_H2c zenon_H15d zenon_Heb zenon_H48 zenon_H177 zenon_H89 zenon_H104 zenon_H201 zenon_H91. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.02 apply (zenon_L20_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.02 apply (zenon_L1094_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.02 apply (zenon_L1095_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.02 apply (zenon_L251_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.02 apply (zenon_L1096_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.02 apply (zenon_L239_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.02 apply (zenon_L744_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.02 apply (zenon_L1097_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.02 apply (zenon_L701_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.02 apply (zenon_L46_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.02 apply (zenon_L1098_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.02 apply (zenon_L954_); trivial. % 21.88/22.02 apply (zenon_L192_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.02 apply (zenon_L151_); trivial. % 21.88/22.02 apply (zenon_L201_); trivial. % 21.88/22.02 apply (zenon_L456_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.02 apply (zenon_L20_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.02 apply (zenon_L1094_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.02 apply (zenon_L1099_); trivial. % 21.88/22.02 apply (zenon_L1100_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.02 apply (zenon_L20_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.02 apply (zenon_L1094_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.02 apply (zenon_L1103_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.02 apply (zenon_L701_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.02 apply (zenon_L1059_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.02 apply (zenon_L68_); trivial. % 21.88/22.02 apply (zenon_L154_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.02 apply (zenon_L20_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.02 apply (zenon_L1094_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.02 apply (zenon_L645_); trivial. % 21.88/22.02 apply (zenon_L1100_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.02 apply (zenon_L20_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.02 apply (zenon_L1094_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.02 apply (zenon_L1095_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.02 apply (zenon_L251_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.02 apply (zenon_L1096_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.02 apply (zenon_L239_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.02 apply (zenon_L744_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.02 apply (zenon_L1097_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.88/22.02 apply (zenon_L297_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.88/22.02 apply (zenon_L1104_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.88/22.02 apply (zenon_L1105_); trivial. % 21.88/22.02 apply (zenon_L1106_); trivial. % 21.88/22.02 apply (zenon_L456_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.02 apply (zenon_L20_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.02 apply (zenon_L1094_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.02 apply (zenon_L1099_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.02 apply (zenon_L251_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.02 apply (zenon_L1096_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.02 apply (zenon_L239_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.02 apply (zenon_L744_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.02 apply (zenon_L1097_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.02 apply (zenon_L701_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.02 apply (zenon_L701_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.88/22.02 apply (zenon_L297_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.88/22.02 apply (zenon_L1104_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.88/22.02 apply (zenon_L1105_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.88/22.02 apply (zenon_L53_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.88/22.02 apply (zenon_L1104_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.02 apply (zenon_L46_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.02 apply (zenon_L1098_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.02 apply (zenon_L1107_); trivial. % 21.88/22.02 apply (zenon_L157_); trivial. % 21.88/22.02 apply (zenon_L802_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.02 apply (zenon_L47_); trivial. % 21.88/22.02 apply (zenon_L201_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.02 apply (zenon_L178_); trivial. % 21.88/22.02 apply (zenon_L115_); trivial. % 21.88/22.02 apply (zenon_L456_); trivial. % 21.88/22.02 apply (zenon_L196_); trivial. % 21.88/22.02 (* end of lemma zenon_L1108_ *) % 21.88/22.02 assert (zenon_L1109_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_Hb2 zenon_Ha9 zenon_H67 zenon_Hb6 zenon_H3c zenon_Ha0 zenon_H2d zenon_Hbb zenon_Hbc. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.02 apply (zenon_L701_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.02 apply (zenon_L46_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.02 apply (zenon_L67_); trivial. % 21.88/22.02 apply (zenon_L48_); trivial. % 21.88/22.02 (* end of lemma zenon_L1109_ *) % 21.88/22.02 assert (zenon_L1110_ : (((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) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H13a zenon_Ha9 zenon_H6f zenon_H1f1 zenon_H266 zenon_H16b zenon_He4 zenon_Hbb zenon_He2 zenon_H1d8 zenon_H2f zenon_H177 zenon_H31 zenon_H141 zenon_H109 zenon_Hf0 zenon_H13d zenon_H164 zenon_H2d zenon_H55 zenon_H16a zenon_H2c zenon_H67 zenon_H1ba zenon_H8b zenon_H18d zenon_Hb6 zenon_H1b7 zenon_H68 zenon_H48 zenon_Ha0 zenon_H19a zenon_H77 zenon_H7e zenon_H18a. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.02 apply (zenon_L701_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.02 apply (zenon_L705_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.02 apply (zenon_L178_); trivial. % 21.88/22.02 apply (zenon_L1074_); trivial. % 21.88/22.02 (* end of lemma zenon_L1110_ *) % 21.88/22.02 assert (zenon_L1111_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_Ha9 zenon_H6d zenon_Hbb zenon_H1cd. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.88/22.02 apply (zenon_L55_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.88/22.02 exact (zenon_H159 zenon_H10c). % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.88/22.02 apply (zenon_L289_); trivial. % 21.88/22.02 apply (zenon_L360_); trivial. % 21.88/22.02 (* end of lemma zenon_L1111_ *) % 21.88/22.02 assert (zenon_L1112_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H15c zenon_H67 zenon_H1c6 zenon_Hbb zenon_H1cd zenon_H6d zenon_Ha9 zenon_Hb6 zenon_H48 zenon_H31 zenon_Hf5 zenon_H15d zenon_H7a zenon_H40 zenon_H87 zenon_H77 zenon_Heb. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.88/22.02 apply (zenon_L344_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.02 apply (zenon_L251_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.02 apply (zenon_L1111_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.02 apply (zenon_L239_); trivial. % 21.88/22.02 apply (zenon_L1082_); trivial. % 21.88/22.02 (* end of lemma zenon_L1112_ *) % 21.88/22.02 assert (zenon_L1113_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H158 zenon_He3 zenon_H40 zenon_H1b3 zenon_H159. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 21.88/22.02 exact (zenon_He3 zenon_He7). % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 21.88/22.02 exact (zenon_H40 zenon_H3f). % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 21.88/22.02 exact (zenon_H1b3 zenon_Hef). % 21.88/22.02 exact (zenon_H159 zenon_H10c). % 21.88/22.02 (* end of lemma zenon_L1113_ *) % 21.88/22.02 assert (zenon_L1114_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((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)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H15c zenon_H1b3 zenon_H158 zenon_H68 zenon_H67 zenon_Heb zenon_H72 zenon_H77 zenon_H40 zenon_H48 zenon_Hb2 zenon_Hbb zenon_Hbc zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_He2 zenon_H7d zenon_H6d zenon_He3 zenon_H31 zenon_H1d8 zenon_H1fe. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.02 apply (zenon_L20_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.02 apply (zenon_L60_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.88/22.02 apply (zenon_L701_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.88/22.02 apply (zenon_L66_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.88/22.02 apply (zenon_L67_); trivial. % 21.88/22.02 apply (zenon_L48_); trivial. % 21.88/22.02 apply (zenon_L1087_); trivial. % 21.88/22.02 apply (zenon_L1113_); trivial. % 21.88/22.02 (* end of lemma zenon_L1114_ *) % 21.88/22.02 assert (zenon_L1115_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H1a8 zenon_H77 zenon_H3d zenon_H1b3 zenon_H189 zenon_H93 zenon_H160 zenon_H1cd. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.88/22.02 apply (zenon_L214_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.88/22.02 exact (zenon_H1b3 zenon_Hef). % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.88/22.02 apply (zenon_L439_); trivial. % 21.88/22.02 apply (zenon_L240_); trivial. % 21.88/22.02 (* end of lemma zenon_L1115_ *) % 21.88/22.02 assert (zenon_L1116_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H15d zenon_H67 zenon_H93 zenon_H189 zenon_H1b3 zenon_H77 zenon_H1a8 zenon_H48 zenon_H31 zenon_H1bb zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.02 apply (zenon_L251_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.02 apply (zenon_L1115_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.02 apply (zenon_L239_); trivial. % 21.88/22.02 apply (zenon_L816_); trivial. % 21.88/22.02 (* end of lemma zenon_L1116_ *) % 21.88/22.02 assert (zenon_L1117_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H25 zenon_H1b3 zenon_H160 zenon_H163 zenon_H93 zenon_H195. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.88/22.02 apply (zenon_L171_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.88/22.02 exact (zenon_H1b3 zenon_Hef). % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.88/22.02 apply (zenon_L227_); trivial. % 21.88/22.02 apply (zenon_L228_); trivial. % 21.88/22.02 (* end of lemma zenon_L1117_ *) % 21.88/22.02 assert (zenon_L1118_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_Hfa zenon_H77 zenon_H3c zenon_H1b3 zenon_H160 zenon_H163 zenon_H93 zenon_H195. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.88/22.02 apply (zenon_L24_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.88/22.02 exact (zenon_H1b3 zenon_Hef). % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.88/22.02 apply (zenon_L227_); trivial. % 21.88/22.02 apply (zenon_L228_); trivial. % 21.88/22.02 (* end of lemma zenon_L1118_ *) % 21.88/22.02 assert (zenon_L1119_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (((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) (e3)) = (e3))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H82 zenon_H196 zenon_H177 zenon_H3d zenon_H139 zenon_H195 zenon_H93 zenon_H163 zenon_H160 zenon_H1b3 zenon_H77 zenon_Hfa zenon_H48 zenon_H2d zenon_H1bb zenon_H162 zenon_H18a zenon_H181 zenon_Hc4. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.02 apply (zenon_L818_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.02 apply (zenon_L1118_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.02 apply (zenon_L217_); trivial. % 21.88/22.02 apply (zenon_L211_); trivial. % 21.88/22.02 (* end of lemma zenon_L1119_ *) % 21.88/22.02 assert (zenon_L1120_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H1fe zenon_H26d zenon_H18a zenon_H48 zenon_Hfa zenon_H77 zenon_H1b3 zenon_H163 zenon_H93 zenon_H195 zenon_H139 zenon_Hb6 zenon_Hbb zenon_Ha9 zenon_H13a zenon_H177 zenon_H196 zenon_H82 zenon_H31 zenon_Ha0 zenon_H19a zenon_Hbc zenon_H212 zenon_H18d zenon_H33 zenon_H12e zenon_H68 zenon_H109 zenon_H164 zenon_H15d zenon_H1bb zenon_H162 zenon_H1c7 zenon_H160 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H181 zenon_Hc4. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.02 apply (zenon_L877_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.02 apply (zenon_L1117_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.02 apply (zenon_L891_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.02 apply (zenon_L1119_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.02 apply (zenon_L239_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.02 apply (zenon_L850_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.02 apply (zenon_L1118_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.02 apply (zenon_L217_); trivial. % 21.88/22.02 apply (zenon_L211_); trivial. % 21.88/22.02 apply (zenon_L870_); trivial. % 21.88/22.02 (* end of lemma zenon_L1120_ *) % 21.88/22.02 assert (zenon_L1121_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> ((op (e3) (e2)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((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 (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_Hca zenon_Hbb zenon_Hc2 zenon_H139 zenon_H196 zenon_H26d zenon_H31 zenon_H164 zenon_H177 zenon_H18a zenon_H18d zenon_H93 zenon_H77 zenon_H48 zenon_Hbc zenon_H13a zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H33 zenon_H212 zenon_H12e zenon_H162 zenon_H24e zenon_H160 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H1bb zenon_H19a zenon_H68 zenon_Hfa zenon_H195 zenon_H163 zenon_H1b3 zenon_H15d zenon_H82 zenon_H109 zenon_H1fe zenon_Hcb. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.88/22.02 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.88/22.02 apply (zenon_L1120_); trivial. % 21.88/22.02 apply (zenon_L1120_); trivial. % 21.88/22.02 apply (zenon_L895_); trivial. % 21.88/22.02 (* end of lemma zenon_L1121_ *) % 21.88/22.02 assert (zenon_L1122_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.88/22.02 do 0 intro. intros zenon_Hfa zenon_H77 zenon_H3c zenon_H1b3 zenon_H8a zenon_H131 zenon_Hf5 zenon_Hf6. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.88/22.02 apply (zenon_L24_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.88/22.02 exact (zenon_H1b3 zenon_Hef). % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.88/22.02 apply (zenon_L87_); trivial. % 21.88/22.02 apply (zenon_L63_); trivial. % 21.88/22.02 (* end of lemma zenon_L1122_ *) % 21.88/22.02 assert (zenon_L1123_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H139 zenon_H6c zenon_H3d zenon_H68 zenon_H31 zenon_Hfa zenon_H77 zenon_H3c zenon_H1b3 zenon_H8a zenon_H131 zenon_Hf5. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.02 exact (zenon_H6c zenon_H67). % 21.88/22.02 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.02 apply (zenon_L214_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.02 apply (zenon_L264_); trivial. % 21.88/22.02 apply (zenon_L1122_); trivial. % 21.88/22.02 (* end of lemma zenon_L1123_ *) % 21.88/22.02 assert (zenon_L1124_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H1c3 zenon_H9e zenon_Ha9 zenon_H77 zenon_H5c zenon_H8a zenon_H1c2 zenon_H181. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.88/22.02 apply (zenon_L92_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.88/22.02 apply (zenon_L206_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.88/22.02 apply (zenon_L207_); trivial. % 21.88/22.02 exact (zenon_H181 zenon_H17c). % 21.88/22.02 (* end of lemma zenon_L1124_ *) % 21.88/22.02 assert (zenon_L1125_ : (((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)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_H6e zenon_Ha0 zenon_H31 zenon_H1c3 zenon_Ha9 zenon_H77 zenon_H5c zenon_H8a zenon_H1c2 zenon_H181. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.02 apply (zenon_L253_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.02 apply (zenon_L110_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.02 apply (zenon_L68_); trivial. % 21.88/22.02 apply (zenon_L1124_); trivial. % 21.88/22.02 (* end of lemma zenon_L1125_ *) % 21.88/22.02 assert (zenon_L1126_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H1a8 zenon_Ha9 zenon_Hdb zenon_H1b3 zenon_H190 zenon_H8a zenon_H7f zenon_H77. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.88/22.02 apply (zenon_L110_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.88/22.02 exact (zenon_H1b3 zenon_Hef). % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.88/22.02 apply (zenon_L366_); trivial. % 21.88/22.02 apply (zenon_L169_); trivial. % 21.88/22.02 (* end of lemma zenon_L1126_ *) % 21.88/22.02 assert (zenon_L1127_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e0) = (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 (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H15d zenon_Ha9 zenon_Ha0 zenon_H1a8 zenon_H1b3 zenon_H190 zenon_H8a zenon_H77 zenon_Hb6 zenon_H13a zenon_H111 zenon_H1c3 zenon_H1c2 zenon_H181 zenon_H139 zenon_H7f zenon_H192 zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.02 apply (zenon_L251_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.02 apply (zenon_L1125_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.02 apply (zenon_L258_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.02 apply (zenon_L253_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.02 apply (zenon_L1126_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.02 apply (zenon_L68_); trivial. % 21.88/22.02 apply (zenon_L92_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.02 apply (zenon_L146_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.02 apply (zenon_L239_); trivial. % 21.88/22.02 apply (zenon_L192_); trivial. % 21.88/22.02 (* end of lemma zenon_L1127_ *) % 21.88/22.02 assert (zenon_L1128_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 21.88/22.02 do 0 intro. intros zenon_H192 zenon_H6e zenon_H171. % 21.88/22.02 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 21.88/22.02 intro zenon_D_pnotp. % 21.88/22.02 apply zenon_H192. % 21.88/22.02 rewrite <- zenon_D_pnotp. % 21.88/22.02 exact zenon_H6e. % 21.88/22.02 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 21.88/22.02 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 21.88/22.02 congruence. % 21.88/22.02 apply zenon_H193. apply refl_equal. % 21.88/22.02 apply zenon_H172. apply sym_equal. exact zenon_H171. % 21.88/22.02 (* end of lemma zenon_L1128_ *) % 21.88/22.02 assert (zenon_L1129_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H183 zenon_H9d zenon_Ha9 zenon_H6e zenon_H192 zenon_H8a zenon_H104 zenon_H181. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.88/22.02 apply (zenon_L91_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.88/22.02 apply (zenon_L1128_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.88/22.02 apply (zenon_L231_); trivial. % 21.88/22.02 exact (zenon_H181 zenon_H17c). % 21.88/22.02 (* end of lemma zenon_L1129_ *) % 21.88/22.02 assert (zenon_L1130_ : (((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)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 21.88/22.02 do 0 intro. intros zenon_H139 zenon_H6c zenon_H181 zenon_H104 zenon_H192 zenon_H9d zenon_H183 zenon_H8a zenon_H111 zenon_Ha9 zenon_H9e. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.02 exact (zenon_H6c zenon_H67). % 21.88/22.02 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.02 apply (zenon_L1129_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.02 apply (zenon_L258_); trivial. % 21.88/22.02 apply (zenon_L92_); trivial. % 21.88/22.02 (* end of lemma zenon_L1130_ *) % 21.88/22.02 assert (zenon_L1131_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (~((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) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.88/22.02 do 0 intro. intros zenon_H13a zenon_H192 zenon_H102 zenon_H77 zenon_H12e zenon_Hb6 zenon_H3d zenon_H177 zenon_Hbb zenon_Ha9 zenon_Hf6. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.88/22.02 apply (zenon_L71_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.88/22.02 apply (zenon_L146_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.88/22.02 apply (zenon_L363_); trivial. % 21.88/22.02 apply (zenon_L673_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.02 apply (zenon_L55_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.02 apply (zenon_L178_); trivial. % 21.88/22.02 apply (zenon_L92_); trivial. % 21.88/22.02 (* end of lemma zenon_L1131_ *) % 21.88/22.02 assert (zenon_L1132_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H125 zenon_H6c zenon_H77 zenon_H3c zenon_H1ef zenon_H8a zenon_H34 zenon_H68. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.88/22.02 exact (zenon_H6c zenon_H67). % 21.88/22.02 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.88/22.02 apply (zenon_L24_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.88/22.02 apply (zenon_L533_); trivial. % 21.88/22.02 apply (zenon_L291_); trivial. % 21.88/22.02 (* end of lemma zenon_L1132_ *) % 21.88/22.02 assert (zenon_L1133_ : (((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 (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H1fe zenon_H1f zenon_H48 zenon_Ha9 zenon_Hbb zenon_H177 zenon_H3d zenon_Hb6 zenon_H12e zenon_H192 zenon_H13a zenon_H111 zenon_H139 zenon_H125 zenon_H6c zenon_H77 zenon_H3c zenon_H1ef zenon_H8a zenon_H68. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.02 exact (zenon_H1f zenon_H1e). % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.02 apply (zenon_L25_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.02 exact (zenon_H6c zenon_H67). % 21.88/22.02 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.02 apply (zenon_L214_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.02 apply (zenon_L258_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.88/22.02 exact (zenon_H6c zenon_H67). % 21.88/22.02 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.88/22.02 apply (zenon_L24_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.88/22.02 apply (zenon_L27_); trivial. % 21.88/22.02 apply (zenon_L1131_); trivial. % 21.88/22.02 apply (zenon_L1132_); trivial. % 21.88/22.02 (* end of lemma zenon_L1133_ *) % 21.88/22.02 assert (zenon_L1134_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> False). % 21.88/22.02 do 0 intro. intros zenon_H240 zenon_H1f zenon_H48 zenon_H3c zenon_H139 zenon_H68 zenon_H13a zenon_Ha9 zenon_H177 zenon_H192 zenon_Hb6 zenon_Hbb zenon_H12e zenon_H125 zenon_H8a zenon_H111 zenon_H3d zenon_H77 zenon_H1ef zenon_H1fe zenon_H31. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 21.88/22.02 exact (zenon_H237 zenon_H31). % 21.88/22.02 apply (zenon_L1133_); trivial. % 21.88/22.02 (* end of lemma zenon_L1134_ *) % 21.88/22.02 assert (zenon_L1135_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 21.88/22.02 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_H77 zenon_H7f zenon_H8a zenon_H190 zenon_H1b3 zenon_H1a8 zenon_H177 zenon_Hbb zenon_Ha9 zenon_Hf6. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.02 apply (zenon_L253_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.02 apply (zenon_L1126_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.02 apply (zenon_L178_); trivial. % 21.88/22.02 apply (zenon_L92_); trivial. % 21.88/22.02 (* end of lemma zenon_L1135_ *) % 21.88/22.02 assert (zenon_L1136_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H18d zenon_H9e zenon_Hb6 zenon_H234 zenon_H3f zenon_H93 zenon_H77 zenon_H212 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H18a zenon_H160 zenon_Hbb zenon_Hbc. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.88/22.02 apply (zenon_L115_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.88/22.02 apply (zenon_L484_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.88/22.02 apply (zenon_L218_); trivial. % 21.88/22.02 apply (zenon_L873_); trivial. % 21.88/22.02 (* end of lemma zenon_L1136_ *) % 21.88/22.02 assert (zenon_L1137_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((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) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H164 zenon_H1b7 zenon_H1cb zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_H9e zenon_Ha0 zenon_H19a zenon_H212 zenon_H18a zenon_H7f zenon_H7d zenon_Hbc zenon_H160 zenon_H209. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.88/22.02 apply (zenon_L851_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.88/22.02 apply (zenon_L724_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.88/22.02 apply (zenon_L267_); trivial. % 21.88/22.02 apply (zenon_L417_); trivial. % 21.88/22.02 (* end of lemma zenon_L1137_ *) % 21.88/22.02 assert (zenon_L1138_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H15d zenon_H196 zenon_H68 zenon_H12e zenon_H19a zenon_Ha0 zenon_H139 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H177 zenon_H18d zenon_H1cb zenon_H34 zenon_H1c7 zenon_H93 zenon_H189 zenon_H1b3 zenon_H77 zenon_H1a8 zenon_H48 zenon_H31 zenon_H1bb zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.02 apply (zenon_L251_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.02 apply (zenon_L253_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.02 apply (zenon_L110_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.02 apply (zenon_L68_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.88/22.02 apply (zenon_L456_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.88/22.02 apply (zenon_L852_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.88/22.02 apply (zenon_L847_); trivial. % 21.88/22.02 apply (zenon_L848_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.02 apply (zenon_L264_); trivial. % 21.88/22.02 apply (zenon_L167_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.02 apply (zenon_L1115_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.02 apply (zenon_L239_); trivial. % 21.88/22.02 apply (zenon_L816_); trivial. % 21.88/22.02 (* end of lemma zenon_L1138_ *) % 21.88/22.02 assert (zenon_L1139_ : (((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)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e0) (e2)) = (op (e0) (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H164 zenon_H117 zenon_H104 zenon_H234 zenon_He4 zenon_Hcc zenon_H1d8 zenon_H55 zenon_H2c zenon_H141 zenon_H73 zenon_H20b zenon_H129 zenon_H20f zenon_H192 zenon_H163 zenon_Hfa zenon_H195 zenon_H173 zenon_H111 zenon_H4e zenon_H1c6 zenon_H25b zenon_H26d zenon_H82 zenon_H156 zenon_H13f zenon_H131 zenon_H1f1 zenon_H1fe zenon_H121 zenon_Hb2 zenon_H179 zenon_H33 zenon_H186 zenon_H1a2 zenon_H8a zenon_Heb zenon_H15d zenon_H196 zenon_H68 zenon_H12e zenon_H19a zenon_Ha0 zenon_H139 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H177 zenon_H18d zenon_H1cb zenon_H1c7 zenon_H93 zenon_H189 zenon_H1b3 zenon_H77 zenon_H1a8 zenon_H48 zenon_H31 zenon_H1bb zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.02 apply (zenon_L817_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.02 apply (zenon_L1117_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.02 apply (zenon_L251_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.02 apply (zenon_L253_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.02 apply (zenon_L110_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.02 apply (zenon_L178_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.02 apply (zenon_L1118_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.02 apply (zenon_L1136_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.02 apply (zenon_L1043_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.88/22.02 apply (zenon_L1115_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.88/22.02 apply (zenon_L484_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.88/22.02 apply (zenon_L832_); trivial. % 21.88/22.02 apply (zenon_L1137_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.02 apply (zenon_L122_); trivial. % 21.88/22.02 apply (zenon_L167_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.02 apply (zenon_L1115_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.02 apply (zenon_L239_); trivial. % 21.88/22.02 apply (zenon_L816_); trivial. % 21.88/22.02 apply (zenon_L1138_); trivial. % 21.88/22.02 (* end of lemma zenon_L1139_ *) % 21.88/22.02 assert (zenon_L1140_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (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)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H82 zenon_H196 zenon_H3d zenon_H139 zenon_H195 zenon_H163 zenon_H1b3 zenon_Hfa zenon_H2d zenon_H164 zenon_H68 zenon_H93 zenon_H1bb zenon_H20f zenon_H120 zenon_H181 zenon_Hc4 zenon_H18d zenon_H48 zenon_H129 zenon_H1b4 zenon_H77 zenon_H19a zenon_H31 zenon_H177 zenon_H24e zenon_H1b7 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H160 zenon_Hbb zenon_H1cd. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.88/22.02 apply (zenon_L818_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.88/22.02 apply (zenon_L1118_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.88/22.02 apply (zenon_L217_); trivial. % 21.88/22.02 apply (zenon_L867_); trivial. % 21.88/22.02 (* end of lemma zenon_L1140_ *) % 21.88/22.02 assert (zenon_L1141_ : (~((op (e3) (e3)) = (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) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((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)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((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))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((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 (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e0) (e2)) = (op (e0) (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) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (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 (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H181 zenon_H1b4 zenon_H24e zenon_H1b7 zenon_Hbb zenon_H1cd zenon_H31 zenon_H82 zenon_H196 zenon_H139 zenon_H195 zenon_H163 zenon_H1b3 zenon_Hfa zenon_H164 zenon_H68 zenon_H20f zenon_H18d zenon_H19a zenon_H177 zenon_H117 zenon_Ha0 zenon_Hb6 zenon_H104 zenon_H234 zenon_He4 zenon_Hcc zenon_H1d8 zenon_H55 zenon_H2c zenon_H141 zenon_H15d zenon_H73 zenon_H20b zenon_H192 zenon_H173 zenon_H111 zenon_H4e zenon_H1c6 zenon_H25b zenon_H26d zenon_H189 zenon_H1a8 zenon_H13a zenon_H156 zenon_H13f zenon_H131 zenon_H1f1 zenon_H1cb zenon_H1fe zenon_H121 zenon_Hb2 zenon_H179 zenon_H33 zenon_Ha9 zenon_H186 zenon_H1a2 zenon_H8a zenon_Heb zenon_H12e zenon_H48 zenon_Hc4 zenon_H93 zenon_H129 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H160 zenon_H77 zenon_H120. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.88/22.02 apply (zenon_L817_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.88/22.02 apply (zenon_L1117_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.02 apply (zenon_L251_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.02 apply (zenon_L253_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.02 apply (zenon_L110_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.02 apply (zenon_L178_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.02 apply (zenon_L1118_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.02 apply (zenon_L540_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.02 apply (zenon_L1043_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.88/22.02 apply (zenon_L1140_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.88/22.02 apply (zenon_L484_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.88/22.02 apply (zenon_L832_); trivial. % 21.88/22.02 apply (zenon_L527_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.02 apply (zenon_L264_); trivial. % 21.88/22.02 apply (zenon_L167_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.02 apply (zenon_L1140_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.02 apply (zenon_L239_); trivial. % 21.88/22.02 apply (zenon_L816_); trivial. % 21.88/22.02 apply (zenon_L528_); trivial. % 21.88/22.02 (* end of lemma zenon_L1141_ *) % 21.88/22.02 assert (zenon_L1142_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (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))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (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) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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 (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> False). % 21.88/22.02 do 0 intro. intros zenon_H271 zenon_H177 zenon_H12e zenon_H125 zenon_H1ef zenon_H1fe zenon_H24e zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1b7 zenon_H1b4 zenon_H1bb zenon_H196 zenon_H195 zenon_H163 zenon_H18d zenon_H234 zenon_H33 zenon_H179 zenon_Hb2 zenon_H121 zenon_H1cb zenon_He4 zenon_H1f1 zenon_H13f zenon_H117 zenon_H156 zenon_H82 zenon_H189 zenon_H25b zenon_H1c6 zenon_H173 zenon_H19a zenon_H20f zenon_H129 zenon_H20b zenon_H73 zenon_H164 zenon_H141 zenon_H2c zenon_H55 zenon_H4e zenon_Heb zenon_H109 zenon_H31 zenon_H1d8 zenon_H8a zenon_H26d zenon_H139 zenon_H1b3 zenon_H131 zenon_Hf5 zenon_Hfa zenon_H68 zenon_H77 zenon_H1a8 zenon_H190 zenon_H111 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H1c3 zenon_H1c2 zenon_H13a zenon_H192 zenon_H48 zenon_H15d zenon_H104 zenon_H183 zenon_H186 zenon_H1cd zenon_H1a2 zenon_Hcc. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.88/22.02 apply (zenon_L2_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.88/22.02 apply (zenon_L700_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.88/22.02 apply (zenon_L782_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.88/22.02 apply (zenon_L757_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.88/22.02 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 21.88/22.02 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 21.88/22.02 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.88/22.02 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.88/22.02 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 21.88/22.02 exact (zenon_H237 zenon_H31). % 21.88/22.02 apply (zenon_L1123_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.88/22.02 apply (zenon_L11_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.88/22.02 apply (zenon_L787_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.88/22.02 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.88/22.02 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 21.88/22.02 apply (zenon_L1127_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.88/22.02 apply (zenon_L814_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.88/22.02 apply (zenon_L88_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.88/22.02 apply (zenon_L37_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.88/22.02 apply (zenon_L232_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.88/22.02 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.88/22.02 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 21.88/22.02 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.88/22.02 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.88/22.02 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.88/22.02 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 21.88/22.02 exact (zenon_H237 zenon_H31). % 21.88/22.02 apply (zenon_L1130_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.88/22.02 apply (zenon_L1042_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.88/22.02 apply (zenon_L792_); trivial. % 21.88/22.02 apply (zenon_L51_); trivial. % 21.88/22.02 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.88/22.03 apply (zenon_L2_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.88/22.03 apply (zenon_L700_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.88/22.03 apply (zenon_L782_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.88/22.03 apply (zenon_L757_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 21.88/22.03 apply (zenon_L1134_); trivial. % 21.88/22.03 apply (zenon_L1134_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.88/22.03 apply (zenon_L11_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.88/22.03 apply (zenon_L787_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.88/22.03 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.88/22.03 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.88/22.03 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.03 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.03 apply (zenon_L251_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.03 apply (zenon_L1125_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.03 apply (zenon_L258_); trivial. % 21.88/22.03 apply (zenon_L1135_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.03 apply (zenon_L146_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.03 apply (zenon_L239_); trivial. % 21.88/22.03 apply (zenon_L192_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.88/22.03 apply (zenon_L789_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.88/22.03 apply (zenon_L88_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.88/22.03 apply (zenon_L37_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.88/22.03 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.88/22.03 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.88/22.03 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.88/22.03 apply (zenon_L1139_); trivial. % 21.88/22.03 apply (zenon_L1139_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.88/22.03 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.88/22.03 apply (zenon_L1141_); trivial. % 21.88/22.03 apply (zenon_L1141_); trivial. % 21.88/22.03 apply (zenon_L1121_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.88/22.03 apply (zenon_L791_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.88/22.03 apply (zenon_L361_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.88/22.03 apply (zenon_L792_); trivial. % 21.88/22.03 apply (zenon_L51_); trivial. % 21.88/22.03 (* end of lemma zenon_L1142_ *) % 21.88/22.03 assert (zenon_L1143_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H92 zenon_H1ef zenon_H13e zenon_H48 zenon_H2d zenon_H16a zenon_H8b zenon_H77 zenon_H7b zenon_H131 zenon_H4d zenon_Ha0 zenon_Ha9 zenon_H104 zenon_Hbb zenon_Hb6 zenon_H117 zenon_H13f. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.88/22.03 apply (zenon_L217_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.88/22.03 apply (zenon_L378_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.88/22.03 apply (zenon_L128_); trivial. % 21.88/22.03 apply (zenon_L1102_); trivial. % 21.88/22.03 apply (zenon_L755_); trivial. % 21.88/22.03 (* end of lemma zenon_L1143_ *) % 21.88/22.03 assert (zenon_L1144_ : ((op (e0) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (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))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H67 zenon_H93 zenon_H189 zenon_H99 zenon_H109 zenon_H1c3 zenon_H1fe zenon_H1cb zenon_Ha9 zenon_H1f1 zenon_H125 zenon_H94 zenon_H82 zenon_H13c zenon_H141 zenon_H179 zenon_H129 zenon_H163 zenon_Hfa zenon_H131 zenon_H13f zenon_H1c6 zenon_Hb6 zenon_Hf0 zenon_H121 zenon_H104 zenon_H33 zenon_H164 zenon_H11a zenon_H19a zenon_H26d zenon_H18d zenon_H192 zenon_H25e zenon_Hf5 zenon_H20f zenon_H195 zenon_H25b zenon_H12e zenon_H117 zenon_Ha0 zenon_He4 zenon_H55 zenon_H156 zenon_Hb2 zenon_H13a zenon_H48 zenon_H139 zenon_H196 zenon_H177 zenon_H77 zenon_H68 zenon_H31 zenon_H15d zenon_H1a8 zenon_H186 zenon_H4e zenon_H1a2 zenon_H2c zenon_H73 zenon_H4d zenon_H1bb zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.03 apply (zenon_L251_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.03 apply (zenon_L902_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.03 apply (zenon_L184_); trivial. % 21.88/22.03 apply (zenon_L816_); trivial. % 21.88/22.03 (* end of lemma zenon_L1144_ *) % 21.88/22.03 assert (zenon_L1145_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (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) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((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 (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (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 (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))))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (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) (e1)) = (op (e1) (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) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> False). % 21.88/22.03 do 0 intro. intros zenon_He2 zenon_H277 zenon_H201 zenon_H266 zenon_H20b zenon_H158 zenon_H13b zenon_H109 zenon_H1c3 zenon_H1c6 zenon_H33 zenon_H11a zenon_H192 zenon_H25e zenon_Hf5 zenon_H20f zenon_H25b zenon_H212 zenon_H73 zenon_H13c zenon_H12e zenon_H270 zenon_Hcc zenon_Hbc zenon_H111 zenon_H271 zenon_H1bb zenon_H190 zenon_H129 zenon_H24e zenon_H5d zenon_H1f1 zenon_H173 zenon_H18a zenon_H125 zenon_H1d5 zenon_H195 zenon_H163 zenon_H18d zenon_H189 zenon_H1b7 zenon_H19a zenon_H13f zenon_H94 zenon_H1a2 zenon_H1cb zenon_H26a zenon_H22d zenon_H141 zenon_H55 zenon_H1fe zenon_H26d zenon_H1ef zenon_H131 zenon_H13e zenon_H77 zenon_H67 zenon_H82 zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_Hb2 zenon_H24 zenon_H16a zenon_Hf0 zenon_H68 zenon_H1a8 zenon_H186 zenon_H1cd zenon_H1cf zenon_H121 zenon_H1b4 zenon_H104 zenon_H177 zenon_H164 zenon_H179 zenon_H196 zenon_H117 zenon_H2c zenon_H6f zenon_Hfa zenon_H13a zenon_H48 zenon_H4d zenon_H4e zenon_He4 zenon_H7d zenon_H156 zenon_H139 zenon_H15d zenon_H1d8 zenon_H31. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ]. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 21.88/22.03 apply (zenon_L1070_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.88/22.03 apply (zenon_L2_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.88/22.03 apply (zenon_L700_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.88/22.03 apply (zenon_L1143_); trivial. % 21.88/22.03 apply (zenon_L130_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.88/22.03 apply (zenon_L757_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.88/22.03 apply (zenon_L758_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.88/22.03 apply (zenon_L11_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.88/22.03 apply (zenon_L770_); trivial. % 21.88/22.03 apply (zenon_L130_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.88/22.03 apply (zenon_L335_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.88/22.03 apply (zenon_L814_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.88/22.03 apply (zenon_L343_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.88/22.03 apply (zenon_L37_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.88/22.03 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.88/22.03 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.88/22.03 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 21.88/22.03 apply (zenon_L1144_); trivial. % 21.88/22.03 apply (zenon_L1144_); trivial. % 21.88/22.03 apply (zenon_L896_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.88/22.03 apply (zenon_L791_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.88/22.03 apply (zenon_L361_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.88/22.03 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.88/22.03 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.88/22.03 apply (zenon_L1069_); trivial. % 21.88/22.03 apply (zenon_L51_); trivial. % 21.88/22.03 apply (zenon_L1044_); trivial. % 21.88/22.03 (* end of lemma zenon_L1145_ *) % 21.88/22.03 assert (zenon_L1146_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H28 zenon_H38 zenon_H1fb. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 21.88/22.03 apply (zenon_L316_); trivial. % 21.88/22.03 (* end of lemma zenon_L1146_ *) % 21.88/22.03 assert (zenon_L1147_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H2f zenon_H38 zenon_H26d. % 21.88/22.03 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.88/22.03 apply (zenon_L756_); trivial. % 21.88/22.03 (* end of lemma zenon_L1147_ *) % 21.88/22.03 assert (zenon_L1148_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H13a zenon_H47 zenon_Hb6 zenon_H3d zenon_Ha9 zenon_H66 zenon_H38 zenon_Ha0. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.03 apply (zenon_L253_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.03 apply (zenon_L55_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.03 apply (zenon_L193_); trivial. % 21.88/22.03 apply (zenon_L156_); trivial. % 21.88/22.03 (* end of lemma zenon_L1148_ *) % 21.88/22.03 assert (zenon_L1149_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H139 zenon_H77 zenon_Ha0 zenon_Ha9 zenon_H3d zenon_Hb6 zenon_H47 zenon_H13a zenon_H38 zenon_H68. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.03 apply (zenon_L251_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.03 apply (zenon_L214_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.03 apply (zenon_L1148_); trivial. % 21.88/22.03 apply (zenon_L165_); trivial. % 21.88/22.03 (* end of lemma zenon_L1149_ *) % 21.88/22.03 assert (zenon_L1150_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Hef zenon_H14c zenon_H191 zenon_H1a3. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.88/22.03 apply (zenon_L95_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.88/22.03 apply (zenon_L265_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.88/22.03 exact (zenon_H191 zenon_H110). % 21.88/22.03 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.03 (* end of lemma zenon_L1150_ *) % 21.88/22.03 assert (zenon_L1151_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_Hb9 zenon_Hb6 zenon_H106 zenon_H1cb. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.88/22.03 apply (zenon_L246_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.88/22.03 apply (zenon_L17_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.88/22.03 apply (zenon_L182_); trivial. % 21.88/22.03 apply (zenon_L846_); trivial. % 21.88/22.03 (* end of lemma zenon_L1151_ *) % 21.88/22.03 assert (zenon_L1152_ : (((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) (e1)) = (e2)) -> (~((op (e2) (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) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H117 zenon_H9f zenon_H2c zenon_Ha9 zenon_H6d zenon_H191 zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_Hb6 zenon_H106 zenon_H1cb. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.88/22.03 apply (zenon_L1065_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.88/22.03 apply (zenon_L289_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.88/22.03 exact (zenon_H191 zenon_H110). % 21.88/22.03 apply (zenon_L1151_); trivial. % 21.88/22.03 (* end of lemma zenon_L1152_ *) % 21.88/22.03 assert (zenon_L1153_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H183 zenon_H68 zenon_H34 zenon_Hac zenon_Ha9 zenon_H106 zenon_H77 zenon_Hf7 zenon_H20f. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.88/22.03 apply (zenon_L291_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.88/22.03 apply (zenon_L371_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.88/22.03 apply (zenon_L367_); trivial. % 21.88/22.03 apply (zenon_L570_); trivial. % 21.88/22.03 (* end of lemma zenon_L1153_ *) % 21.88/22.03 assert (zenon_L1154_ : (((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) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H121 zenon_H33 zenon_H9f zenon_H20f zenon_Hf7 zenon_H77 zenon_H106 zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_Hc4. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.88/22.03 apply (zenon_L245_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.88/22.03 apply (zenon_L1153_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.88/22.03 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.03 exact (zenon_Hc4 zenon_Hc3). % 21.88/22.03 (* end of lemma zenon_L1154_ *) % 21.88/22.03 assert (zenon_L1155_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e2)) -> False). % 21.88/22.03 do 0 intro. intros zenon_H278 zenon_H17c. % 21.88/22.03 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 21.88/22.03 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 21.88/22.03 congruence. % 21.88/22.03 exact (zenon_H181 zenon_H17c). % 21.88/22.03 exact (zenon_H181 zenon_H17c). % 21.88/22.03 (* end of lemma zenon_L1155_ *) % 21.88/22.03 assert (zenon_L1156_ : (~((op (e3) (op (e3) (e3))) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> False). % 21.88/22.03 do 0 intro. intros zenon_H279 zenon_H17c. % 21.88/22.03 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 21.88/22.03 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 21.88/22.03 congruence. % 21.88/22.03 apply zenon_Ha2. apply refl_equal. % 21.88/22.03 exact (zenon_H181 zenon_H17c). % 21.88/22.03 (* end of lemma zenon_L1156_ *) % 21.88/22.03 assert (zenon_L1157_ : ((op (e2) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> False). % 21.88/22.03 do 0 intro. intros zenon_H14c zenon_H106 zenon_H17c. % 21.88/22.03 apply (zenon_notand_s _ _ ax9); [ zenon_intro zenon_H273 | zenon_intro zenon_H27a ]. % 21.88/22.03 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H24b ]. % 21.88/22.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (e3) (e3))))). % 21.88/22.03 intro zenon_D_pnotp. % 21.88/22.03 apply zenon_H273. % 21.88/22.03 rewrite <- zenon_D_pnotp. % 21.88/22.03 exact zenon_H24a. % 21.88/22.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 21.88/22.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H274]. % 21.88/22.03 congruence. % 21.88/22.03 cut (((op (e2) (e2)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 21.88/22.03 intro zenon_D_pnotp. % 21.88/22.03 apply zenon_H274. % 21.88/22.03 rewrite <- zenon_D_pnotp. % 21.88/22.03 exact zenon_H14c. % 21.88/22.03 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.88/22.03 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 21.88/22.03 congruence. % 21.88/22.03 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H24b ]. % 21.88/22.03 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))))). % 21.88/22.03 intro zenon_D_pnotp. % 21.88/22.03 apply zenon_H27b. % 21.88/22.03 rewrite <- zenon_D_pnotp. % 21.88/22.03 exact zenon_H24a. % 21.88/22.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 21.88/22.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 21.88/22.03 congruence. % 21.88/22.03 apply (zenon_L1155_); trivial. % 21.88/22.03 apply zenon_H24b. apply refl_equal. % 21.88/22.03 apply zenon_H24b. apply refl_equal. % 21.88/22.03 apply zenon_H46. apply refl_equal. % 21.88/22.03 apply zenon_H24b. apply refl_equal. % 21.88/22.03 apply zenon_H24b. apply refl_equal. % 21.88/22.03 apply (zenon_notand_s _ _ zenon_H27a); [ zenon_intro zenon_H27c | zenon_intro zenon_H243 ]. % 21.88/22.03 apply zenon_H27c. apply sym_equal. exact zenon_H17c. % 21.88/22.03 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H244 | zenon_intro zenon_H245 ]. % 21.88/22.03 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((e1) = (op (e3) (op (e3) (e3))))). % 21.88/22.03 intro zenon_D_pnotp. % 21.88/22.03 apply zenon_H243. % 21.88/22.03 rewrite <- zenon_D_pnotp. % 21.88/22.03 exact zenon_H244. % 21.88/22.03 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 21.88/22.03 cut (((op (e3) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H246]. % 21.88/22.03 congruence. % 21.88/22.03 cut (((op (e3) (e2)) = (e1)) = ((op (e3) (op (e3) (e3))) = (e1))). % 21.88/22.03 intro zenon_D_pnotp. % 21.88/22.03 apply zenon_H246. % 21.88/22.03 rewrite <- zenon_D_pnotp. % 21.88/22.03 exact zenon_H106. % 21.88/22.03 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.88/22.03 cut (((op (e3) (e2)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H27d]. % 21.88/22.03 congruence. % 21.88/22.03 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H244 | zenon_intro zenon_H245 ]. % 21.88/22.03 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e2)) = (op (e3) (op (e3) (e3))))). % 21.88/22.03 intro zenon_D_pnotp. % 21.88/22.03 apply zenon_H27d. % 21.88/22.03 rewrite <- zenon_D_pnotp. % 21.88/22.03 exact zenon_H244. % 21.88/22.03 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 21.88/22.03 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 21.88/22.03 congruence. % 21.88/22.03 apply (zenon_L1156_); trivial. % 21.88/22.03 apply zenon_H245. apply refl_equal. % 21.88/22.03 apply zenon_H245. apply refl_equal. % 21.88/22.03 apply zenon_H4a. apply refl_equal. % 21.88/22.03 apply zenon_H245. apply refl_equal. % 21.88/22.03 apply zenon_H245. apply refl_equal. % 21.88/22.03 (* end of lemma zenon_L1157_ *) % 21.88/22.03 assert (zenon_L1158_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> False). % 21.88/22.03 do 0 intro. intros zenon_H1c3 zenon_H38 zenon_Hc4 zenon_H1a3 zenon_H183 zenon_H68 zenon_H34 zenon_Ha9 zenon_H77 zenon_H20f zenon_H9f zenon_H33 zenon_H121 zenon_H8a zenon_H1c2 zenon_H14c zenon_H106. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.88/22.03 apply (zenon_L165_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.88/22.03 apply (zenon_L1154_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.88/22.03 apply (zenon_L207_); trivial. % 21.88/22.03 apply (zenon_L1157_); trivial. % 21.88/22.03 (* end of lemma zenon_L1158_ *) % 21.88/22.03 assert (zenon_L1159_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H93 zenon_H77 zenon_H106 zenon_H1cb. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.88/22.03 apply (zenon_L246_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.88/22.03 apply (zenon_L413_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.88/22.03 apply (zenon_L218_); trivial. % 21.88/22.03 apply (zenon_L846_); trivial. % 21.88/22.03 (* end of lemma zenon_L1159_ *) % 21.88/22.03 assert (zenon_L1160_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((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 (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H16a zenon_H67 zenon_Hb6 zenon_H3c zenon_H5d zenon_H191 zenon_H2c zenon_H117 zenon_H14c zenon_H1c2 zenon_H121 zenon_H33 zenon_H9f zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_H1c3 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H106 zenon_H1cb. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.88/22.03 apply (zenon_L180_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.88/22.03 apply (zenon_L1152_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.88/22.03 apply (zenon_L1158_); trivial. % 21.88/22.03 apply (zenon_L1159_); trivial. % 21.88/22.03 (* end of lemma zenon_L1160_ *) % 21.88/22.03 assert (zenon_L1161_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((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 (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H201 zenon_Hef zenon_H1a2 zenon_H4e zenon_H16a zenon_H67 zenon_Hb6 zenon_H3c zenon_H5d zenon_H191 zenon_H2c zenon_H117 zenon_H14c zenon_H1c2 zenon_H121 zenon_H33 zenon_H9f zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_H1c3 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.88/22.03 apply (zenon_L1150_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.88/22.03 apply (zenon_L14_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.88/22.03 apply (zenon_L255_); trivial. % 21.88/22.03 apply (zenon_L1160_); trivial. % 21.88/22.03 (* end of lemma zenon_L1161_ *) % 21.88/22.03 assert (zenon_L1162_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 21.88/22.03 do 0 intro. intros zenon_H196 zenon_H38 zenon_H115. % 21.88/22.03 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 21.88/22.03 intro zenon_D_pnotp. % 21.88/22.03 apply zenon_H196. % 21.88/22.03 rewrite <- zenon_D_pnotp. % 21.88/22.03 exact zenon_H38. % 21.88/22.03 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 21.88/22.03 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 21.88/22.03 congruence. % 21.88/22.03 apply zenon_Hf9. apply refl_equal. % 21.88/22.03 apply zenon_H1fa. apply sym_equal. exact zenon_H115. % 21.88/22.03 (* end of lemma zenon_L1162_ *) % 21.88/22.03 assert (zenon_L1163_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (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 (e2) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.88/22.03 do 0 intro. intros zenon_H141 zenon_H109 zenon_He7 zenon_Hf0 zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H1c3 zenon_H1a3 zenon_H183 zenon_H68 zenon_H34 zenon_Ha9 zenon_H9f zenon_H33 zenon_H121 zenon_H1c2 zenon_H117 zenon_H2c zenon_H191 zenon_H5d zenon_H3c zenon_Hb6 zenon_H67 zenon_H16a zenon_H4e zenon_H1a2 zenon_Hef zenon_H201 zenon_H196 zenon_H38. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.88/22.03 apply (zenon_L359_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.88/22.03 apply (zenon_L929_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.88/22.03 apply (zenon_L1161_); trivial. % 21.88/22.03 apply (zenon_L1162_); trivial. % 21.88/22.03 (* end of lemma zenon_L1163_ *) % 21.88/22.03 assert (zenon_L1164_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_Ha9 zenon_H6d zenon_H1c7. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.88/22.03 apply (zenon_L55_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.88/22.03 exact (zenon_H159 zenon_H10c). % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.88/22.03 apply (zenon_L289_); trivial. % 21.88/22.03 exact (zenon_H1c7 zenon_Hac). % 21.88/22.03 (* end of lemma zenon_L1164_ *) % 21.88/22.03 assert (zenon_L1165_ : (((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) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H231 zenon_H34 zenon_Hbc zenon_H7f zenon_H1cd zenon_H1cb zenon_H17c zenon_H1a3. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H11d | zenon_intro zenon_H232 ]. % 21.88/22.03 apply (zenon_L328_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H106 | zenon_intro zenon_H233 ]. % 21.88/22.03 apply (zenon_L331_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H160 | zenon_intro zenon_Hbb ]. % 21.88/22.03 apply (zenon_L236_); trivial. % 21.88/22.03 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.03 (* end of lemma zenon_L1165_ *) % 21.88/22.03 assert (zenon_L1166_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H212 zenon_H1a3 zenon_H1cb zenon_H1cd zenon_Hbc zenon_H231 zenon_H7f zenon_H18a zenon_H17c zenon_Hac zenon_H7d. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H34 | zenon_intro zenon_H213 ]. % 21.88/22.03 apply (zenon_L1165_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H7e | zenon_intro zenon_H214 ]. % 21.88/22.03 apply (zenon_L31_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H102 | zenon_intro zenon_H9d ]. % 21.88/22.03 apply (zenon_L268_); trivial. % 21.88/22.03 apply (zenon_L44_); trivial. % 21.88/22.03 (* end of lemma zenon_L1166_ *) % 21.88/22.03 assert (zenon_L1167_ : (((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) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H121 zenon_H33 zenon_H9f zenon_H7d zenon_H17c zenon_H18a zenon_H7f zenon_H231 zenon_Hbc zenon_H1cd zenon_H1cb zenon_H212 zenon_H1a3 zenon_Hc4. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.88/22.03 apply (zenon_L245_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.88/22.03 apply (zenon_L1166_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.88/22.03 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.03 exact (zenon_Hc4 zenon_Hc3). % 21.88/22.03 (* end of lemma zenon_L1167_ *) % 21.88/22.03 assert (zenon_L1168_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((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)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H8a zenon_H104 zenon_H121 zenon_H33 zenon_H9f zenon_H7d zenon_H18a zenon_H7f zenon_H231 zenon_Hbc zenon_H1cd zenon_H1cb zenon_H212 zenon_H1a3 zenon_Hc4. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.88/22.03 apply (zenon_L291_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.88/22.03 apply (zenon_L169_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.88/22.03 apply (zenon_L231_); trivial. % 21.88/22.03 apply (zenon_L1167_); trivial. % 21.88/22.03 (* end of lemma zenon_L1168_ *) % 21.88/22.03 assert (zenon_L1169_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (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 (e0) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((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))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H12e zenon_H48 zenon_H212 zenon_H1cb zenon_Hbc zenon_H231 zenon_H18a zenon_H104 zenon_H14c zenon_H1c2 zenon_H8a zenon_H121 zenon_H33 zenon_H9f zenon_H20f zenon_Ha9 zenon_H1a3 zenon_Hc4 zenon_H38 zenon_H1c3 zenon_H183 zenon_H68 zenon_He7 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H77. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.88/22.03 apply (zenon_L456_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.88/22.03 apply (zenon_L1168_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.88/22.03 apply (zenon_L1158_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.88/22.03 apply (zenon_L291_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.88/22.03 apply (zenon_L964_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.88/22.03 apply (zenon_L848_); trivial. % 21.88/22.03 apply (zenon_L884_); trivial. % 21.88/22.03 (* end of lemma zenon_L1169_ *) % 21.88/22.03 assert (zenon_L1170_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Ha9 zenon_H72 zenon_H14c zenon_Ha0 zenon_H1a3. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.88/22.03 apply (zenon_L95_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.88/22.03 apply (zenon_L436_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.88/22.03 apply (zenon_L278_); trivial. % 21.88/22.03 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.03 (* end of lemma zenon_L1170_ *) % 21.88/22.03 assert (zenon_L1171_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H1cf zenon_H1d5 zenon_H67 zenon_H1a3 zenon_Ha0 zenon_H14c zenon_Ha9 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H93 zenon_H1c2 zenon_H171 zenon_H1cd. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.88/22.03 apply (zenon_L252_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.88/22.03 apply (zenon_L1170_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.88/22.03 apply (zenon_L207_); trivial. % 21.88/22.03 apply (zenon_L240_); trivial. % 21.88/22.03 (* end of lemma zenon_L1171_ *) % 21.88/22.03 assert (zenon_L1172_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e0) (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 (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H201 zenon_H1cd zenon_H1c2 zenon_H1a2 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H1a3 zenon_H67 zenon_H1d5 zenon_H1cf zenon_H171 zenon_He7 zenon_H163 zenon_H192 zenon_H3d zenon_H34 zenon_H12e zenon_H14c zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H93 zenon_H77 zenon_H1cb. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.88/22.03 apply (zenon_L1171_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.88/22.03 apply (zenon_L965_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.88/22.03 apply (zenon_L255_); trivial. % 21.88/22.03 apply (zenon_L1159_); trivial. % 21.88/22.03 (* end of lemma zenon_L1172_ *) % 21.88/22.03 assert (zenon_L1173_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H1a2 zenon_Ha9 zenon_H66 zenon_H186 zenon_Ha5 zenon_H190 zenon_H10d zenon_H1a3. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.88/22.03 apply (zenon_L193_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.88/22.03 apply (zenon_L308_); trivial. % 21.88/22.03 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.88/22.03 apply (zenon_L163_); trivial. % 21.88/22.03 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.03 (* end of lemma zenon_L1173_ *) % 21.88/22.03 assert (zenon_L1174_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.88/22.03 do 0 intro. intros zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_H1a3 zenon_H190 zenon_Ha5 zenon_H186 zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H1c7. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.88/22.04 apply (zenon_L55_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.88/22.04 exact (zenon_H159 zenon_H10c). % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.88/22.04 apply (zenon_L1173_); trivial. % 21.88/22.04 exact (zenon_H1c7 zenon_Hac). % 21.88/22.04 (* end of lemma zenon_L1174_ *) % 21.88/22.04 assert (zenon_L1175_ : (((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 (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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (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)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H1cf zenon_H1a2 zenon_Ha9 zenon_H186 zenon_H190 zenon_H1a3 zenon_H159 zenon_Hb6 zenon_H1c6 zenon_H156 zenon_Hef zenon_H93 zenon_H1c2 zenon_H12e zenon_H48 zenon_H3d zenon_H192 zenon_H4d zenon_H163 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.88/22.04 apply (zenon_L900_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.88/22.04 exact (zenon_H159 zenon_H10c). % 21.88/22.04 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.88/22.04 apply (zenon_L124_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.88/22.04 apply (zenon_L1174_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.88/22.04 apply (zenon_L100_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.88/22.04 apply (zenon_L207_); trivial. % 21.88/22.04 apply (zenon_L853_); trivial. % 21.88/22.04 (* end of lemma zenon_L1175_ *) % 21.88/22.04 assert (zenon_L1176_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((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)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha0 zenon_H73 zenon_H163 zenon_H1d4 zenon_H4e zenon_H25 zenon_H1ec zenon_H131 zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_H156 zenon_H159 zenon_Ha9 zenon_H1cf zenon_Hc3 zenon_H1b4. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.04 exact (zenon_Ha4 zenon_H9f). % 21.88/22.04 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.04 apply (zenon_L53_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.04 apply (zenon_L276_); trivial. % 21.88/22.04 apply (zenon_L602_); trivial. % 21.88/22.04 (* end of lemma zenon_L1176_ *) % 21.88/22.04 assert (zenon_L1177_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H169 zenon_Ha4 zenon_Ha0 zenon_H2a zenon_H1cf zenon_H163 zenon_H4e zenon_H25 zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H40 zenon_H156 zenon_H159 zenon_H158 zenon_Ha9 zenon_H1b4 zenon_Hc3 zenon_H13a. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 21.88/22.04 apply (zenon_L1176_); trivial. % 21.88/22.04 apply (zenon_L304_); trivial. % 21.88/22.04 (* end of lemma zenon_L1177_ *) % 21.88/22.04 assert (zenon_L1178_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H28 zenon_H13a zenon_Hc3 zenon_H1b4 zenon_Ha9 zenon_H158 zenon_H159 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_Ha4. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 21.88/22.04 apply (zenon_L1177_); trivial. % 21.88/22.04 apply (zenon_L1177_); trivial. % 21.88/22.04 (* end of lemma zenon_L1178_ *) % 21.88/22.04 assert (zenon_L1179_ : (((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 (e2) (e2)) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H191 zenon_H8b zenon_H266 zenon_H2d zenon_H55 zenon_H190 zenon_H1ba zenon_H6f zenon_H1ef zenon_H13e zenon_Ha0 zenon_H31 zenon_Hc3 zenon_H1b4. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.04 exact (zenon_Ha4 zenon_H9f). % 21.88/22.04 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.04 apply (zenon_L730_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.04 apply (zenon_L68_); trivial. % 21.88/22.04 apply (zenon_L602_); trivial. % 21.88/22.04 (* end of lemma zenon_L1179_ *) % 21.88/22.04 assert (zenon_L1180_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.88/22.04 do 0 intro. intros zenon_H36 zenon_Hc3. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.88/22.04 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.88/22.04 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.88/22.04 apply (zenon_L50_); trivial. % 21.88/22.04 (* end of lemma zenon_L1180_ *) % 21.88/22.04 assert (zenon_L1181_ : ((op (e3) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_Hc3 zenon_Ha5 zenon_H20f. % 21.88/22.04 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.88/22.04 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 21.88/22.04 intro zenon_D_pnotp. % 21.88/22.04 apply zenon_H20f. % 21.88/22.04 rewrite <- zenon_D_pnotp. % 21.88/22.04 exact zenon_H12a. % 21.88/22.04 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.88/22.04 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 21.88/22.04 congruence. % 21.88/22.04 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 21.88/22.04 intro zenon_D_pnotp. % 21.88/22.04 apply zenon_H210. % 21.88/22.04 rewrite <- zenon_D_pnotp. % 21.88/22.04 exact zenon_Hc3. % 21.88/22.04 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 21.88/22.04 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.88/22.04 congruence. % 21.88/22.04 apply zenon_H12b. apply refl_equal. % 21.88/22.04 apply zenon_H1ac. apply sym_equal. exact zenon_Ha5. % 21.88/22.04 apply zenon_H12b. apply refl_equal. % 21.88/22.04 apply zenon_H12b. apply refl_equal. % 21.88/22.04 (* end of lemma zenon_L1181_ *) % 21.88/22.04 assert (zenon_L1182_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H13c zenon_Hb6 zenon_H3c zenon_H159 zenon_Hfe zenon_H73 zenon_Hc3 zenon_H20f. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.88/22.04 apply (zenon_L46_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.88/22.04 exact (zenon_H159 zenon_H10c). % 21.88/22.04 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.88/22.04 apply (zenon_L89_); trivial. % 21.88/22.04 apply (zenon_L1181_); trivial. % 21.88/22.04 (* end of lemma zenon_L1182_ *) % 21.88/22.04 assert (zenon_L1183_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H3d zenon_H20f zenon_H73 zenon_H159 zenon_H3c zenon_Hb6 zenon_H13c zenon_Hc3 zenon_H1b4. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.04 exact (zenon_Ha4 zenon_H9f). % 21.88/22.04 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.04 apply (zenon_L55_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.04 apply (zenon_L1182_); trivial. % 21.88/22.04 apply (zenon_L602_); trivial. % 21.88/22.04 (* end of lemma zenon_L1183_ *) % 21.88/22.04 assert (zenon_L1184_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H3a zenon_H13a zenon_Ha4 zenon_H20f zenon_H73 zenon_H159 zenon_Hb6 zenon_H13c zenon_Hc3 zenon_H1b4. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 21.88/22.04 apply (zenon_L1183_); trivial. % 21.88/22.04 (* end of lemma zenon_L1184_ *) % 21.88/22.04 assert (zenon_L1185_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_Hc3 zenon_Hac zenon_H1b7. % 21.88/22.04 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H12a | zenon_intro zenon_H12b ]. % 21.88/22.04 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 21.88/22.04 intro zenon_D_pnotp. % 21.88/22.04 apply zenon_H1b7. % 21.88/22.04 rewrite <- zenon_D_pnotp. % 21.88/22.04 exact zenon_H12a. % 21.88/22.04 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.88/22.04 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 21.88/22.04 congruence. % 21.88/22.04 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 21.88/22.04 intro zenon_D_pnotp. % 21.88/22.04 apply zenon_H1b8. % 21.88/22.04 rewrite <- zenon_D_pnotp. % 21.88/22.04 exact zenon_Hc3. % 21.88/22.04 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 21.88/22.04 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 21.88/22.04 congruence. % 21.88/22.04 apply zenon_H12b. apply refl_equal. % 21.88/22.04 apply zenon_H207. apply sym_equal. exact zenon_Hac. % 21.88/22.04 apply zenon_H12b. apply refl_equal. % 21.88/22.04 apply zenon_H12b. apply refl_equal. % 21.88/22.04 (* end of lemma zenon_L1185_ *) % 21.88/22.04 assert (zenon_L1186_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hb6 zenon_H4d zenon_H191 zenon_Hc3 zenon_H1cb. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.88/22.04 apply (zenon_L193_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.88/22.04 apply (zenon_L124_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.88/22.04 exact (zenon_H191 zenon_H110). % 21.88/22.04 apply (zenon_L622_); trivial. % 21.88/22.04 (* end of lemma zenon_L1186_ *) % 21.88/22.04 assert (zenon_L1187_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H27e zenon_H38 zenon_H196 zenon_H5c zenon_H195 zenon_H189 zenon_H6d zenon_Hc3 zenon_H129. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H115 | zenon_intro zenon_H27f ]. % 21.88/22.04 apply (zenon_L1162_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H128 | zenon_intro zenon_H280 ]. % 21.88/22.04 apply (zenon_L149_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H93 | zenon_intro zenon_Hb9 ]. % 21.88/22.04 apply (zenon_L439_); trivial. % 21.88/22.04 apply (zenon_L189_); trivial. % 21.88/22.04 (* end of lemma zenon_L1187_ *) % 21.88/22.04 assert (zenon_L1188_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H5a zenon_H25b zenon_H38 zenon_Hf5 zenon_H186 zenon_H195 zenon_H93 zenon_Hc3 zenon_H20f. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H136 | zenon_intro zenon_H25c ]. % 21.88/22.04 apply (zenon_L663_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H5c | zenon_intro zenon_H25d ]. % 21.88/22.04 apply (zenon_L138_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Ha5 ]. % 21.88/22.04 apply (zenon_L228_); trivial. % 21.88/22.04 apply (zenon_L1181_); trivial. % 21.88/22.04 (* end of lemma zenon_L1188_ *) % 21.88/22.04 assert (zenon_L1189_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (((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)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hb6 zenon_H189 zenon_H53 zenon_H27e zenon_H196 zenon_H129 zenon_H48 zenon_H18d zenon_H8b zenon_H5a zenon_H25b zenon_H38 zenon_Hf5 zenon_H186 zenon_H195 zenon_Hc3 zenon_H20f. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.88/22.04 exact (zenon_H7b zenon_H65). % 21.88/22.04 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.88/22.04 apply (zenon_L246_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.88/22.04 apply (zenon_L1187_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.88/22.04 apply (zenon_L139_); trivial. % 21.88/22.04 apply (zenon_L81_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.88/22.04 exact (zenon_H8b zenon_H8a). % 21.88/22.04 apply (zenon_L1188_); trivial. % 21.88/22.04 (* end of lemma zenon_L1189_ *) % 21.88/22.04 assert (zenon_L1190_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((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 (e2) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (((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)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H236 zenon_H77 zenon_Ha9 zenon_H68 zenon_H139 zenon_H1b7 zenon_H159 zenon_H1c6 zenon_H1cb zenon_H191 zenon_H4d zenon_Ha0 zenon_H1a2 zenon_H16a zenon_H7b zenon_Hb6 zenon_H189 zenon_H53 zenon_H27e zenon_H196 zenon_H129 zenon_H48 zenon_H18d zenon_H8b zenon_H5a zenon_H25b zenon_Hf5 zenon_H186 zenon_H195 zenon_Hc3 zenon_H20f. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.04 apply (zenon_L20_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.88/22.04 apply (zenon_L110_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.88/22.04 exact (zenon_H159 zenon_H10c). % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.88/22.04 apply (zenon_L113_); trivial. % 21.88/22.04 apply (zenon_L1185_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.04 apply (zenon_L1186_); trivial. % 21.88/22.04 apply (zenon_L321_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.88/22.04 apply (zenon_L53_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.88/22.04 exact (zenon_H159 zenon_H10c). % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.88/22.04 apply (zenon_L113_); trivial. % 21.88/22.04 apply (zenon_L1185_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 21.88/22.04 apply (zenon_L762_); trivial. % 21.88/22.04 apply (zenon_L1189_); trivial. % 21.88/22.04 (* end of lemma zenon_L1190_ *) % 21.88/22.04 assert (zenon_L1191_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.88/22.04 do 0 intro. intros zenon_H61 zenon_Hc3. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.88/22.04 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.88/22.04 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.88/22.04 apply (zenon_L50_); trivial. % 21.88/22.04 (* end of lemma zenon_L1191_ *) % 21.88/22.04 assert (zenon_L1192_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H65 zenon_Hdb zenon_H6f zenon_H191 zenon_Hc3 zenon_H129. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.88/22.04 apply (zenon_L43_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.88/22.04 apply (zenon_L205_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.88/22.04 exact (zenon_H191 zenon_H110). % 21.88/22.04 apply (zenon_L189_); trivial. % 21.88/22.04 (* end of lemma zenon_L1192_ *) % 21.88/22.04 assert (zenon_L1193_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H129 zenon_H191 zenon_H6f zenon_H65 zenon_H117 zenon_Ha9 zenon_H66 zenon_Hc3 zenon_H1b4. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.04 exact (zenon_Ha4 zenon_H9f). % 21.88/22.04 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.04 apply (zenon_L1192_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.04 apply (zenon_L193_); trivial. % 21.88/22.04 apply (zenon_L602_); trivial. % 21.88/22.04 (* end of lemma zenon_L1193_ *) % 21.88/22.04 assert (zenon_L1194_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H63 zenon_H13a zenon_Ha4 zenon_H129 zenon_H191 zenon_H6f zenon_H117 zenon_Ha9 zenon_Hc3 zenon_H1b4. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 21.88/22.04 apply (zenon_L1193_); trivial. % 21.88/22.04 (* end of lemma zenon_L1194_ *) % 21.88/22.04 assert (zenon_L1195_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_Ha9 zenon_H6d zenon_Hc3 zenon_H1b7. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.88/22.04 apply (zenon_L55_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.88/22.04 exact (zenon_H159 zenon_H10c). % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.88/22.04 apply (zenon_L289_); trivial. % 21.88/22.04 apply (zenon_L1185_); trivial. % 21.88/22.04 (* end of lemma zenon_L1195_ *) % 21.88/22.04 assert (zenon_L1196_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Ha9 zenon_H72 zenon_H191 zenon_Hc3 zenon_H1cb. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.88/22.04 apply (zenon_L95_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.88/22.04 apply (zenon_L436_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.88/22.04 exact (zenon_H191 zenon_H110). % 21.88/22.04 apply (zenon_L622_); trivial. % 21.88/22.04 (* end of lemma zenon_L1196_ *) % 21.88/22.04 assert (zenon_L1197_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (((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)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H15d zenon_H48 zenon_H1e zenon_H1b7 zenon_H6d zenon_H159 zenon_H1c6 zenon_H1cb zenon_Hc3 zenon_H191 zenon_H72 zenon_Ha9 zenon_Hb6 zenon_H1a2 zenon_H5c zenon_Hf5. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.04 apply (zenon_L13_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.04 apply (zenon_L1195_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.04 apply (zenon_L1196_); trivial. % 21.88/22.04 apply (zenon_L192_); trivial. % 21.88/22.04 (* end of lemma zenon_L1197_ *) % 21.88/22.04 assert (zenon_L1198_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (((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)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_H77 zenon_H15d zenon_H48 zenon_H1e zenon_H1b7 zenon_H6d zenon_H159 zenon_H1c6 zenon_H1cb zenon_Hc3 zenon_H191 zenon_H72 zenon_Ha9 zenon_Hb6 zenon_H1a2 zenon_Hf5. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.04 exact (zenon_H7a zenon_H3c). % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.04 exact (zenon_H40 zenon_H3f). % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.04 apply (zenon_L59_); trivial. % 21.88/22.04 apply (zenon_L1197_); trivial. % 21.88/22.04 (* end of lemma zenon_L1198_ *) % 21.88/22.04 assert (zenon_L1199_ : (((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 (e1) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Ha9 zenon_H72 zenon_H191 zenon_Hc3 zenon_H1cb. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.88/22.04 apply (zenon_L68_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.88/22.04 apply (zenon_L436_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.88/22.04 exact (zenon_H191 zenon_H110). % 21.88/22.04 apply (zenon_L622_); trivial. % 21.88/22.04 (* end of lemma zenon_L1199_ *) % 21.88/22.04 assert (zenon_L1200_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.88/22.04 do 0 intro. intros zenon_H1c3 zenon_H68 zenon_H38 zenon_H72 zenon_H186 zenon_H189 zenon_H6d zenon_Ha9 zenon_Hc3. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.88/22.04 apply (zenon_L165_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.88/22.04 apply (zenon_L438_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.88/22.04 apply (zenon_L439_); trivial. % 21.88/22.04 apply (zenon_L133_); trivial. % 21.88/22.04 (* end of lemma zenon_L1200_ *) % 21.88/22.04 assert (zenon_L1201_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.88/22.04 do 0 intro. intros zenon_H99 zenon_Hc3. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.88/22.04 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.88/22.04 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.88/22.04 apply (zenon_L50_); trivial. % 21.88/22.04 (* end of lemma zenon_L1201_ *) % 21.88/22.04 assert (zenon_L1202_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H9b zenon_Hc3 zenon_H1b4. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 21.88/22.04 apply (zenon_L602_); trivial. % 21.88/22.04 (* end of lemma zenon_L1202_ *) % 21.88/22.04 assert (zenon_L1203_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_Hb1 zenon_Hc3 zenon_H20f. % 21.88/22.04 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.88/22.04 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 21.88/22.04 apply (zenon_L1181_); trivial. % 21.88/22.04 (* end of lemma zenon_L1203_ *) % 21.88/22.04 assert (zenon_L1204_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> False). % 21.88/22.04 do 0 intro. intros zenon_Hc5. % 21.88/22.04 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_Hc3. zenon_intro zenon_Hc6. % 21.88/22.04 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc3. zenon_intro zenon_H39. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.88/22.04 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.88/22.04 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.88/22.04 apply (zenon_L50_); trivial. % 21.88/22.04 (* end of lemma zenon_L1204_ *) % 21.88/22.04 assert (zenon_L1205_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((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)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (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) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.88/22.04 do 0 intro. intros zenon_Hcc zenon_H1fb zenon_H26d zenon_H159 zenon_H73 zenon_H13c zenon_H18d zenon_Hb6 zenon_H196 zenon_H195 zenon_H27e zenon_H48 zenon_Hf5 zenon_H25b zenon_H16a zenon_H190 zenon_H13e zenon_H13a zenon_H6f zenon_H191 zenon_H117 zenon_Ha9 zenon_H189 zenon_H186 zenon_H38 zenon_H68 zenon_H1c3 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc3. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.88/22.04 apply (zenon_L2_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.88/22.04 apply (zenon_L1146_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.88/22.04 apply (zenon_L1147_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.88/22.04 apply (zenon_L1180_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 21.88/22.04 exact (zenon_H238 zenon_H38). % 21.88/22.04 apply (zenon_L1183_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.88/22.04 apply (zenon_L11_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.88/22.04 apply (zenon_L1189_); trivial. % 21.88/22.04 apply (zenon_L1189_); trivial. % 21.88/22.04 apply (zenon_L176_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.88/22.04 apply (zenon_L1191_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 21.88/22.04 exact (zenon_H238 zenon_H38). % 21.88/22.04 apply (zenon_L1193_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 21.88/22.04 apply (zenon_L1200_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.88/22.04 apply (zenon_L37_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.88/22.04 apply (zenon_L1201_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.88/22.04 apply (zenon_L1202_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.88/22.04 apply (zenon_L1203_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.88/22.04 apply (zenon_L190_); trivial. % 21.88/22.04 apply (zenon_L1204_); trivial. % 21.88/22.04 (* end of lemma zenon_L1205_ *) % 21.88/22.04 assert (zenon_L1206_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H3a zenon_H5c zenon_H5d. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 21.88/22.04 apply (zenon_L17_); trivial. % 21.88/22.04 (* end of lemma zenon_L1206_ *) % 21.88/22.04 assert (zenon_L1207_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H5a zenon_H5c zenon_H186. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.88/22.04 apply (zenon_L138_); trivial. % 21.88/22.04 (* end of lemma zenon_L1207_ *) % 21.88/22.04 assert (zenon_L1208_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H63 zenon_H93 zenon_H94. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 21.88/22.04 apply (zenon_L38_); trivial. % 21.88/22.04 (* end of lemma zenon_L1208_ *) % 21.88/22.04 assert (zenon_L1209_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H87 zenon_H93 zenon_H189. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.88/22.04 apply (zenon_L439_); trivial. % 21.88/22.04 (* end of lemma zenon_L1209_ *) % 21.88/22.04 assert (zenon_L1210_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.88/22.04 do 0 intro. intros zenon_Hcc zenon_H1fb zenon_H26d zenon_H38 zenon_H5d zenon_H186 zenon_H5c zenon_H94 zenon_H189 zenon_H93 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc3. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.88/22.04 apply (zenon_L2_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.88/22.04 apply (zenon_L1146_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.88/22.04 apply (zenon_L1147_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.88/22.04 apply (zenon_L1180_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.88/22.04 apply (zenon_L1206_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.88/22.04 apply (zenon_L11_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.88/22.04 apply (zenon_L1207_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.88/22.04 apply (zenon_L1191_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.88/22.04 apply (zenon_L1208_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.88/22.04 apply (zenon_L1209_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.88/22.04 apply (zenon_L37_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.88/22.04 apply (zenon_L1201_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.88/22.04 apply (zenon_L1202_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.88/22.04 apply (zenon_L1203_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.88/22.04 apply (zenon_L190_); trivial. % 21.88/22.04 apply (zenon_L1204_); trivial. % 21.88/22.04 (* end of lemma zenon_L1210_ *) % 21.88/22.04 assert (zenon_L1211_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H25b zenon_H38 zenon_Hf5 zenon_H128 zenon_H195 zenon_H93 zenon_Hc3 zenon_H20f. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H136 | zenon_intro zenon_H25c ]. % 21.88/22.04 apply (zenon_L663_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H5c | zenon_intro zenon_H25d ]. % 21.88/22.04 apply (zenon_L149_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Ha5 ]. % 21.88/22.04 apply (zenon_L228_); trivial. % 21.88/22.04 apply (zenon_L1181_); trivial. % 21.88/22.04 (* end of lemma zenon_L1211_ *) % 21.88/22.04 assert (zenon_L1212_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.88/22.04 do 0 intro. intros zenon_H18d zenon_H48 zenon_H129 zenon_H1b4 zenon_H189 zenon_H94 zenon_H186 zenon_H5d zenon_H26d zenon_H1fb zenon_Hcc zenon_H20f zenon_H93 zenon_H195 zenon_Hf5 zenon_H38 zenon_H25b zenon_Hb6 zenon_Hc3. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.88/22.04 apply (zenon_L246_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.88/22.04 apply (zenon_L1210_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.88/22.04 apply (zenon_L1211_); trivial. % 21.88/22.04 apply (zenon_L81_); trivial. % 21.88/22.04 (* end of lemma zenon_L1212_ *) % 21.88/22.04 assert (zenon_L1213_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H281 zenon_H94 zenon_H5d zenon_H38 zenon_H1fb zenon_H26d zenon_Hc3 zenon_H13a zenon_H1b4 zenon_H159 zenon_H73 zenon_H20f zenon_H13c zenon_Hb6 zenon_H18d zenon_H196 zenon_H195 zenon_H189 zenon_H129 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H16a zenon_H190 zenon_H13e zenon_Ha9 zenon_H6f zenon_H117 zenon_H68 zenon_H1c3 zenon_Hcc. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H191 | zenon_intro zenon_H93 ]. % 21.88/22.04 apply (zenon_L1205_); trivial. % 21.88/22.04 apply (zenon_L1212_); trivial. % 21.88/22.04 (* end of lemma zenon_L1213_ *) % 21.88/22.04 assert (zenon_L1214_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H27e zenon_H38 zenon_H196 zenon_H5c zenon_H195 zenon_H94 zenon_H65 zenon_Hc3 zenon_H129. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H115 | zenon_intro zenon_H27f ]. % 21.88/22.04 apply (zenon_L1162_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H128 | zenon_intro zenon_H280 ]. % 21.88/22.04 apply (zenon_L149_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H93 | zenon_intro zenon_Hb9 ]. % 21.88/22.04 apply (zenon_L38_); trivial. % 21.88/22.04 apply (zenon_L189_); trivial. % 21.88/22.04 (* end of lemma zenon_L1214_ *) % 21.88/22.04 assert (zenon_L1215_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((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)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.88/22.04 do 0 intro. intros zenon_Hcc zenon_H1fb zenon_H26d zenon_H5d zenon_H186 zenon_H94 zenon_H189 zenon_H195 zenon_H5c zenon_H196 zenon_H38 zenon_H27e zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc3. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.88/22.04 apply (zenon_L2_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.88/22.04 apply (zenon_L1146_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.88/22.04 apply (zenon_L1147_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.88/22.04 apply (zenon_L1180_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.88/22.04 apply (zenon_L1206_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.88/22.04 apply (zenon_L11_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.88/22.04 apply (zenon_L1207_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.88/22.04 apply (zenon_L1191_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 21.88/22.04 apply (zenon_L1214_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.88/22.04 apply (zenon_L1187_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.88/22.04 apply (zenon_L37_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.88/22.04 apply (zenon_L1201_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.88/22.04 apply (zenon_L1202_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.88/22.04 apply (zenon_L1203_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.88/22.04 apply (zenon_L190_); trivial. % 21.88/22.04 apply (zenon_L1204_); trivial. % 21.88/22.04 (* end of lemma zenon_L1215_ *) % 21.88/22.04 assert (zenon_L1216_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H282 zenon_Hcc zenon_H1c3 zenon_H68 zenon_H117 zenon_H6f zenon_Ha9 zenon_H13e zenon_H190 zenon_H16a zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H129 zenon_H189 zenon_H195 zenon_H196 zenon_H18d zenon_Hb6 zenon_H13c zenon_H20f zenon_H73 zenon_H1b4 zenon_H13a zenon_Hc3 zenon_H26d zenon_H1fb zenon_H38 zenon_H5d zenon_H94 zenon_H281. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H159 | zenon_intro zenon_H5c ]. % 21.88/22.04 apply (zenon_L1213_); trivial. % 21.88/22.04 apply (zenon_L1215_); trivial. % 21.88/22.04 (* end of lemma zenon_L1216_ *) % 21.88/22.04 assert (zenon_L1217_ : (((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 (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((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))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H236 zenon_H1c6 zenon_H6d zenon_H1b7 zenon_H15d zenon_H77 zenon_H7a zenon_Heb zenon_H159 zenon_H156 zenon_H40 zenon_H173 zenon_H158 zenon_H1cb zenon_H191 zenon_H72 zenon_Ha0 zenon_H1a2 zenon_H282 zenon_Hcc zenon_H1c3 zenon_H68 zenon_H117 zenon_H6f zenon_Ha9 zenon_H13e zenon_H190 zenon_H16a zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H129 zenon_H189 zenon_H195 zenon_H196 zenon_H18d zenon_Hb6 zenon_H13c zenon_H20f zenon_H73 zenon_H1b4 zenon_H13a zenon_Hc3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 21.88/22.04 apply (zenon_L1198_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 21.88/22.04 apply (zenon_L273_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 21.88/22.04 apply (zenon_L1199_); trivial. % 21.88/22.04 apply (zenon_L1216_); trivial. % 21.88/22.04 (* end of lemma zenon_L1217_ *) % 21.88/22.04 assert (zenon_L1218_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.88/22.04 do 0 intro. intros zenon_H92 zenon_Ha4 zenon_H13e zenon_H8b zenon_H55 zenon_H190 zenon_H1ba zenon_H6f zenon_H266 zenon_H2d zenon_H1ef zenon_Ha0 zenon_H31 zenon_H1b4 zenon_Hc3 zenon_H13a zenon_H93. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.88/22.04 exact (zenon_H16b zenon_H93). % 21.88/22.04 apply (zenon_L1179_); trivial. % 21.88/22.04 (* end of lemma zenon_L1218_ *) % 21.88/22.04 assert (zenon_L1219_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (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 (e1) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((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 (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.88/22.04 do 0 intro. intros zenon_H92 zenon_H139 zenon_H7b zenon_H77 zenon_H8b zenon_H196 zenon_H16a zenon_H4d zenon_H1cb zenon_H1a2 zenon_Ha9 zenon_H159 zenon_Hb6 zenon_H53 zenon_H1b7 zenon_Hc3 zenon_H1c6 zenon_H68 zenon_Ha0 zenon_H25b zenon_H20f zenon_H186 zenon_Hf5 zenon_H5a zenon_H48 zenon_H27e zenon_H129 zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H93. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.88/22.04 exact (zenon_H16b zenon_H93). % 21.88/22.04 apply (zenon_L1190_); trivial. % 21.88/22.04 (* end of lemma zenon_L1219_ *) % 21.88/22.04 assert (zenon_L1220_ : ((~((op (e2) (e3)) = (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) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> False). % 21.88/22.04 do 0 intro. intros zenon_H92 zenon_H13d zenon_H190 zenon_H53 zenon_H8b zenon_H13e zenon_H93. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 21.88/22.04 exact (zenon_H16b zenon_H93). % 21.88/22.04 apply (zenon_L144_); trivial. % 21.88/22.04 (* end of lemma zenon_L1220_ *) % 21.88/22.04 assert (zenon_L1221_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> False). % 21.88/22.04 do 0 intro. intros zenon_H89 zenon_H93 zenon_H13e zenon_H53 zenon_H190 zenon_H13d zenon_H92. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.88/22.04 apply (zenon_L1220_); trivial. % 21.88/22.04 apply (zenon_L1220_); trivial. % 21.88/22.04 (* end of lemma zenon_L1221_ *) % 21.88/22.04 assert (zenon_L1222_ : (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((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 (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 21.88/22.04 do 0 intro. intros zenon_Ha4 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H159 zenon_H158 zenon_Ha9 zenon_H1b4 zenon_Hc3 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H20f zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H129 zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H191 | zenon_intro zenon_H93 ]. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.88/22.04 apply (zenon_L2_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.88/22.04 apply (zenon_L1178_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.88/22.04 apply (zenon_L1179_); trivial. % 21.88/22.04 apply (zenon_L1179_); trivial. % 21.88/22.04 apply (zenon_L645_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.88/22.04 apply (zenon_L1180_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.88/22.04 apply (zenon_L1184_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.88/22.04 apply (zenon_L11_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.88/22.04 apply (zenon_L1190_); trivial. % 21.88/22.04 apply (zenon_L1190_); trivial. % 21.88/22.04 apply (zenon_L176_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.88/22.04 apply (zenon_L1191_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.88/22.04 apply (zenon_L1194_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 21.88/22.04 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 21.88/22.04 apply (zenon_L1217_); trivial. % 21.88/22.04 apply (zenon_L1217_); trivial. % 21.88/22.04 apply (zenon_L102_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.88/22.04 apply (zenon_L37_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.88/22.04 apply (zenon_L1201_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.88/22.04 apply (zenon_L1202_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.88/22.04 apply (zenon_L1203_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.88/22.04 apply (zenon_L190_); trivial. % 21.88/22.04 apply (zenon_L1204_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.88/22.04 apply (zenon_L2_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.88/22.04 apply (zenon_L1178_); trivial. % 21.88/22.04 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.88/22.04 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.88/22.05 apply (zenon_L1218_); trivial. % 21.88/22.05 apply (zenon_L1218_); trivial. % 21.88/22.05 apply (zenon_L796_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.88/22.05 apply (zenon_L1180_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.88/22.05 apply (zenon_L1184_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.88/22.05 apply (zenon_L11_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.88/22.05 apply (zenon_L1219_); trivial. % 21.88/22.05 apply (zenon_L1219_); trivial. % 21.88/22.05 apply (zenon_L1221_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.88/22.05 apply (zenon_L1191_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.88/22.05 apply (zenon_L1208_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.88/22.05 apply (zenon_L1209_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.88/22.05 apply (zenon_L37_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.88/22.05 apply (zenon_L1201_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.88/22.05 apply (zenon_L1202_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.88/22.05 apply (zenon_L1203_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.88/22.05 apply (zenon_L190_); trivial. % 21.88/22.05 apply (zenon_L1204_); trivial. % 21.88/22.05 (* end of lemma zenon_L1222_ *) % 21.88/22.05 assert (zenon_L1223_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((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))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.88/22.05 do 0 intro. intros zenon_H15c zenon_Ha4 zenon_Ha0 zenon_H2a zenon_H1cf zenon_H163 zenon_H4e zenon_H25 zenon_H1d4 zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H40 zenon_H156 zenon_H158 zenon_Ha9 zenon_H1b4 zenon_Hc3 zenon_H13a zenon_H5c. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.88/22.05 exact (zenon_Hec zenon_H5c). % 21.88/22.05 apply (zenon_L1176_); trivial. % 21.88/22.05 (* end of lemma zenon_L1223_ *) % 21.88/22.05 assert (zenon_L1224_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.88/22.05 do 0 intro. intros zenon_H15c zenon_H173 zenon_H2a zenon_H40 zenon_H1b3 zenon_H158 zenon_H5c. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.88/22.05 exact (zenon_Hec zenon_H5c). % 21.88/22.05 apply (zenon_L304_); trivial. % 21.88/22.05 (* end of lemma zenon_L1224_ *) % 21.88/22.05 assert (zenon_L1225_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (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 (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 21.88/22.05 do 0 intro. intros zenon_H169 zenon_H5c zenon_H13a zenon_Hc3 zenon_H1b4 zenon_Ha9 zenon_H158 zenon_H156 zenon_H40 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H25 zenon_H4e zenon_H163 zenon_H1cf zenon_H2a zenon_Ha0 zenon_Ha4 zenon_H15c. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 21.88/22.05 apply (zenon_L1223_); trivial. % 21.88/22.05 apply (zenon_L1224_); trivial. % 21.88/22.05 (* end of lemma zenon_L1225_ *) % 21.88/22.05 assert (zenon_L1226_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.05 do 0 intro. intros zenon_H25e zenon_H115 zenon_Hf5 zenon_H5c zenon_H196 zenon_H93 zenon_Hc3 zenon_H1b4. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H38 | zenon_intro zenon_H25f ]. % 21.88/22.05 apply (zenon_L1162_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H155 | zenon_intro zenon_H260 ]. % 21.88/22.05 apply (zenon_L192_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H9e ]. % 21.88/22.05 apply (zenon_L167_); trivial. % 21.88/22.05 apply (zenon_L602_); trivial. % 21.88/22.05 (* end of lemma zenon_L1226_ *) % 21.88/22.05 assert (zenon_L1227_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e0) (e2)) = (op (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 (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.88/22.05 do 0 intro. intros zenon_H19a zenon_Hcc zenon_H1c3 zenon_H68 zenon_H117 zenon_H6f zenon_Ha9 zenon_H13e zenon_H190 zenon_H16a zenon_H25b zenon_H186 zenon_H27e zenon_H129 zenon_H189 zenon_H195 zenon_H18d zenon_Hb6 zenon_H13c zenon_H20f zenon_H73 zenon_H159 zenon_H13a zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H48 zenon_H1b4 zenon_H93 zenon_H196 zenon_H5c zenon_Hf5 zenon_H25e zenon_Ha0 zenon_Hc3. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.88/22.05 apply (zenon_L1213_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.88/22.05 apply (zenon_L157_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.88/22.05 apply (zenon_L1226_); trivial. % 21.88/22.05 apply (zenon_L505_); trivial. % 21.88/22.05 (* end of lemma zenon_L1227_ *) % 21.88/22.05 assert (zenon_L1228_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.88/22.05 do 0 intro. intros zenon_H2f zenon_H19a zenon_H26d zenon_H48 zenon_H1b4 zenon_H93 zenon_H196 zenon_H5c zenon_Hf5 zenon_H25e zenon_Ha0 zenon_Hc3. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.88/22.05 apply (zenon_L756_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.88/22.05 apply (zenon_L157_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.88/22.05 apply (zenon_L1226_); trivial. % 21.88/22.05 apply (zenon_L505_); trivial. % 21.88/22.05 (* end of lemma zenon_L1228_ *) % 21.88/22.05 assert (zenon_L1229_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.88/22.05 do 0 intro. intros zenon_Hcc zenon_H1c3 zenon_H68 zenon_H117 zenon_H6f zenon_Ha9 zenon_H13e zenon_H190 zenon_H16a zenon_H25b zenon_H27e zenon_H195 zenon_H18d zenon_Hb6 zenon_H13c zenon_H73 zenon_H13a zenon_H1fb zenon_H281 zenon_Ha0 zenon_H25e zenon_Hf5 zenon_H196 zenon_H48 zenon_H26d zenon_H19a zenon_H5d zenon_H186 zenon_H5c zenon_H94 zenon_H189 zenon_H93 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc3. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.88/22.05 apply (zenon_L2_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.88/22.05 exact (zenon_Hec zenon_H5c). % 21.88/22.05 apply (zenon_L1227_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.88/22.05 apply (zenon_L1228_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.88/22.05 apply (zenon_L1180_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.88/22.05 apply (zenon_L1206_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.88/22.05 apply (zenon_L11_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.88/22.05 apply (zenon_L1207_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.88/22.05 apply (zenon_L1191_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.88/22.05 apply (zenon_L1208_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.88/22.05 apply (zenon_L1209_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.88/22.05 apply (zenon_L37_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.88/22.05 apply (zenon_L1201_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.88/22.05 apply (zenon_L1202_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.88/22.05 apply (zenon_L1203_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.88/22.05 apply (zenon_L190_); trivial. % 21.88/22.05 apply (zenon_L1204_); trivial. % 21.88/22.05 (* end of lemma zenon_L1229_ *) % 21.88/22.05 assert (zenon_L1230_ : (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((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 (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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 21.88/22.05 do 0 intro. intros zenon_Ha4 zenon_H129 zenon_H20f zenon_H189 zenon_H94 zenon_H5c zenon_H186 zenon_H5d zenon_H19a zenon_H26d zenon_H48 zenon_H196 zenon_Hf5 zenon_H25e zenon_H281 zenon_H1fb zenon_H13a zenon_H73 zenon_H13c zenon_Hb6 zenon_H18d zenon_H195 zenon_H27e zenon_H25b zenon_H16a zenon_H190 zenon_H13e zenon_Ha9 zenon_H6f zenon_H117 zenon_H68 zenon_H1c3 zenon_Hcc zenon_H8b zenon_H1ba zenon_H191 zenon_Ha0 zenon_H31 zenon_Hc3 zenon_H1b4. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.05 exact (zenon_Ha4 zenon_H9f). % 21.88/22.05 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.88/22.05 apply (zenon_L1192_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.88/22.05 exact (zenon_H1ba zenon_H6d). % 21.88/22.05 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.88/22.05 exact (zenon_H8b zenon_H8a). % 21.88/22.05 apply (zenon_L1229_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.05 apply (zenon_L68_); trivial. % 21.88/22.05 apply (zenon_L602_); trivial. % 21.88/22.05 (* end of lemma zenon_L1230_ *) % 21.88/22.05 assert (zenon_L1231_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> False). % 21.88/22.05 do 0 intro. intros zenon_H89 zenon_Ha4 zenon_H5c zenon_H19a zenon_Ha0 zenon_H25e zenon_Hcc zenon_H1c3 zenon_H68 zenon_H13e zenon_H190 zenon_H16a zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H196 zenon_H18d zenon_Hb6 zenon_H13c zenon_H20f zenon_H73 zenon_H1b4 zenon_H13a zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H1ba zenon_Ha9 zenon_H6f zenon_H191 zenon_H129 zenon_Hc3 zenon_H117 zenon_H31. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.88/22.05 apply (zenon_L1230_); trivial. % 21.88/22.05 apply (zenon_L1230_); trivial. % 21.88/22.05 (* end of lemma zenon_L1231_ *) % 21.88/22.05 assert (zenon_L1232_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((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)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.88/22.05 do 0 intro. intros zenon_H15c zenon_H15d zenon_Hf5 zenon_H72 zenon_H191 zenon_H1cb zenon_H1a2 zenon_Hb6 zenon_Ha9 zenon_H6d zenon_H1b7 zenon_Hc3 zenon_H1c6 zenon_H48 zenon_H158 zenon_H156 zenon_H40 zenon_H173 zenon_Ha0 zenon_Hcc zenon_H1c3 zenon_H68 zenon_H117 zenon_H6f zenon_H13e zenon_H190 zenon_H16a zenon_H25b zenon_H186 zenon_H27e zenon_H129 zenon_H189 zenon_H195 zenon_H196 zenon_H18d zenon_H13c zenon_H20f zenon_H73 zenon_H1b4 zenon_H13a zenon_H26d zenon_H1fb zenon_H236 zenon_H5c. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.88/22.05 exact (zenon_Hec zenon_H5c). % 21.88/22.05 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 21.88/22.05 apply (zenon_L1197_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 21.88/22.05 apply (zenon_L273_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 21.88/22.05 apply (zenon_L1199_); trivial. % 21.88/22.05 apply (zenon_L1205_); trivial. % 21.88/22.05 (* end of lemma zenon_L1232_ *) % 21.88/22.05 assert (zenon_L1233_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 21.88/22.05 do 0 intro. intros zenon_H1ec zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H19a zenon_H25e zenon_H94 zenon_H281 zenon_H1ef zenon_H5d zenon_Ha4 zenon_H15d zenon_Hf5 zenon_H191 zenon_H1cb zenon_H1a2 zenon_Hb6 zenon_Ha9 zenon_H1b7 zenon_H1c6 zenon_H48 zenon_H158 zenon_H156 zenon_H173 zenon_Ha0 zenon_Hcc zenon_H1c3 zenon_H68 zenon_H117 zenon_H6f zenon_H13e zenon_H190 zenon_H16a zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H195 zenon_H196 zenon_H18d zenon_H13c zenon_H73 zenon_H13a zenon_H26d zenon_H1fb zenon_H236 zenon_H5c zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc3. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.88/22.05 apply (zenon_L2_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 21.88/22.05 apply (zenon_L1225_); trivial. % 21.88/22.05 apply (zenon_L1225_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.88/22.05 apply (zenon_L1231_); trivial. % 21.88/22.05 apply (zenon_L645_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.88/22.05 apply (zenon_L1180_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.88/22.05 apply (zenon_L1206_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.88/22.05 apply (zenon_L11_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.88/22.05 apply (zenon_L1207_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.88/22.05 apply (zenon_L1191_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.88/22.05 apply (zenon_L1194_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.88/22.05 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 21.88/22.05 apply (zenon_L1232_); trivial. % 21.88/22.05 apply (zenon_L1232_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.88/22.05 apply (zenon_L37_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.88/22.05 apply (zenon_L1201_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.88/22.05 apply (zenon_L1202_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.88/22.05 apply (zenon_L1203_); trivial. % 21.88/22.05 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.88/22.05 apply (zenon_L190_); trivial. % 21.88/22.05 apply (zenon_L1204_); trivial. % 21.88/22.05 (* end of lemma zenon_L1233_ *) % 21.88/22.05 assert (zenon_L1234_ : ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 21.88/22.05 do 0 intro. intros zenon_H5c zenon_H13a zenon_Hc3 zenon_H1b4 zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_Ha4 zenon_H19a zenon_H25e zenon_Hcc zenon_H1c3 zenon_H68 zenon_H13e zenon_H190 zenon_H16a zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H196 zenon_H18d zenon_Hb6 zenon_H13c zenon_H20f zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H6f zenon_H129 zenon_H117 zenon_H1ef zenon_H15d zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H236. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H191 | zenon_intro zenon_H93 ]. % 21.88/22.05 apply (zenon_L1233_); trivial. % 21.88/22.05 apply (zenon_L1229_); trivial. % 21.88/22.05 (* end of lemma zenon_L1234_ *) % 21.88/22.05 assert (zenon_L1235_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((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 (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> False). % 21.88/22.05 do 0 intro. intros zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H1b4 zenon_Hc3 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H20f zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H129 zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H38 ]. % 21.88/22.05 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H159 | zenon_intro zenon_H5c ]. % 21.88/22.06 apply (zenon_L1222_); trivial. % 21.88/22.06 apply (zenon_L1234_); trivial. % 21.88/22.06 apply (zenon_L1216_); trivial. % 21.88/22.06 (* end of lemma zenon_L1235_ *) % 21.88/22.06 assert (zenon_L1236_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H5c zenon_H129 zenon_H93 zenon_H1bb. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 21.88/22.06 apply (zenon_L413_); trivial. % 21.88/22.06 apply (zenon_L1235_); trivial. % 21.88/22.06 (* end of lemma zenon_L1236_ *) % 21.88/22.06 assert (zenon_L1237_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H100 zenon_H141 zenon_H54 zenon_Hc4 zenon_H1d5 zenon_H67 zenon_H201 zenon_He7 zenon_H192 zenon_H3d zenon_H34 zenon_H12e zenon_H9f zenon_H24 zenon_H1a3 zenon_H159 zenon_H1c2 zenon_H24e zenon_H7d zenon_H1cd zenon_H1c7 zenon_H1a8 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H129 zenon_H93 zenon_H1bb. % 21.88/22.06 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.06 apply (zenon_L69_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.88/22.06 apply (zenon_L214_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.88/22.06 apply (zenon_L186_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.88/22.06 apply (zenon_L439_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.88/22.06 apply (zenon_L55_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.88/22.06 exact (zenon_H159 zenon_H10c). % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.88/22.06 apply (zenon_L217_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.88/22.06 apply (zenon_L152_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.88/22.06 apply (zenon_L1172_); trivial. % 21.88/22.06 apply (zenon_L1162_); trivial. % 21.88/22.06 exact (zenon_H1c7 zenon_Hac). % 21.88/22.06 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.88/22.06 apply (zenon_L214_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.88/22.06 apply (zenon_L1175_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.88/22.06 apply (zenon_L439_); trivial. % 21.88/22.06 apply (zenon_L965_); trivial. % 21.88/22.06 apply (zenon_L1236_); trivial. % 21.88/22.06 (* end of lemma zenon_L1237_ *) % 21.88/22.06 assert (zenon_L1238_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H1cf zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Ha9 zenon_H1a2 zenon_H48 zenon_H77 zenon_H201 zenon_Hf3 zenon_H68 zenon_H93 zenon_H1c2 zenon_H171 zenon_H1cd. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.88/22.06 apply (zenon_L365_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.88/22.06 apply (zenon_L62_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.88/22.06 apply (zenon_L207_); trivial. % 21.88/22.06 apply (zenon_L240_); trivial. % 21.88/22.06 (* end of lemma zenon_L1238_ *) % 21.88/22.06 assert (zenon_L1239_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((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). % 21.88/22.06 do 0 intro. intros zenon_H141 zenon_H54 zenon_He7 zenon_Hf0 zenon_H1cd zenon_H171 zenon_H1c2 zenon_H93 zenon_H68 zenon_Hf3 zenon_H201 zenon_H77 zenon_H48 zenon_H1a2 zenon_Ha9 zenon_Ha0 zenon_Hb6 zenon_H1cf zenon_H196 zenon_H38. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.88/22.06 apply (zenon_L217_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.88/22.06 apply (zenon_L929_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.88/22.06 apply (zenon_L1238_); trivial. % 21.88/22.06 apply (zenon_L1162_); trivial. % 21.88/22.06 (* end of lemma zenon_L1239_ *) % 21.88/22.06 assert (zenon_L1240_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((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)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((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). % 21.88/22.06 do 0 intro. intros zenon_H1a8 zenon_H3d zenon_H3f zenon_H189 zenon_H141 zenon_H54 zenon_He7 zenon_Hf0 zenon_H1cd zenon_H1c2 zenon_H93 zenon_H68 zenon_Hf3 zenon_H201 zenon_H77 zenon_H48 zenon_H1a2 zenon_Ha9 zenon_Ha0 zenon_Hb6 zenon_H1cf zenon_H196 zenon_H38. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.88/22.06 apply (zenon_L214_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.88/22.06 apply (zenon_L186_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.88/22.06 apply (zenon_L439_); trivial. % 21.88/22.06 apply (zenon_L1239_); trivial. % 21.88/22.06 (* end of lemma zenon_L1240_ *) % 21.88/22.06 assert (zenon_L1241_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H36 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H20f zenon_H5c zenon_H129 zenon_H93 zenon_H1bb. % 21.88/22.06 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 21.88/22.06 apply (zenon_L1236_); trivial. % 21.88/22.06 (* end of lemma zenon_L1241_ *) % 21.88/22.06 assert (zenon_L1242_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_Ha0 zenon_Hdd zenon_H1c7. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.88/22.06 apply (zenon_L55_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.88/22.06 exact (zenon_H159 zenon_H10c). % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.88/22.06 apply (zenon_L152_); trivial. % 21.88/22.06 exact (zenon_H1c7 zenon_Hac). % 21.88/22.06 (* end of lemma zenon_L1242_ *) % 21.88/22.06 assert (zenon_L1243_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e1) (e2)) = (e0)) -> (((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 (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 21.88/22.06 do 0 intro. intros zenon_He2 zenon_H1bb zenon_H93 zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H36 zenon_Hf3 zenon_H1a8 zenon_H141 zenon_H54 zenon_Hf0 zenon_H1cd zenon_H1c2 zenon_H201 zenon_H38 zenon_H100 zenon_H1c7 zenon_Ha0 zenon_H159 zenon_H3d zenon_Hb6 zenon_H1c6 zenon_H7d zenon_H34. % 21.88/22.06 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.88/22.06 apply (zenon_L317_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.88/22.06 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.88/22.06 apply (zenon_L69_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.88/22.06 apply (zenon_L1240_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.88/22.06 apply (zenon_L117_); trivial. % 21.88/22.06 apply (zenon_L1241_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.88/22.06 apply (zenon_L1242_); trivial. % 21.88/22.06 apply (zenon_L802_); trivial. % 21.88/22.06 (* end of lemma zenon_L1243_ *) % 21.88/22.06 assert (zenon_L1244_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.88/22.06 do 0 intro. intros zenon_H141 zenon_H48 zenon_H54 zenon_He7 zenon_Hf0 zenon_Hef zenon_H133 zenon_H196 zenon_H38. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.88/22.06 apply (zenon_L217_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.88/22.06 apply (zenon_L929_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.88/22.06 apply (zenon_L265_); trivial. % 21.88/22.06 apply (zenon_L1162_); trivial. % 21.88/22.06 (* end of lemma zenon_L1244_ *) % 21.88/22.06 assert (zenon_L1245_ : (((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 (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H38 zenon_H196 zenon_Hef zenon_Hf0 zenon_He7 zenon_H54 zenon_H48 zenon_H141 zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_H1a3 zenon_H190 zenon_H186 zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H1c7. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.88/22.06 apply (zenon_L900_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.88/22.06 exact (zenon_H159 zenon_H10c). % 21.88/22.06 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.88/22.06 apply (zenon_L1244_); trivial. % 21.88/22.06 apply (zenon_L1174_); trivial. % 21.88/22.06 (* end of lemma zenon_L1245_ *) % 21.88/22.06 assert (zenon_L1246_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (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)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H1c6 zenon_Hb6 zenon_H159 zenon_H93 zenon_H68 zenon_H201 zenon_H66 zenon_H171 zenon_He7 zenon_H163 zenon_H192 zenon_H3d zenon_H34 zenon_H12e zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb zenon_Ha0 zenon_H54 zenon_H141 zenon_H1c7. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.88/22.06 apply (zenon_L55_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.88/22.06 exact (zenon_H159 zenon_H10c). % 21.88/22.06 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.88/22.06 apply (zenon_L217_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.88/22.06 apply (zenon_L152_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.88/22.06 apply (zenon_L94_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.88/22.06 apply (zenon_L965_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.88/22.06 apply (zenon_L255_); trivial. % 21.88/22.06 apply (zenon_L1159_); trivial. % 21.88/22.06 apply (zenon_L158_); trivial. % 21.88/22.06 exact (zenon_H1c7 zenon_Hac). % 21.88/22.06 (* end of lemma zenon_L1246_ *) % 21.88/22.06 assert (zenon_L1247_ : (((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)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H125 zenon_H1d5 zenon_H66 zenon_H77 zenon_H3c zenon_H94 zenon_H93 zenon_H34 zenon_H68. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.88/22.06 apply (zenon_L252_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.88/22.06 apply (zenon_L24_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.88/22.06 apply (zenon_L38_); trivial. % 21.88/22.06 apply (zenon_L291_); trivial. % 21.88/22.06 (* end of lemma zenon_L1247_ *) % 21.88/22.06 assert (zenon_L1248_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H13a zenon_Hc4 zenon_H1a3 zenon_H10c zenon_H11a zenon_H33 zenon_H121 zenon_Hb6 zenon_H3d zenon_Ha9 zenon_H66 zenon_H38 zenon_Ha0. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.06 apply (zenon_L538_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.06 apply (zenon_L55_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.06 apply (zenon_L193_); trivial. % 21.88/22.06 apply (zenon_L156_); trivial. % 21.88/22.06 (* end of lemma zenon_L1248_ *) % 21.88/22.06 assert (zenon_L1249_ : (((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)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_H173 zenon_H10c zenon_Ha9 zenon_H66 zenon_H38 zenon_Ha0. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.06 apply (zenon_L253_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.06 apply (zenon_L120_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.06 apply (zenon_L193_); trivial. % 21.88/22.06 apply (zenon_L156_); trivial. % 21.88/22.06 (* end of lemma zenon_L1249_ *) % 21.88/22.06 assert (zenon_L1250_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H139 zenon_H77 zenon_H121 zenon_H209 zenon_H11a zenon_H177 zenon_Hc4 zenon_Ha0 zenon_Ha9 zenon_H10c zenon_H173 zenon_H47 zenon_Hb6 zenon_H13a zenon_H38 zenon_H68. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.06 apply (zenon_L251_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.06 apply (zenon_L253_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.06 apply (zenon_L110_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.06 apply (zenon_L393_); trivial. % 21.88/22.06 apply (zenon_L156_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.06 apply (zenon_L1249_); trivial. % 21.88/22.06 apply (zenon_L165_); trivial. % 21.88/22.06 (* end of lemma zenon_L1250_ *) % 21.88/22.06 assert (zenon_L1251_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (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 (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H13a zenon_H1a3 zenon_H33 zenon_Hb6 zenon_H3d zenon_Hc4 zenon_H177 zenon_H10c zenon_H11a zenon_H209 zenon_H121 zenon_H38 zenon_Ha0. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.06 apply (zenon_L538_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.06 apply (zenon_L55_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.06 apply (zenon_L393_); trivial. % 21.88/22.06 apply (zenon_L156_); trivial. % 21.88/22.06 (* end of lemma zenon_L1251_ *) % 21.88/22.06 assert (zenon_L1252_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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 (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H13a zenon_Hc4 zenon_H1a3 zenon_H11a zenon_H33 zenon_H121 zenon_H173 zenon_H10c zenon_Hb6 zenon_H153 zenon_H38 zenon_Ha0. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.06 apply (zenon_L538_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.06 apply (zenon_L120_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.06 apply (zenon_L95_); trivial. % 21.88/22.06 apply (zenon_L156_); trivial. % 21.88/22.06 (* end of lemma zenon_L1252_ *) % 21.88/22.06 assert (zenon_L1253_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.88/22.06 do 0 intro. intros zenon_H15d zenon_H68 zenon_Ha9 zenon_H77 zenon_H139 zenon_H209 zenon_H177 zenon_Ha0 zenon_Hb6 zenon_H10c zenon_H173 zenon_H121 zenon_H33 zenon_H11a zenon_H1a3 zenon_Hc4 zenon_H13a zenon_H38 zenon_H48. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.88/22.06 apply (zenon_L1250_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.88/22.06 apply (zenon_L1251_); trivial. % 21.88/22.06 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.88/22.06 apply (zenon_L1252_); trivial. % 21.88/22.06 apply (zenon_L246_); trivial. % 21.88/22.07 (* end of lemma zenon_L1253_ *) % 21.88/22.07 assert (zenon_L1254_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H13a zenon_H47 zenon_Ha9 zenon_H6e zenon_Hb6 zenon_H153 zenon_H38 zenon_Ha0. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.07 apply (zenon_L253_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.07 apply (zenon_L110_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.07 apply (zenon_L95_); trivial. % 21.88/22.07 apply (zenon_L156_); trivial. % 21.88/22.07 (* end of lemma zenon_L1254_ *) % 21.88/22.07 assert (zenon_L1255_ : (~((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H162 zenon_Hb9 zenon_H1bb zenon_H129 zenon_H5c zenon_H20f zenon_H38 zenon_H1b4 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H102 zenon_H18a. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.88/22.07 apply (zenon_L166_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.88/22.07 apply (zenon_L206_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.88/22.07 apply (zenon_L1236_); trivial. % 21.88/22.07 apply (zenon_L268_); trivial. % 21.88/22.07 (* end of lemma zenon_L1255_ *) % 21.88/22.07 assert (zenon_L1256_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H24e zenon_H34 zenon_H7d zenon_H106 zenon_H1cd zenon_H1b7 zenon_H17c zenon_H10c zenon_H11a. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_He0 | zenon_intro zenon_H24f ]. % 21.88/22.07 apply (zenon_L802_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H7f | zenon_intro zenon_H250 ]. % 21.88/22.07 apply (zenon_L331_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H171 | zenon_intro zenon_Hac ]. % 21.88/22.07 apply (zenon_L188_); trivial. % 21.88/22.07 apply (zenon_L79_); trivial. % 21.88/22.07 (* end of lemma zenon_L1256_ *) % 21.88/22.07 assert (zenon_L1257_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H183 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H5c zenon_H129 zenon_Hb9 zenon_H162 zenon_H6e zenon_H192 zenon_H1c7 zenon_H1bb zenon_H18a zenon_H1cb zenon_Hc4 zenon_H1f1 zenon_H53 zenon_H48 zenon_H12e zenon_H24e zenon_H34 zenon_H7d zenon_H106 zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.88/22.07 apply (zenon_L1255_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.88/22.07 apply (zenon_L1128_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.88/22.07 apply (zenon_L849_); trivial. % 21.88/22.07 apply (zenon_L1256_); trivial. % 21.88/22.07 (* end of lemma zenon_L1257_ *) % 21.88/22.07 assert (zenon_L1258_ : ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H65 zenon_H191 zenon_H183 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H5c zenon_H129 zenon_H162 zenon_H6e zenon_H192 zenon_H1c7 zenon_H1bb zenon_H18a zenon_H1cb zenon_Hc4 zenon_H1f1 zenon_H53 zenon_H48 zenon_H12e zenon_H24e zenon_H34 zenon_H7d zenon_H106 zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.88/22.07 apply (zenon_L43_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.88/22.07 apply (zenon_L113_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.88/22.07 exact (zenon_H191 zenon_H110). % 21.88/22.07 apply (zenon_L1257_); trivial. % 21.88/22.07 (* end of lemma zenon_L1258_ *) % 21.88/22.07 assert (zenon_L1259_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H1c3 zenon_H68 zenon_H38 zenon_H77 zenon_H5c zenon_H8a zenon_H1c2 zenon_H102 zenon_H18a. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.88/22.07 apply (zenon_L165_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.88/22.07 apply (zenon_L206_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.88/22.07 apply (zenon_L207_); trivial. % 21.88/22.07 apply (zenon_L268_); trivial. % 21.88/22.07 (* end of lemma zenon_L1259_ *) % 21.88/22.07 assert (zenon_L1260_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H160 zenon_H1cb. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.88/22.07 apply (zenon_L165_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.88/22.07 apply (zenon_L206_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.88/22.07 apply (zenon_L413_); trivial. % 21.88/22.07 apply (zenon_L236_); trivial. % 21.88/22.07 (* end of lemma zenon_L1260_ *) % 21.88/22.07 assert (zenon_L1261_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (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)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H183 zenon_H18a zenon_H1c2 zenon_H8a zenon_H6e zenon_H192 zenon_H1cb zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H5c zenon_H129 zenon_Hc4 zenon_H77 zenon_H68 zenon_H1c3 zenon_H24e zenon_H34 zenon_H7d zenon_H106 zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.88/22.07 apply (zenon_L1259_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.88/22.07 apply (zenon_L1128_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.88/22.07 apply (zenon_L1260_); trivial. % 21.88/22.07 apply (zenon_L1256_); trivial. % 21.88/22.07 (* end of lemma zenon_L1261_ *) % 21.88/22.07 assert (zenon_L1262_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (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 (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) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H201 zenon_H47 zenon_H14c zenon_H12e zenon_H1f1 zenon_H1c7 zenon_H162 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H196 zenon_H16a zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H191 zenon_H53 zenon_H11a zenon_H10c zenon_H1b7 zenon_H1cd zenon_H7d zenon_H34 zenon_H24e zenon_H1c3 zenon_H68 zenon_H5c zenon_H192 zenon_H6e zenon_H1c2 zenon_H18a zenon_H183 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.88/22.07 apply (zenon_L1254_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.88/22.07 apply (zenon_L138_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.88/22.07 apply (zenon_L255_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.88/22.07 apply (zenon_L1258_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.88/22.07 apply (zenon_L56_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.88/22.07 apply (zenon_L1261_); trivial. % 21.88/22.07 apply (zenon_L1159_); trivial. % 21.88/22.07 (* end of lemma zenon_L1262_ *) % 21.88/22.07 assert (zenon_L1263_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 21.88/22.07 do 0 intro. intros zenon_H266 zenon_H2d zenon_H55 zenon_H105 zenon_H190 zenon_H8a zenon_Hf0 zenon_H10c. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_Hdd | zenon_intro zenon_H267 ]. % 21.88/22.07 apply (zenon_L702_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H53 | zenon_intro zenon_H268 ]. % 21.88/22.07 apply (zenon_L143_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H6d | zenon_intro zenon_H10d ]. % 21.88/22.07 apply (zenon_L366_); trivial. % 21.88/22.07 apply (zenon_L74_); trivial. % 21.88/22.07 (* end of lemma zenon_L1263_ *) % 21.88/22.07 assert (zenon_L1264_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.88/22.07 do 0 intro. intros zenon_H13f zenon_H7f zenon_H1f1 zenon_H1bb zenon_H129 zenon_H20f zenon_H38 zenon_H1b4 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H2d zenon_Hf0 zenon_H10c zenon_H6e zenon_H195 zenon_H5c. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.88/22.07 apply (zenon_L217_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.88/22.07 apply (zenon_L284_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.88/22.07 apply (zenon_L27_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.88/22.07 apply (zenon_L21_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.88/22.07 apply (zenon_L1263_); trivial. % 21.88/22.07 apply (zenon_L1236_); trivial. % 21.88/22.07 apply (zenon_L149_); trivial. % 21.88/22.07 (* end of lemma zenon_L1264_ *) % 21.88/22.07 assert (zenon_L1265_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Ha0 zenon_Hf3 zenon_H191 zenon_H1a3. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.88/22.07 apply (zenon_L95_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.88/22.07 apply (zenon_L162_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.88/22.07 exact (zenon_H191 zenon_H110). % 21.88/22.07 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.07 (* end of lemma zenon_L1265_ *) % 21.88/22.07 assert (zenon_L1266_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (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 (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H1cf zenon_Ha0 zenon_Ha9 zenon_H10c zenon_H173 zenon_H47 zenon_Hb6 zenon_H13a zenon_H4e zenon_H76 zenon_H1ef zenon_H65 zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H1cb. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.88/22.07 apply (zenon_L1249_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.88/22.07 apply (zenon_L83_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.88/22.07 apply (zenon_L533_); trivial. % 21.88/22.07 apply (zenon_L1260_); trivial. % 21.88/22.07 (* end of lemma zenon_L1266_ *) % 21.88/22.07 assert (zenon_L1267_ : ((op (e2) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H2d zenon_H6e zenon_H72 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H5c zenon_H129 zenon_H1bb. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.88/22.07 apply (zenon_L27_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.88/22.07 apply (zenon_L21_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.88/22.07 apply (zenon_L87_); trivial. % 21.88/22.07 apply (zenon_L1236_); trivial. % 21.88/22.07 (* end of lemma zenon_L1267_ *) % 21.88/22.07 assert (zenon_L1268_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.88/22.07 do 0 intro. intros zenon_H13f zenon_H65 zenon_H77 zenon_H7f zenon_H1f1 zenon_H48 zenon_H14c zenon_H195 zenon_H5c. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.88/22.07 apply (zenon_L30_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.88/22.07 apply (zenon_L284_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.88/22.07 apply (zenon_L255_); trivial. % 21.88/22.07 apply (zenon_L149_); trivial. % 21.88/22.07 (* end of lemma zenon_L1268_ *) % 21.88/22.07 assert (zenon_L1269_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.88/22.07 do 0 intro. intros zenon_He4 zenon_H6e zenon_H234 zenon_Hdd zenon_H13f zenon_H65 zenon_H77 zenon_H1f1 zenon_H48 zenon_H14c zenon_H195 zenon_H5c. % 21.88/22.07 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.88/22.07 apply (zenon_L214_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.88/22.07 apply (zenon_L484_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.88/22.07 apply (zenon_L111_); trivial. % 21.88/22.07 apply (zenon_L1268_); trivial. % 21.88/22.07 (* end of lemma zenon_L1269_ *) % 21.88/22.07 assert (zenon_L1270_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 21.88/22.07 do 0 intro. intros zenon_H140 zenon_Ha0 zenon_Hfe zenon_H72 zenon_H68 zenon_H5c zenon_H195 zenon_H48 zenon_H1f1 zenon_H77 zenon_H65 zenon_H13f zenon_Hdd zenon_H234 zenon_H6e zenon_He4 zenon_Hbc zenon_H34. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.88/22.07 apply (zenon_L68_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.88/22.07 apply (zenon_L62_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.88/22.07 apply (zenon_L1269_); trivial. % 21.88/22.07 apply (zenon_L328_); trivial. % 21.88/22.07 (* end of lemma zenon_L1270_ *) % 21.88/22.07 assert (zenon_L1271_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((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 (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.88/22.07 do 0 intro. intros zenon_Hfa zenon_Hc4 zenon_H47 zenon_H10c zenon_H38 zenon_H196 zenon_H13f zenon_H65 zenon_H7f zenon_H1f1 zenon_H48 zenon_H195 zenon_H140 zenon_Ha0 zenon_Hfe zenon_H68 zenon_H234 zenon_H6e zenon_He4 zenon_Hbc zenon_H34 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H141 zenon_H5c zenon_H77. % 21.88/22.07 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.88/22.07 apply (zenon_L1266_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.88/22.07 apply (zenon_L226_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.88/22.07 apply (zenon_L1267_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.88/22.07 apply (zenon_L1270_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.88/22.07 apply (zenon_L1268_); trivial. % 21.88/22.07 apply (zenon_L1162_); trivial. % 21.88/22.07 apply (zenon_L206_); trivial. % 21.88/22.07 (* end of lemma zenon_L1271_ *) % 21.88/22.07 assert (zenon_L1272_ : ((op (e3) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (op (e3) (op (e3) (e3))))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H11d zenon_H17c zenon_H255. % 21.88/22.07 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H244 | zenon_intro zenon_H245 ]. % 21.88/22.07 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((e0) = (op (e3) (op (e3) (e3))))). % 21.88/22.07 intro zenon_D_pnotp. % 21.88/22.07 apply zenon_H255. % 21.88/22.07 rewrite <- zenon_D_pnotp. % 21.88/22.07 exact zenon_H244. % 21.88/22.07 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 21.88/22.07 cut (((op (e3) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H256]. % 21.88/22.07 congruence. % 21.88/22.07 cut (((op (e3) (e2)) = (e0)) = ((op (e3) (op (e3) (e3))) = (e0))). % 21.88/22.07 intro zenon_D_pnotp. % 21.88/22.07 apply zenon_H256. % 21.88/22.07 rewrite <- zenon_D_pnotp. % 21.88/22.07 exact zenon_H11d. % 21.88/22.07 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 21.88/22.07 cut (((op (e3) (e2)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H27d]. % 21.88/22.07 congruence. % 21.88/22.07 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H244 | zenon_intro zenon_H245 ]. % 21.88/22.07 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e2)) = (op (e3) (op (e3) (e3))))). % 21.88/22.07 intro zenon_D_pnotp. % 21.88/22.07 apply zenon_H27d. % 21.88/22.07 rewrite <- zenon_D_pnotp. % 21.88/22.07 exact zenon_H244. % 21.88/22.07 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 21.88/22.07 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 21.88/22.07 congruence. % 21.88/22.07 apply (zenon_L1156_); trivial. % 21.88/22.07 apply zenon_H245. apply refl_equal. % 21.88/22.07 apply zenon_H245. apply refl_equal. % 21.88/22.07 apply zenon_H46. apply refl_equal. % 21.88/22.07 apply zenon_H245. apply refl_equal. % 21.88/22.07 apply zenon_H245. apply refl_equal. % 21.88/22.07 (* end of lemma zenon_L1272_ *) % 21.88/22.07 assert (zenon_L1273_ : ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 21.88/22.07 do 0 intro. intros zenon_H105 zenon_H11d zenon_H17c. % 21.88/22.07 apply (zenon_notand_s _ _ ax15); [ zenon_intro zenon_H286 | zenon_intro zenon_H285 ]. % 21.88/22.07 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H24b ]. % 21.88/22.07 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e1) = (op (op (e3) (e3)) (op (e3) (e3))))). % 21.88/22.07 intro zenon_D_pnotp. % 21.88/22.07 apply zenon_H286. % 21.88/22.07 rewrite <- zenon_D_pnotp. % 21.88/22.07 exact zenon_H24a. % 21.88/22.07 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 21.88/22.07 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 21.88/22.07 congruence. % 21.88/22.07 cut (((op (e2) (e2)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 21.88/22.07 intro zenon_D_pnotp. % 21.88/22.07 apply zenon_H287. % 21.88/22.07 rewrite <- zenon_D_pnotp. % 21.88/22.07 exact zenon_H105. % 21.88/22.07 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 21.88/22.07 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 21.88/22.07 congruence. % 21.88/22.07 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H24b ]. % 21.88/22.07 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))))). % 21.88/22.07 intro zenon_D_pnotp. % 21.88/22.07 apply zenon_H27b. % 21.88/22.07 rewrite <- zenon_D_pnotp. % 21.88/22.07 exact zenon_H24a. % 21.88/22.07 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 21.88/22.07 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 21.88/22.07 congruence. % 21.88/22.07 apply (zenon_L1155_); trivial. % 21.88/22.07 apply zenon_H24b. apply refl_equal. % 21.88/22.07 apply zenon_H24b. apply refl_equal. % 21.88/22.07 apply zenon_H4a. apply refl_equal. % 21.88/22.07 apply zenon_H24b. apply refl_equal. % 21.88/22.07 apply zenon_H24b. apply refl_equal. % 21.88/22.07 apply (zenon_notand_s _ _ zenon_H285); [ zenon_intro zenon_H27c | zenon_intro zenon_H255 ]. % 21.88/22.07 apply zenon_H27c. apply sym_equal. exact zenon_H17c. % 21.88/22.07 apply (zenon_L1272_); trivial. % 21.88/22.07 (* end of lemma zenon_L1273_ *) % 21.88/22.07 assert (zenon_L1274_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H231 zenon_H105 zenon_H7f zenon_H1cd zenon_H1cb zenon_H17c zenon_H1a3. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H11d | zenon_intro zenon_H232 ]. % 21.88/22.07 apply (zenon_L1273_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H106 | zenon_intro zenon_H233 ]. % 21.88/22.07 apply (zenon_L331_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H160 | zenon_intro zenon_Hbb ]. % 21.88/22.07 apply (zenon_L236_); trivial. % 21.88/22.07 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.07 (* end of lemma zenon_L1274_ *) % 21.88/22.07 assert (zenon_L1275_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H183 zenon_H18a zenon_H1c2 zenon_H5c zenon_H77 zenon_H38 zenon_H68 zenon_H1c3 zenon_H6e zenon_H192 zenon_H8a zenon_H104 zenon_H231 zenon_H105 zenon_H7f zenon_H1cd zenon_H1cb zenon_H1a3. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.88/22.07 apply (zenon_L1259_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.88/22.07 apply (zenon_L1128_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.88/22.07 apply (zenon_L231_); trivial. % 21.88/22.07 apply (zenon_L1274_); trivial. % 21.88/22.07 (* end of lemma zenon_L1275_ *) % 21.88/22.07 assert (zenon_L1276_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.88/22.07 do 0 intro. intros zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H93 zenon_H77 zenon_H7f zenon_H1b7. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.88/22.07 apply (zenon_L246_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.88/22.07 apply (zenon_L413_); trivial. % 21.88/22.07 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.88/22.07 apply (zenon_L218_); trivial. % 21.88/22.07 apply (zenon_L780_); trivial. % 21.88/22.07 (* end of lemma zenon_L1276_ *) % 21.88/22.07 assert (zenon_L1277_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (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 (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (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) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e1) (e1)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (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) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H141 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H16a zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H34 zenon_Hbc zenon_He4 zenon_H234 zenon_Hfe zenon_Ha0 zenon_H140 zenon_H195 zenon_H1f1 zenon_H13f zenon_H196 zenon_H10c zenon_H47 zenon_Hfa zenon_H6f zenon_H1a3 zenon_H1cb zenon_H1cd zenon_H105 zenon_H231 zenon_H104 zenon_H192 zenon_H6e zenon_H1c3 zenon_H68 zenon_H5c zenon_H1c2 zenon_H18a zenon_H183 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H7f zenon_H1b7. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.88/22.08 apply (zenon_L1271_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.88/22.08 apply (zenon_L21_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.88/22.08 apply (zenon_L1275_); trivial. % 21.88/22.08 apply (zenon_L1276_); trivial. % 21.88/22.08 (* end of lemma zenon_L1277_ *) % 21.88/22.08 assert (zenon_L1278_ : (((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 (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H18d zenon_H48 zenon_H38 zenon_H77 zenon_Hf7 zenon_Hb9 zenon_Hb6 zenon_H106 zenon_H1cb. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.88/22.08 apply (zenon_L246_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.88/22.08 apply (zenon_L206_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.88/22.08 apply (zenon_L182_); trivial. % 21.88/22.08 apply (zenon_L846_); trivial. % 21.88/22.08 (* end of lemma zenon_L1278_ *) % 21.88/22.08 assert (zenon_L1279_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H1c3 zenon_H162 zenon_Ha0 zenon_H5c zenon_H68 zenon_H19a zenon_H1cb zenon_H106 zenon_Hb6 zenon_Hb9 zenon_H77 zenon_H38 zenon_H48 zenon_H18d zenon_H8a zenon_H1c2 zenon_H171 zenon_H1b7. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.88/22.08 apply (zenon_L166_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.88/22.08 apply (zenon_L1278_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.88/22.08 apply (zenon_L207_); trivial. % 21.88/22.08 apply (zenon_L188_); trivial. % 21.88/22.08 (* end of lemma zenon_L1279_ *) % 21.88/22.08 assert (zenon_L1280_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (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 (e0) (e3)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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 (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H183 zenon_H18a zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H1c2 zenon_H18d zenon_H48 zenon_H38 zenon_H77 zenon_Hb9 zenon_Hb6 zenon_H1cb zenon_H19a zenon_H68 zenon_H5c zenon_Ha0 zenon_H162 zenon_H1c3 zenon_H8a zenon_H104 zenon_H24e zenon_H34 zenon_H7d zenon_H106 zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.88/22.08 apply (zenon_L1255_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.88/22.08 apply (zenon_L1279_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.88/22.08 apply (zenon_L231_); trivial. % 21.88/22.08 apply (zenon_L1256_); trivial. % 21.88/22.08 (* end of lemma zenon_L1280_ *) % 21.88/22.08 assert (zenon_L1281_ : ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (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 (e0) (e3)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H54 zenon_Hf0 zenon_H191 zenon_H183 zenon_H18a zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H1c2 zenon_H18d zenon_H48 zenon_H38 zenon_H77 zenon_Hb6 zenon_H1cb zenon_H19a zenon_H68 zenon_H5c zenon_Ha0 zenon_H162 zenon_H1c3 zenon_H8a zenon_H104 zenon_H24e zenon_H34 zenon_H7d zenon_H106 zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.88/22.08 apply (zenon_L151_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.88/22.08 apply (zenon_L74_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.88/22.08 exact (zenon_H191 zenon_H110). % 21.88/22.08 apply (zenon_L1280_); trivial. % 21.88/22.08 (* end of lemma zenon_L1281_ *) % 21.88/22.08 assert (zenon_L1282_ : ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (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 (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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.08 do 0 intro. intros zenon_Hdd zenon_H11a zenon_H10c zenon_H1b7 zenon_H1cd zenon_H7d zenon_H34 zenon_H24e zenon_H104 zenon_H1c3 zenon_H162 zenon_Ha0 zenon_H5c zenon_H68 zenon_H19a zenon_Hb6 zenon_H1c2 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H196 zenon_H16a zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H18a zenon_H183 zenon_H191 zenon_Hf0 zenon_H54 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H106 zenon_H1cb. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.88/22.08 apply (zenon_L30_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.88/22.08 apply (zenon_L54_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.88/22.08 apply (zenon_L1281_); trivial. % 21.88/22.08 apply (zenon_L1159_); trivial. % 21.88/22.08 (* end of lemma zenon_L1282_ *) % 21.88/22.08 assert (zenon_L1283_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((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 (e3) (e1)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (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 (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (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 (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (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)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((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)) = (e1)) -> False). % 21.88/22.08 do 0 intro. intros zenon_Hf0 zenon_H191 zenon_H162 zenon_H24e zenon_H7d zenon_H11a zenon_Hdd zenon_Hf3 zenon_H201 zenon_H1b7 zenon_H7f zenon_H77 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H183 zenon_H18a zenon_H1c2 zenon_H68 zenon_H1c3 zenon_H6e zenon_H192 zenon_H104 zenon_H231 zenon_H1cd zenon_H1cb zenon_H1a3 zenon_H6f zenon_Hfa zenon_H47 zenon_H10c zenon_H196 zenon_H13f zenon_H1f1 zenon_H140 zenon_Ha0 zenon_Hfe zenon_H234 zenon_He4 zenon_Hbc zenon_H34 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H141 zenon_H195 zenon_H5c. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.88/22.08 apply (zenon_L1265_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.88/22.08 apply (zenon_L117_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.88/22.08 apply (zenon_L1277_); trivial. % 21.88/22.08 apply (zenon_L1282_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.88/22.08 apply (zenon_L284_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.88/22.08 apply (zenon_L1277_); trivial. % 21.88/22.08 apply (zenon_L149_); trivial. % 21.88/22.08 (* end of lemma zenon_L1283_ *) % 21.88/22.08 assert (zenon_L1284_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H139 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H47 zenon_H13a zenon_H153 zenon_H77 zenon_H38 zenon_H68. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.08 apply (zenon_L251_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.08 apply (zenon_L1254_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.08 apply (zenon_L94_); trivial. % 21.88/22.08 apply (zenon_L165_); trivial. % 21.88/22.08 (* end of lemma zenon_L1284_ *) % 21.88/22.08 assert (zenon_L1285_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 21.88/22.08 do 0 intro. intros zenon_H201 zenon_H68 zenon_H38 zenon_H77 zenon_H13a zenon_H47 zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H139 zenon_H186 zenon_H5c zenon_H48 zenon_H14c zenon_H1cd zenon_H7f. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.88/22.08 apply (zenon_L1284_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.88/22.08 apply (zenon_L138_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.88/22.08 apply (zenon_L255_); trivial. % 21.88/22.08 apply (zenon_L331_); trivial. % 21.88/22.08 (* end of lemma zenon_L1285_ *) % 21.88/22.08 assert (zenon_L1286_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (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 (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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H201 zenon_H67 zenon_Hfe zenon_Hdd zenon_H11a zenon_H10c zenon_H1b7 zenon_H1cd zenon_H7d zenon_H34 zenon_H24e zenon_H104 zenon_H1c3 zenon_H162 zenon_Ha0 zenon_H5c zenon_H68 zenon_H19a zenon_Hb6 zenon_H1c2 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H196 zenon_H16a zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H18a zenon_H183 zenon_H191 zenon_Hf0 zenon_H54 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.88/22.08 apply (zenon_L95_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.88/22.08 apply (zenon_L138_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.88/22.08 apply (zenon_L446_); trivial. % 21.88/22.08 apply (zenon_L1282_); trivial. % 21.88/22.08 (* end of lemma zenon_L1286_ *) % 21.88/22.08 assert (zenon_L1287_ : (((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)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H139 zenon_H2c zenon_H65 zenon_H77 zenon_Ha0 zenon_Ha9 zenon_H3d zenon_Hb6 zenon_H47 zenon_H13a zenon_H38 zenon_H68. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.08 apply (zenon_L180_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.08 apply (zenon_L214_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.08 apply (zenon_L1148_); trivial. % 21.88/22.08 apply (zenon_L165_); trivial. % 21.88/22.08 (* end of lemma zenon_L1287_ *) % 21.88/22.08 assert (zenon_L1288_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (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) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H65 zenon_Hdb zenon_H6f zenon_H14c zenon_Ha0 zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_Hb6 zenon_H106 zenon_H1cb. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.88/22.08 apply (zenon_L43_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.88/22.08 apply (zenon_L205_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.88/22.08 apply (zenon_L278_); trivial. % 21.88/22.08 apply (zenon_L1151_); trivial. % 21.88/22.08 (* end of lemma zenon_L1288_ *) % 21.88/22.08 assert (zenon_L1289_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (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) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H201 zenon_H66 zenon_H77 zenon_H4e zenon_H53 zenon_H190 zenon_H117 zenon_Ha9 zenon_H65 zenon_Hdb zenon_H6f zenon_H14c zenon_Ha0 zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_Hb6 zenon_H1cb. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.88/22.08 apply (zenon_L94_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.88/22.08 apply (zenon_L14_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.88/22.08 apply (zenon_L143_); trivial. % 21.88/22.08 apply (zenon_L1288_); trivial. % 21.88/22.08 (* end of lemma zenon_L1289_ *) % 21.88/22.08 assert (zenon_L1290_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_Hb9 zenon_Hb6 zenon_H7f zenon_H1b7. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 21.88/22.08 apply (zenon_L246_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 21.88/22.08 apply (zenon_L17_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 21.88/22.08 apply (zenon_L182_); trivial. % 21.88/22.08 apply (zenon_L780_); trivial. % 21.88/22.08 (* end of lemma zenon_L1290_ *) % 21.88/22.08 assert (zenon_L1291_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e1)) -> False). % 21.88/22.08 do 0 intro. intros zenon_H117 zenon_H109 zenon_H9d zenon_Hdb zenon_H6f zenon_H14c zenon_Ha0 zenon_Hb6 zenon_H128. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.88/22.08 apply (zenon_L73_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.88/22.08 apply (zenon_L205_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.88/22.08 apply (zenon_L278_); trivial. % 21.88/22.08 apply (zenon_L182_); trivial. % 21.88/22.08 (* end of lemma zenon_L1291_ *) % 21.88/22.08 assert (zenon_L1292_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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 (e2) (e0)) = (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 (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H13f zenon_H77 zenon_H1f1 zenon_H1b7 zenon_H7f zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_H65 zenon_Ha9 zenon_H117 zenon_H109 zenon_H9d zenon_Hdb zenon_H6f zenon_H14c zenon_Ha0 zenon_Hb6. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.88/22.08 apply (zenon_L30_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.88/22.08 apply (zenon_L284_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.88/22.08 apply (zenon_L43_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.88/22.08 apply (zenon_L205_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.88/22.08 apply (zenon_L400_); trivial. % 21.88/22.08 apply (zenon_L1290_); trivial. % 21.88/22.08 apply (zenon_L1291_); trivial. % 21.88/22.08 (* end of lemma zenon_L1292_ *) % 21.88/22.08 assert (zenon_L1293_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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 (e2) (e0)) = (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 (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 21.88/22.08 do 0 intro. intros zenon_He4 zenon_H23c zenon_H1cb zenon_H190 zenon_H4e zenon_H66 zenon_H201 zenon_H13f zenon_H77 zenon_H1f1 zenon_H1b7 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_H65 zenon_Ha9 zenon_H117 zenon_H109 zenon_H9d zenon_Hdb zenon_H6f zenon_H14c zenon_Ha0 zenon_Hb6. % 21.88/22.08 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.88/22.08 apply (zenon_L55_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.88/22.08 apply (zenon_L492_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.88/22.08 apply (zenon_L1289_); trivial. % 21.88/22.08 apply (zenon_L1292_); trivial. % 21.88/22.08 (* end of lemma zenon_L1293_ *) % 21.88/22.08 assert (zenon_L1294_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H13a zenon_H33 zenon_Hb6 zenon_H14c zenon_H6f zenon_H9d zenon_H109 zenon_H117 zenon_H65 zenon_H18d zenon_H48 zenon_H5d zenon_H3c zenon_H1b7 zenon_H1f1 zenon_H77 zenon_H13f zenon_H201 zenon_H4e zenon_H190 zenon_H1cb zenon_H23c zenon_He4 zenon_Ha9 zenon_H66 zenon_H38 zenon_Ha0. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.08 apply (zenon_L245_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.08 apply (zenon_L1293_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.08 apply (zenon_L193_); trivial. % 21.88/22.08 apply (zenon_L156_); trivial. % 21.88/22.08 (* end of lemma zenon_L1294_ *) % 21.88/22.08 assert (zenon_L1295_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((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 (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H1cf zenon_Ha0 zenon_H38 zenon_Ha9 zenon_He4 zenon_H23c zenon_H190 zenon_H4e zenon_H201 zenon_H13f zenon_H77 zenon_H1f1 zenon_H1b7 zenon_H3c zenon_H5d zenon_H48 zenon_H18d zenon_H117 zenon_H109 zenon_H9d zenon_H6f zenon_H14c zenon_Hb6 zenon_H33 zenon_H13a zenon_Hf7 zenon_H186 zenon_H1ef zenon_H65 zenon_H1bb zenon_H18a zenon_H34 zenon_H106 zenon_H1cb zenon_Hc4. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.88/22.08 apply (zenon_L1294_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.88/22.08 apply (zenon_L438_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.88/22.08 apply (zenon_L533_); trivial. % 21.88/22.08 apply (zenon_L847_); trivial. % 21.88/22.08 (* end of lemma zenon_L1295_ *) % 21.88/22.08 assert (zenon_L1296_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H121 zenon_H1cb zenon_H106 zenon_H34 zenon_H18a zenon_H1bb zenon_H65 zenon_H1ef zenon_H186 zenon_Hf7 zenon_H13a zenon_H33 zenon_Hb6 zenon_H14c zenon_H6f zenon_H109 zenon_H117 zenon_H18d zenon_H48 zenon_H5d zenon_H3c zenon_H1b7 zenon_H1f1 zenon_H77 zenon_H13f zenon_H201 zenon_H4e zenon_H190 zenon_H23c zenon_He4 zenon_H38 zenon_Ha0 zenon_H1cf zenon_H171 zenon_Ha9 zenon_H1a3 zenon_Hc4. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.88/22.08 apply (zenon_L1295_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.88/22.08 apply (zenon_L371_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.88/22.08 exact (zenon_H1a3 zenon_Hbb). % 21.88/22.08 exact (zenon_Hc4 zenon_Hc3). % 21.88/22.08 (* end of lemma zenon_L1296_ *) % 21.88/22.08 assert (zenon_L1297_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H25b zenon_H38 zenon_Hf5 zenon_H5d zenon_H3c zenon_H20f zenon_H17c zenon_Hb9 zenon_H195. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H136 | zenon_intro zenon_H25c ]. % 21.88/22.08 apply (zenon_L663_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H5c | zenon_intro zenon_H25d ]. % 21.88/22.08 apply (zenon_L17_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Ha5 ]. % 21.88/22.08 apply (zenon_L570_); trivial. % 21.88/22.08 apply (zenon_L172_); trivial. % 21.88/22.08 (* end of lemma zenon_L1297_ *) % 21.88/22.08 assert (zenon_L1298_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H26a zenon_Ha0 zenon_H1a3 zenon_H10d zenon_H190 zenon_H186 zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H195 zenon_H17c zenon_H20f zenon_H3c zenon_H5d zenon_Hf5 zenon_H38 zenon_H25b zenon_Hc4. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H9e | zenon_intro zenon_H26b ]. % 21.88/22.08 apply (zenon_L156_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H26c ]. % 21.88/22.08 apply (zenon_L1173_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc3 ]. % 21.88/22.08 apply (zenon_L1297_); trivial. % 21.88/22.08 exact (zenon_Hc4 zenon_Hc3). % 21.88/22.08 (* end of lemma zenon_L1298_ *) % 21.88/22.08 assert (zenon_L1299_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H183 zenon_H18d zenon_H48 zenon_H129 zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H121 zenon_H34 zenon_H18a zenon_H65 zenon_H1ef zenon_H13a zenon_H33 zenon_Hb6 zenon_H14c zenon_H6f zenon_H109 zenon_H117 zenon_H1b7 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H68 zenon_H1c3 zenon_H106 zenon_H77 zenon_H26a zenon_Ha0 zenon_H1a3 zenon_H10d zenon_H190 zenon_H186 zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H195 zenon_H20f zenon_H3c zenon_H5d zenon_Hf5 zenon_H38 zenon_H25b zenon_Hc4. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.88/22.08 apply (zenon_L291_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.88/22.08 apply (zenon_L165_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.88/22.08 apply (zenon_L1296_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.88/22.08 apply (zenon_L1159_); trivial. % 21.88/22.08 apply (zenon_L1298_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.88/22.08 apply (zenon_L367_); trivial. % 21.88/22.08 apply (zenon_L1298_); trivial. % 21.88/22.08 (* end of lemma zenon_L1299_ *) % 21.88/22.08 assert (zenon_L1300_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (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))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H13a zenon_Hc4 zenon_H104 zenon_H1c7 zenon_H33 zenon_H121 zenon_Hb6 zenon_H3d zenon_H111 zenon_H110 zenon_H38 zenon_Ha0. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.88/22.08 apply (zenon_L819_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.88/22.08 apply (zenon_L55_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.88/22.08 apply (zenon_L75_); trivial. % 21.88/22.08 apply (zenon_L156_); trivial. % 21.88/22.08 (* end of lemma zenon_L1300_ *) % 21.88/22.08 assert (zenon_L1301_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (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) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e2) = (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)) = (op (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) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.88/22.08 do 0 intro. intros zenon_H139 zenon_H2c zenon_H1cb zenon_Hb6 zenon_H3c zenon_H5d zenon_H48 zenon_H18d zenon_H13a zenon_Hc4 zenon_H104 zenon_H1c7 zenon_H33 zenon_H121 zenon_H3d zenon_H111 zenon_Ha0 zenon_H183 zenon_H129 zenon_H1b4 zenon_H1bb zenon_H34 zenon_H18a zenon_H65 zenon_H1ef zenon_H14c zenon_H6f zenon_H109 zenon_H117 zenon_H1b7 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H1c3 zenon_H77 zenon_H26a zenon_H1a3 zenon_H190 zenon_H186 zenon_Ha9 zenon_H1a2 zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1d8 zenon_H38 zenon_H68. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.88/22.08 apply (zenon_L180_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.88/22.08 apply (zenon_L214_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.88/22.08 apply (zenon_L738_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.88/22.08 apply (zenon_L14_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.88/22.08 apply (zenon_L255_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.88/22.08 apply (zenon_L43_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.88/22.08 apply (zenon_L1299_); trivial. % 21.88/22.08 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.88/22.08 apply (zenon_L1300_); trivial. % 21.88/22.08 apply (zenon_L1151_); trivial. % 21.88/22.08 apply (zenon_L165_); trivial. % 21.88/22.08 (* end of lemma zenon_L1301_ *) % 21.88/22.08 assert (zenon_L1302_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (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)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (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) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.97/22.09 do 0 intro. intros zenon_H82 zenon_H68 zenon_H38 zenon_H1d8 zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H1a2 zenon_Ha9 zenon_H186 zenon_H190 zenon_H1a3 zenon_H26a zenon_H1c3 zenon_H1cf zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H1b7 zenon_H117 zenon_H109 zenon_H6f zenon_H14c zenon_H1ef zenon_H18a zenon_H1bb zenon_H1b4 zenon_H129 zenon_H183 zenon_Ha0 zenon_H111 zenon_H3d zenon_H121 zenon_H33 zenon_H1c7 zenon_H104 zenon_Hc4 zenon_H13a zenon_H18d zenon_H5d zenon_Hb6 zenon_H1cb zenon_H2c zenon_H139 zenon_H65 zenon_H77 zenon_H34 zenon_H48. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.97/22.09 apply (zenon_L1287_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.97/22.09 apply (zenon_L1301_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.97/22.09 apply (zenon_L30_); trivial. % 21.97/22.09 apply (zenon_L456_); trivial. % 21.97/22.09 (* end of lemma zenon_L1302_ *) % 21.97/22.09 assert (zenon_L1303_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e2))) -> ((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) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.97/22.09 do 0 intro. intros zenon_H1c3 zenon_H162 zenon_Ha0 zenon_H5c zenon_H68 zenon_H19a zenon_H1cb zenon_Hb6 zenon_Hb9 zenon_H77 zenon_H38 zenon_H48 zenon_H18d zenon_H189 zenon_H6d zenon_H24e zenon_H34 zenon_H7d zenon_H106 zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.97/22.09 apply (zenon_L166_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.97/22.09 apply (zenon_L1278_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.97/22.09 apply (zenon_L439_); trivial. % 21.97/22.09 apply (zenon_L1256_); trivial. % 21.97/22.09 (* end of lemma zenon_L1303_ *) % 21.97/22.09 assert (zenon_L1304_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((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) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (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 (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (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 (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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.09 do 0 intro. intros zenon_H2c zenon_H1c7 zenon_H33 zenon_H121 zenon_H3d zenon_H111 zenon_H14c zenon_H109 zenon_H1f1 zenon_H13f zenon_H201 zenon_H23c zenon_He4 zenon_H26a zenon_H1a3 zenon_H1d8 zenon_H82 zenon_H11a zenon_H10c zenon_H1b7 zenon_H1cd zenon_H7d zenon_H34 zenon_H24e zenon_H104 zenon_H1c3 zenon_H162 zenon_Ha0 zenon_H5c zenon_H68 zenon_H19a zenon_Hb6 zenon_H1c2 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H196 zenon_H16a zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H18a zenon_H183 zenon_H191 zenon_Hf0 zenon_H54 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H106 zenon_H1cb. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.09 apply (zenon_L1302_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.97/22.09 apply (zenon_L151_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.97/22.09 apply (zenon_L289_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.97/22.09 exact (zenon_H191 zenon_H110). % 21.97/22.09 apply (zenon_L1303_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.09 apply (zenon_L1281_); trivial. % 21.97/22.09 apply (zenon_L1159_); trivial. % 21.97/22.09 (* end of lemma zenon_L1304_ *) % 21.97/22.09 assert (zenon_L1305_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((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) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (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 (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (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) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.97/22.09 do 0 intro. intros zenon_H196 zenon_H2c zenon_H1c7 zenon_H33 zenon_H121 zenon_H3d zenon_H111 zenon_H109 zenon_H1f1 zenon_H13f zenon_H201 zenon_H23c zenon_He4 zenon_H26a zenon_H1a3 zenon_H1d8 zenon_H82 zenon_H11a zenon_H10c zenon_H1b7 zenon_H1cd zenon_H7d zenon_H34 zenon_H24e zenon_H104 zenon_H1c3 zenon_H162 zenon_H5c zenon_H68 zenon_H19a zenon_Hb6 zenon_H1c2 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H16a zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H18a zenon_H183 zenon_H191 zenon_Hf0 zenon_H54 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1cb zenon_H67 zenon_H141 zenon_H38 zenon_Ha0. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.97/22.09 apply (zenon_L538_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.97/22.09 apply (zenon_L55_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.09 apply (zenon_L217_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.09 apply (zenon_L1286_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.09 apply (zenon_L95_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.09 apply (zenon_L138_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.09 apply (zenon_L255_); trivial. % 21.97/22.09 apply (zenon_L1304_); trivial. % 21.97/22.09 apply (zenon_L1162_); trivial. % 21.97/22.09 apply (zenon_L156_); trivial. % 21.97/22.09 (* end of lemma zenon_L1305_ *) % 21.97/22.09 assert (zenon_L1306_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (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 (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 (e2) (e0)) = (op (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) (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 (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((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 (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.97/22.09 do 0 intro. intros zenon_H141 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_H48 zenon_H18d zenon_H54 zenon_Hf0 zenon_H191 zenon_H183 zenon_H18a zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1c2 zenon_H19a zenon_H5c zenon_H162 zenon_H1c3 zenon_H104 zenon_H24e zenon_H34 zenon_H7d zenon_H1cd zenon_H1b7 zenon_H82 zenon_H1d8 zenon_H26a zenon_He4 zenon_H23c zenon_H201 zenon_H13f zenon_H1f1 zenon_H109 zenon_H111 zenon_H1c7 zenon_H2c zenon_H196 zenon_H77 zenon_Ha0 zenon_Ha9 zenon_H3d zenon_Hb6 zenon_H121 zenon_H33 zenon_H11a zenon_H10c zenon_H1a3 zenon_Hc4 zenon_H13a zenon_H38 zenon_H68. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.09 apply (zenon_L1305_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.09 apply (zenon_L214_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.09 apply (zenon_L1248_); trivial. % 21.97/22.09 apply (zenon_L165_); trivial. % 21.97/22.09 (* end of lemma zenon_L1306_ *) % 21.97/22.09 assert (zenon_L1307_ : (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (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) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.97/22.09 do 0 intro. intros zenon_H68 zenon_H38 zenon_H13a zenon_Hc4 zenon_H1a3 zenon_H10c zenon_H11a zenon_H33 zenon_H121 zenon_Hb6 zenon_H3d zenon_Ha9 zenon_Ha0 zenon_H77 zenon_H196 zenon_H2c zenon_H1c7 zenon_H111 zenon_H109 zenon_H1f1 zenon_H13f zenon_H201 zenon_H23c zenon_He4 zenon_H26a zenon_H1d8 zenon_H82 zenon_H1b7 zenon_H1cd zenon_H7d zenon_H24e zenon_H104 zenon_H1c3 zenon_H162 zenon_H5c zenon_H19a zenon_H1c2 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H16a zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H18a zenon_H183 zenon_H191 zenon_Hf0 zenon_H18d zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H141 zenon_H34 zenon_H48. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.97/22.09 apply (zenon_L1149_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.97/22.09 apply (zenon_L17_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.97/22.09 apply (zenon_L1306_); trivial. % 21.97/22.09 apply (zenon_L456_); trivial. % 21.97/22.09 (* end of lemma zenon_L1307_ *) % 21.97/22.09 assert (zenon_L1308_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.97/22.09 do 0 intro. intros zenon_H1c3 zenon_H162 zenon_Ha0 zenon_H5c zenon_H68 zenon_H19a zenon_H1cb zenon_Hb6 zenon_Hb9 zenon_H120 zenon_H77 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H24e zenon_H34 zenon_H7d zenon_H106 zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.97/22.09 apply (zenon_L166_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.97/22.09 apply (zenon_L1278_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.97/22.09 apply (zenon_L555_); trivial. % 21.97/22.09 apply (zenon_L1256_); trivial. % 21.97/22.09 (* end of lemma zenon_L1308_ *) % 21.97/22.09 assert (zenon_L1309_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.97/22.09 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H195 zenon_H14c zenon_H65 zenon_H13f zenon_H191 zenon_H1c3 zenon_H162 zenon_Ha0 zenon_H5c zenon_H68 zenon_H19a zenon_H1cb zenon_Hb6 zenon_H120 zenon_H77 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H24e zenon_H34 zenon_H7d zenon_H106 zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.97/22.09 apply (zenon_L43_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.97/22.09 apply (zenon_L256_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.97/22.09 exact (zenon_H191 zenon_H110). % 21.97/22.09 apply (zenon_L1308_); trivial. % 21.97/22.09 (* end of lemma zenon_L1309_ *) % 21.97/22.09 assert (zenon_L1310_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (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) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((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) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 21.97/22.09 do 0 intro. intros zenon_H201 zenon_H173 zenon_H121 zenon_H33 zenon_H1a3 zenon_H13a zenon_H186 zenon_H16a zenon_Hb6 zenon_H19a zenon_Ha0 zenon_H162 zenon_H191 zenon_H13f zenon_H14c zenon_H195 zenon_Ha9 zenon_H117 zenon_H53 zenon_H11a zenon_H10c zenon_H1b7 zenon_H1cd zenon_H7d zenon_H34 zenon_H24e zenon_H1c3 zenon_H68 zenon_H5c zenon_H1cb zenon_H192 zenon_H6e zenon_H1c2 zenon_H18a zenon_H183 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H120. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.09 apply (zenon_L1252_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.09 apply (zenon_L138_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.09 apply (zenon_L255_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.09 apply (zenon_L1309_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.09 apply (zenon_L56_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.09 apply (zenon_L1261_); trivial. % 21.97/22.09 apply (zenon_L555_); trivial. % 21.97/22.09 (* end of lemma zenon_L1310_ *) % 21.97/22.09 assert (zenon_L1311_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 21.97/22.09 do 0 intro. intros zenon_H201 zenon_Ha0 zenon_H38 zenon_Hb6 zenon_H6e zenon_Ha9 zenon_H47 zenon_H13a zenon_H186 zenon_H5c zenon_H231 zenon_H1a3 zenon_H162 zenon_H120 zenon_H1cb zenon_H1bb zenon_H104 zenon_H34 zenon_Hbc zenon_Hc2 zenon_H1cd zenon_H7f. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.09 apply (zenon_L1254_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.09 apply (zenon_L138_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.09 apply (zenon_L477_); trivial. % 21.97/22.09 apply (zenon_L331_); trivial. % 21.97/22.09 (* end of lemma zenon_L1311_ *) % 21.97/22.09 assert (zenon_L1312_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.97/22.09 do 0 intro. intros zenon_H1cf zenon_H1d5 zenon_H67 zenon_H4e zenon_H76 zenon_H190 zenon_H6d zenon_H1bb zenon_H162 zenon_H120 zenon_H1cb zenon_Hc4. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.97/22.09 apply (zenon_L252_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.97/22.09 apply (zenon_L83_); trivial. % 21.97/22.09 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.97/22.09 apply (zenon_L366_); trivial. % 21.97/22.09 apply (zenon_L237_); trivial. % 21.97/22.09 (* end of lemma zenon_L1312_ *) % 21.97/22.09 assert (zenon_L1313_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (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 (e0) (e3)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (((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 (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.97/22.10 do 0 intro. intros zenon_H183 zenon_H18a zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1c2 zenon_H8a zenon_H18d zenon_H48 zenon_H38 zenon_H77 zenon_Hb9 zenon_Hb6 zenon_H19a zenon_H68 zenon_H5c zenon_Ha0 zenon_H1c3 zenon_Hc4 zenon_H1cb zenon_H120 zenon_H162 zenon_H1bb zenon_H24e zenon_H34 zenon_H7d zenon_H106 zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.97/22.10 apply (zenon_L1255_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.97/22.10 apply (zenon_L1279_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.97/22.10 apply (zenon_L237_); trivial. % 21.97/22.10 apply (zenon_L1256_); trivial. % 21.97/22.10 (* end of lemma zenon_L1313_ *) % 21.97/22.10 assert (zenon_L1314_ : ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (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 (e0) (e3)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.97/22.10 do 0 intro. intros zenon_H54 zenon_Hf0 zenon_H191 zenon_H183 zenon_H18a zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1c2 zenon_H8a zenon_H18d zenon_H48 zenon_H38 zenon_H77 zenon_Hb6 zenon_H19a zenon_H68 zenon_H5c zenon_Ha0 zenon_H1c3 zenon_Hc4 zenon_H1cb zenon_H120 zenon_H162 zenon_H1bb zenon_H24e zenon_H34 zenon_H7d zenon_H106 zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.97/22.10 apply (zenon_L151_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.97/22.10 apply (zenon_L74_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.97/22.10 exact (zenon_H191 zenon_H110). % 21.97/22.10 apply (zenon_L1313_); trivial. % 21.97/22.10 (* end of lemma zenon_L1314_ *) % 21.97/22.10 assert (zenon_L1315_ : ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (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 (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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.10 do 0 intro. intros zenon_H76 zenon_H67 zenon_H1d5 zenon_H11a zenon_H10c zenon_H1b7 zenon_H1cd zenon_H7d zenon_H34 zenon_H24e zenon_H162 zenon_H120 zenon_H1c3 zenon_Ha0 zenon_H5c zenon_H68 zenon_H19a zenon_Hb6 zenon_H1c2 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H196 zenon_H16a zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H18a zenon_H183 zenon_H191 zenon_Hf0 zenon_H54 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H106 zenon_H1cb. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.10 apply (zenon_L30_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.10 apply (zenon_L1312_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.10 apply (zenon_L1314_); trivial. % 21.97/22.10 apply (zenon_L1159_); trivial. % 21.97/22.10 (* end of lemma zenon_L1315_ *) % 21.97/22.10 assert (zenon_L1316_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 21.97/22.10 do 0 intro. intros zenon_H140 zenon_H48 zenon_Ha0 zenon_H1a3 zenon_H191 zenon_Hef zenon_H153 zenon_Hb6 zenon_H1a2 zenon_Hbc zenon_H34. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.97/22.10 apply (zenon_L239_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.97/22.10 apply (zenon_L1265_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.97/22.10 apply (zenon_L1150_); trivial. % 21.97/22.10 apply (zenon_L328_); trivial. % 21.97/22.10 (* end of lemma zenon_L1316_ *) % 21.97/22.10 assert (zenon_L1317_ : (((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 (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (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 (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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.10 do 0 intro. intros zenon_H201 zenon_H140 zenon_H231 zenon_H1a3 zenon_H104 zenon_Hbc zenon_Hc2 zenon_H2c zenon_H67 zenon_Hef zenon_H11a zenon_H10c zenon_H1b7 zenon_H1cd zenon_H7d zenon_H34 zenon_H24e zenon_H162 zenon_H120 zenon_H1c3 zenon_Ha0 zenon_H5c zenon_H68 zenon_H19a zenon_Hb6 zenon_H1c2 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H196 zenon_H16a zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H18a zenon_H183 zenon_H191 zenon_Hf0 zenon_H54 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.10 apply (zenon_L1316_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.10 apply (zenon_L138_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.10 apply (zenon_L477_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.10 apply (zenon_L180_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.10 apply (zenon_L61_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.10 apply (zenon_L1314_); trivial. % 21.97/22.10 apply (zenon_L1159_); trivial. % 21.97/22.10 (* end of lemma zenon_L1317_ *) % 21.97/22.10 assert (zenon_L1318_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((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)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (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 (e0) (e3)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.97/22.10 do 0 intro. intros zenon_Hfa zenon_H1d5 zenon_Hfe zenon_H3d zenon_H1d8 zenon_H1cb zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H54 zenon_Hf0 zenon_H191 zenon_H183 zenon_H18a zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1c2 zenon_Hb6 zenon_H19a zenon_Ha0 zenon_H1c3 zenon_H120 zenon_H162 zenon_H24e zenon_H34 zenon_H7d zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a zenon_H67 zenon_H2c zenon_Hc2 zenon_Hbc zenon_H104 zenon_H1a3 zenon_H231 zenon_H140 zenon_H201 zenon_Hf3 zenon_H68 zenon_H5c zenon_H77. % 21.97/22.10 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.10 apply (zenon_L738_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.10 apply (zenon_L117_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.10 apply (zenon_L446_); trivial. % 21.97/22.10 apply (zenon_L1315_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.97/22.10 apply (zenon_L1317_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.97/22.10 apply (zenon_L62_); trivial. % 21.97/22.10 apply (zenon_L206_); trivial. % 21.97/22.10 (* end of lemma zenon_L1318_ *) % 21.97/22.10 assert (zenon_L1319_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (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 (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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.10 do 0 intro. intros zenon_H201 zenon_H1d8 zenon_H3d zenon_H14c zenon_H76 zenon_H67 zenon_H1d5 zenon_H11a zenon_H10c zenon_H1b7 zenon_H1cd zenon_H7d zenon_H34 zenon_H24e zenon_H162 zenon_H120 zenon_H1c3 zenon_Ha0 zenon_H5c zenon_H68 zenon_H19a zenon_Hb6 zenon_H1c2 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H196 zenon_H16a zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H18a zenon_H183 zenon_H191 zenon_Hf0 zenon_H54 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.10 apply (zenon_L738_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.10 apply (zenon_L138_); trivial. % 21.97/22.10 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.10 apply (zenon_L255_); trivial. % 21.97/22.10 apply (zenon_L1315_); trivial. % 21.97/22.10 (* end of lemma zenon_L1319_ *) % 21.97/22.10 assert (zenon_L1320_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (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 (e0) (e3)) = (op (e2) (e3)))) -> (((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 (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((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) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 21.97/22.10 do 0 intro. intros zenon_H140 zenon_H231 zenon_H1a3 zenon_H104 zenon_Hc2 zenon_H2c zenon_Hfe zenon_Hfa zenon_H1cb zenon_H77 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H54 zenon_Hf0 zenon_H191 zenon_H183 zenon_H18a zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1c2 zenon_Hb6 zenon_H19a zenon_H68 zenon_H5c zenon_Ha0 zenon_H1c3 zenon_H120 zenon_H162 zenon_H24e zenon_H7d zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a zenon_H1d5 zenon_H67 zenon_H76 zenon_H3d zenon_H1d8 zenon_H201 zenon_Hbc zenon_H34. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.97/22.11 apply (zenon_L756_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.97/22.11 apply (zenon_L1318_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.97/22.11 apply (zenon_L1319_); trivial. % 21.97/22.11 apply (zenon_L328_); trivial. % 21.97/22.11 (* end of lemma zenon_L1320_ *) % 21.97/22.11 assert (zenon_L1321_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((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) (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 (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> False). % 21.97/22.11 do 0 intro. intros zenon_Hcb zenon_H231 zenon_H162 zenon_H120 zenon_H1cb zenon_H1bb zenon_H105 zenon_H104 zenon_H34 zenon_Hbc zenon_Hc2. % 21.97/22.11 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.97/22.11 apply (zenon_L477_); trivial. % 21.97/22.11 apply (zenon_L434_); trivial. % 21.97/22.11 (* end of lemma zenon_L1321_ *) % 21.97/22.11 assert (zenon_L1322_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.97/22.11 do 0 intro. intros zenon_H1cf zenon_H153 zenon_H77 zenon_Hf7 zenon_H186 zenon_H1ef zenon_H65 zenon_H1bb zenon_H162 zenon_H120 zenon_H1cb zenon_Hc4. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.97/22.11 apply (zenon_L94_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.97/22.11 apply (zenon_L438_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.97/22.11 apply (zenon_L533_); trivial. % 21.97/22.11 apply (zenon_L237_); trivial. % 21.97/22.11 (* end of lemma zenon_L1322_ *) % 21.97/22.11 assert (zenon_L1323_ : ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.97/22.11 do 0 intro. intros zenon_H133 zenon_H162 zenon_H120 zenon_H104 zenon_Hbc zenon_H231 zenon_H121 zenon_H1cb zenon_H34 zenon_H18a zenon_H1bb zenon_H65 zenon_H1ef zenon_H186 zenon_Hf7 zenon_H13a zenon_H33 zenon_Hb6 zenon_H14c zenon_H6f zenon_H109 zenon_H117 zenon_H18d zenon_H48 zenon_H5d zenon_H3c zenon_H1b7 zenon_H1f1 zenon_H77 zenon_H13f zenon_H201 zenon_H4e zenon_H190 zenon_H23c zenon_He4 zenon_H38 zenon_Ha0 zenon_H1cf zenon_H171 zenon_Ha9 zenon_H1a3 zenon_Hc4. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.11 apply (zenon_L1322_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.11 apply (zenon_L124_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.11 apply (zenon_L476_); trivial. % 21.97/22.11 apply (zenon_L1296_); trivial. % 21.97/22.11 (* end of lemma zenon_L1323_ *) % 21.97/22.11 assert (zenon_L1324_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (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) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.97/22.11 do 0 intro. intros zenon_H183 zenon_H1b7 zenon_H18d zenon_H48 zenon_H129 zenon_H1b4 zenon_H1bb zenon_H120 zenon_H133 zenon_H162 zenon_H104 zenon_Hbc zenon_H231 zenon_H121 zenon_H1cb zenon_H34 zenon_H18a zenon_H65 zenon_H1ef zenon_H13a zenon_H33 zenon_Hb6 zenon_H14c zenon_H6f zenon_H109 zenon_H117 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H68 zenon_H1c3 zenon_H106 zenon_H77 zenon_H26a zenon_Ha0 zenon_H1a3 zenon_H10d zenon_H190 zenon_H186 zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H195 zenon_H20f zenon_H3c zenon_H5d zenon_Hf5 zenon_H38 zenon_H25b zenon_Hc4. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.97/22.11 apply (zenon_L291_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.97/22.11 apply (zenon_L165_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.97/22.11 apply (zenon_L1323_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.97/22.11 apply (zenon_L555_); trivial. % 21.97/22.11 apply (zenon_L188_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.97/22.11 apply (zenon_L367_); trivial. % 21.97/22.11 apply (zenon_L1298_); trivial. % 21.97/22.11 (* end of lemma zenon_L1324_ *) % 21.97/22.11 assert (zenon_L1325_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (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 (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.97/22.11 do 0 intro. intros zenon_H139 zenon_H2c zenon_H1cb zenon_Hb6 zenon_H3c zenon_H5d zenon_H48 zenon_H18d zenon_Ha0 zenon_H14c zenon_Hc4 zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H1a2 zenon_Ha9 zenon_H186 zenon_H190 zenon_H26a zenon_H77 zenon_H1c3 zenon_H1cf zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H117 zenon_H109 zenon_H6f zenon_H33 zenon_H13a zenon_H1ef zenon_H65 zenon_H18a zenon_H34 zenon_H121 zenon_H231 zenon_Hbc zenon_H104 zenon_H162 zenon_H120 zenon_H1bb zenon_H1b4 zenon_H129 zenon_H1b7 zenon_H183 zenon_H1a3 zenon_Hcb zenon_Hc2 zenon_H3d zenon_H1d8 zenon_H38 zenon_H68. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.11 apply (zenon_L180_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.11 apply (zenon_L214_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.11 apply (zenon_L738_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.11 apply (zenon_L14_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.11 apply (zenon_L1321_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.97/22.11 apply (zenon_L43_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.97/22.11 apply (zenon_L193_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.97/22.11 apply (zenon_L1324_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.97/22.11 apply (zenon_L278_); trivial. % 21.97/22.11 exact (zenon_H1a3 zenon_Hbb). % 21.97/22.11 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.97/22.11 apply (zenon_L278_); trivial. % 21.97/22.11 apply (zenon_L1151_); trivial. % 21.97/22.11 apply (zenon_L165_); trivial. % 21.97/22.11 (* end of lemma zenon_L1325_ *) % 21.97/22.11 assert (zenon_L1326_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (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) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (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) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e2) = (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)) = (op (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 (e3) (e3)) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (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) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.97/22.11 do 0 intro. intros zenon_H82 zenon_H68 zenon_H38 zenon_H1d8 zenon_H3d zenon_Hc2 zenon_Hcb zenon_H1a3 zenon_H183 zenon_H1b7 zenon_H129 zenon_H1b4 zenon_H1bb zenon_H120 zenon_H162 zenon_H104 zenon_Hbc zenon_H231 zenon_H121 zenon_H18a zenon_H1ef zenon_H13a zenon_H33 zenon_H6f zenon_H109 zenon_H117 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H1c3 zenon_H26a zenon_H190 zenon_H186 zenon_Ha9 zenon_H1a2 zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_Hc4 zenon_H14c zenon_Ha0 zenon_H18d zenon_H5d zenon_Hb6 zenon_H1cb zenon_H2c zenon_H139 zenon_H65 zenon_H77 zenon_H34 zenon_H48. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.97/22.11 apply (zenon_L1287_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.97/22.11 apply (zenon_L1325_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.97/22.11 apply (zenon_L30_); trivial. % 21.97/22.11 apply (zenon_L456_); trivial. % 21.97/22.11 (* end of lemma zenon_L1326_ *) % 21.97/22.11 assert (zenon_L1327_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (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 (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (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 (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.11 do 0 intro. intros zenon_H16a zenon_H139 zenon_H2c zenon_H5d zenon_H14c zenon_H25b zenon_Hf5 zenon_H195 zenon_H1a2 zenon_H186 zenon_H190 zenon_H26a zenon_H1cf zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H109 zenon_H6f zenon_H33 zenon_H13a zenon_H1ef zenon_H18a zenon_H121 zenon_H231 zenon_Hbc zenon_H104 zenon_H183 zenon_H1a3 zenon_Hcb zenon_Hc2 zenon_H3d zenon_H1d8 zenon_H82 zenon_H11a zenon_H10c zenon_H1b7 zenon_H1cd zenon_H7d zenon_H34 zenon_H24e zenon_H120 zenon_Hb6 zenon_H19a zenon_H68 zenon_H5c zenon_Ha0 zenon_H162 zenon_H1c3 zenon_H191 zenon_Ha9 zenon_H54 zenon_H117 zenon_H72 zenon_H131 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.11 apply (zenon_L1170_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.11 apply (zenon_L59_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.11 apply (zenon_L255_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.11 apply (zenon_L1326_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.97/22.11 apply (zenon_L151_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.97/22.11 apply (zenon_L289_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.97/22.11 exact (zenon_H191 zenon_H110). % 21.97/22.11 apply (zenon_L1308_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.11 apply (zenon_L87_); trivial. % 21.97/22.11 apply (zenon_L1159_); trivial. % 21.97/22.11 (* end of lemma zenon_L1327_ *) % 21.97/22.11 assert (zenon_L1328_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (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) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (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) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (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) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 21.97/22.11 do 0 intro. intros zenon_H140 zenon_H26d zenon_H36 zenon_H1cb zenon_H77 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H131 zenon_H72 zenon_H117 zenon_H54 zenon_Ha9 zenon_H191 zenon_H1c3 zenon_H162 zenon_Ha0 zenon_H5c zenon_H68 zenon_H19a zenon_Hb6 zenon_H120 zenon_H24e zenon_H7d zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a zenon_H82 zenon_H1d8 zenon_H3d zenon_Hc2 zenon_Hcb zenon_H1a3 zenon_H183 zenon_H104 zenon_H231 zenon_H121 zenon_H18a zenon_H1ef zenon_H13a zenon_H33 zenon_H6f zenon_H109 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H26a zenon_H190 zenon_H186 zenon_H1a2 zenon_H195 zenon_Hf5 zenon_H25b zenon_H5d zenon_H2c zenon_H139 zenon_H16a zenon_Hbc zenon_H34. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.97/22.11 apply (zenon_L757_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.97/22.11 apply (zenon_L62_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.97/22.11 apply (zenon_L1327_); trivial. % 21.97/22.11 apply (zenon_L328_); trivial. % 21.97/22.11 (* end of lemma zenon_L1328_ *) % 21.97/22.11 assert (zenon_L1329_ : (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (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) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (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) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (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) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((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)) = (op (e0) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.97/22.11 do 0 intro. intros zenon_H77 zenon_H5c zenon_H140 zenon_H26d zenon_H36 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H131 zenon_H117 zenon_H54 zenon_Ha9 zenon_H191 zenon_H1c3 zenon_H162 zenon_H68 zenon_H19a zenon_Hb6 zenon_H120 zenon_H24e zenon_H7d zenon_H1cd zenon_H1b7 zenon_H10c zenon_H11a zenon_H82 zenon_H1d8 zenon_H3d zenon_Hc2 zenon_Hcb zenon_H1a3 zenon_H183 zenon_H104 zenon_H231 zenon_H121 zenon_H18a zenon_H1ef zenon_H13a zenon_H33 zenon_H6f zenon_H109 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H26a zenon_H190 zenon_H186 zenon_H1a2 zenon_H195 zenon_Hf5 zenon_H25b zenon_H5d zenon_H2c zenon_H139 zenon_H16a zenon_Hbc zenon_H34 zenon_H67 zenon_H1c2 zenon_H283 zenon_H163 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H266 zenon_H13c zenon_H196 zenon_H1c6 zenon_H27e zenon_H189 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1fb zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_Hf0 zenon_Hfa zenon_H1d5 zenon_H38 zenon_Ha0. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.97/22.11 apply (zenon_L538_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.97/22.11 apply (zenon_L120_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.97/22.11 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.97/22.11 apply (zenon_L1320_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.97/22.11 apply (zenon_L1317_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.97/22.11 apply (zenon_L1328_); trivial. % 21.97/22.11 apply (zenon_L206_); trivial. % 21.97/22.11 apply (zenon_L156_); trivial. % 21.97/22.11 (* end of lemma zenon_L1329_ *) % 21.97/22.11 assert (zenon_L1330_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (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) (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) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (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 (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.97/22.11 do 0 intro. intros zenon_H1d5 zenon_Hfa zenon_Hf0 zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H1fb zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H189 zenon_H27e zenon_H1c6 zenon_H196 zenon_H13c zenon_H266 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H163 zenon_H283 zenon_H1c2 zenon_H34 zenon_Hbc zenon_H16a zenon_H139 zenon_H2c zenon_H5d zenon_H25b zenon_Hf5 zenon_H195 zenon_H1a2 zenon_H186 zenon_H190 zenon_H26a zenon_H1cf zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H109 zenon_H6f zenon_H1ef zenon_H18a zenon_H231 zenon_H104 zenon_H183 zenon_Hcb zenon_Hc2 zenon_H1d8 zenon_H82 zenon_H1b7 zenon_H1cd zenon_H7d zenon_H24e zenon_H120 zenon_H19a zenon_H162 zenon_H1c3 zenon_H191 zenon_H54 zenon_H117 zenon_H131 zenon_H18d zenon_H48 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H36 zenon_H26d zenon_H140 zenon_H5c zenon_H77 zenon_Ha0 zenon_Ha9 zenon_H3d zenon_Hb6 zenon_H121 zenon_H33 zenon_H11a zenon_H10c zenon_H1a3 zenon_Hc4 zenon_H13a zenon_H38 zenon_H68. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.11 apply (zenon_L1329_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.11 apply (zenon_L214_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.11 apply (zenon_L1248_); trivial. % 21.97/22.11 apply (zenon_L165_); trivial. % 21.97/22.11 (* end of lemma zenon_L1330_ *) % 21.97/22.11 assert (zenon_L1331_ : (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (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) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((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)) = (op (e0) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.97/22.11 do 0 intro. intros zenon_H68 zenon_H38 zenon_H13a zenon_Hc4 zenon_H1a3 zenon_H10c zenon_H11a zenon_H33 zenon_H121 zenon_Hb6 zenon_H3d zenon_Ha9 zenon_Ha0 zenon_H77 zenon_H5c zenon_H140 zenon_H26d zenon_H36 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_H18d zenon_H131 zenon_H117 zenon_H191 zenon_H1c3 zenon_H162 zenon_H19a zenon_H120 zenon_H24e zenon_H7d zenon_H1cd zenon_H1b7 zenon_H82 zenon_H1d8 zenon_Hc2 zenon_Hcb zenon_H183 zenon_H104 zenon_H231 zenon_H18a zenon_H1ef zenon_H6f zenon_H109 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H26a zenon_H190 zenon_H186 zenon_H1a2 zenon_H195 zenon_Hf5 zenon_H25b zenon_H5d zenon_H2c zenon_H139 zenon_H16a zenon_Hbc zenon_H1c2 zenon_H283 zenon_H163 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H266 zenon_H13c zenon_H196 zenon_H1c6 zenon_H27e zenon_H189 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1fb zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_Hf0 zenon_Hfa zenon_H1d5 zenon_H34 zenon_H48. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.97/22.11 apply (zenon_L1149_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.97/22.11 apply (zenon_L17_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.97/22.11 apply (zenon_L1330_); trivial. % 21.97/22.11 apply (zenon_L456_); trivial. % 21.97/22.11 (* end of lemma zenon_L1331_ *) % 21.97/22.11 assert (zenon_L1332_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((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) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((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) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (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 (e2) (e0)) = (op (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) (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> False). % 21.97/22.11 do 0 intro. intros zenon_Hca zenon_H36 zenon_H1d5 zenon_Hc2 zenon_H2c zenon_H1d8 zenon_H111 zenon_H26a zenon_H23c zenon_H82 zenon_H77 zenon_H234 zenon_H5c zenon_H141 zenon_H13a zenon_H38 zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H186 zenon_H1c2 zenon_H191 zenon_H183 zenon_H1f1 zenon_H24e zenon_H1cd zenon_H7d zenon_H12e zenon_H192 zenon_H19a zenon_H162 zenon_H68 zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H18a zenon_H201 zenon_H48 zenon_H34 zenon_H109 zenon_H104 zenon_H231 zenon_He4 zenon_Hbc zenon_H140 zenon_Hfa zenon_Hf0 zenon_H13f zenon_H173 zenon_H33 zenon_H11a zenon_H10c zenon_Hc4 zenon_H121 zenon_Hcb. % 21.97/22.11 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 21.97/22.11 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.11 apply (zenon_L251_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.97/22.11 apply (zenon_L538_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.97/22.11 apply (zenon_L120_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.97/22.11 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.97/22.11 apply (zenon_L214_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.97/22.11 apply (zenon_L484_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.11 apply (zenon_L359_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.11 apply (zenon_L111_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.11 apply (zenon_L1262_); trivial. % 21.97/22.11 apply (zenon_L1162_); trivial. % 21.97/22.11 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.12 apply (zenon_L1264_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.97/22.12 apply (zenon_L68_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.97/22.12 apply (zenon_L1283_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.97/22.12 apply (zenon_L1285_); trivial. % 21.97/22.12 apply (zenon_L328_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.12 apply (zenon_L1285_); trivial. % 21.97/22.12 apply (zenon_L1162_); trivial. % 21.97/22.12 apply (zenon_L156_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.12 apply (zenon_L1249_); trivial. % 21.97/22.12 apply (zenon_L165_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.97/22.12 apply (zenon_L1307_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.97/22.12 apply (zenon_L1252_); trivial. % 21.97/22.12 apply (zenon_L192_); trivial. % 21.97/22.12 apply (zenon_L414_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.12 apply (zenon_L251_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.97/22.12 apply (zenon_L214_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.97/22.12 apply (zenon_L484_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.12 apply (zenon_L359_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.12 apply (zenon_L111_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.12 apply (zenon_L1310_); trivial. % 21.97/22.12 apply (zenon_L1162_); trivial. % 21.97/22.12 apply (zenon_L1311_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.12 apply (zenon_L1249_); trivial. % 21.97/22.12 apply (zenon_L165_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.97/22.12 apply (zenon_L1331_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.97/22.12 apply (zenon_L1252_); trivial. % 21.97/22.12 apply (zenon_L246_); trivial. % 21.97/22.12 apply (zenon_L434_); trivial. % 21.97/22.12 (* end of lemma zenon_L1332_ *) % 21.97/22.12 assert (zenon_L1333_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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 (e0) (e3)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((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) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> False). % 21.97/22.12 do 0 intro. intros zenon_Hc8 zenon_H13f zenon_Hf0 zenon_Hfa zenon_H140 zenon_Hbc zenon_He4 zenon_H231 zenon_H104 zenon_H109 zenon_H34 zenon_H201 zenon_H18a zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H19a zenon_H192 zenon_H12e zenon_H7d zenon_H1cd zenon_H24e zenon_H1f1 zenon_H183 zenon_H191 zenon_H1c2 zenon_H186 zenon_H141 zenon_H234 zenon_H82 zenon_H23c zenon_H26a zenon_H111 zenon_H1d8 zenon_H2c zenon_Hc2 zenon_H1d5 zenon_H36 zenon_Hca zenon_H15d zenon_H48 zenon_H33 zenon_H77 zenon_H13a zenon_H38 zenon_Ha0 zenon_H11a zenon_H10c zenon_H177 zenon_Hc4 zenon_H121 zenon_Ha9 zenon_Hb6 zenon_H173 zenon_H68 zenon_H139 zenon_H1c3 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H5c zenon_Hcb. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.97/22.12 apply (zenon_L1253_); trivial. % 21.97/22.12 apply (zenon_L414_); trivial. % 21.97/22.12 apply (zenon_L1332_); trivial. % 21.97/22.12 (* end of lemma zenon_L1333_ *) % 21.97/22.12 assert (zenon_L1334_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H15d zenon_H1e zenon_H7f zenon_H192 zenon_Ha0 zenon_Hb6 zenon_H10c zenon_H173 zenon_H121 zenon_H33 zenon_H11a zenon_H1a3 zenon_Hc4 zenon_H13a zenon_H38 zenon_H48. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.97/22.12 apply (zenon_L13_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.97/22.12 apply (zenon_L146_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.97/22.12 apply (zenon_L1252_); trivial. % 21.97/22.12 apply (zenon_L246_); trivial. % 21.97/22.12 (* end of lemma zenon_L1334_ *) % 21.97/22.12 assert (zenon_L1335_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (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 (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.97/22.12 do 0 intro. intros zenon_H140 zenon_Hfe zenon_Hdd zenon_H234 zenon_He4 zenon_H13f zenon_H65 zenon_H7f zenon_H1f1 zenon_H163 zenon_H72 zenon_H192 zenon_H6e zenon_H162 zenon_H1bb zenon_H129 zenon_H20f zenon_H38 zenon_H1b4 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H18a zenon_H183 zenon_H191 zenon_Hf0 zenon_H10c zenon_H9d zenon_H109 zenon_H195 zenon_H5c. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.97/22.12 apply (zenon_L68_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.97/22.12 apply (zenon_L62_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.97/22.12 apply (zenon_L1269_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.97/22.12 apply (zenon_L30_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.97/22.12 apply (zenon_L284_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.97/22.12 apply (zenon_L73_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.97/22.12 apply (zenon_L74_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.97/22.12 exact (zenon_H191 zenon_H110). % 21.97/22.12 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.97/22.12 apply (zenon_L1255_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.97/22.12 apply (zenon_L1128_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.97/22.12 apply (zenon_L227_); trivial. % 21.97/22.12 apply (zenon_L1273_); trivial. % 21.97/22.12 apply (zenon_L149_); trivial. % 21.97/22.12 (* end of lemma zenon_L1335_ *) % 21.97/22.12 assert (zenon_L1336_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H61 zenon_H13f zenon_H65 zenon_H77 zenon_H1f1 zenon_H48 zenon_H14c zenon_H195. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 21.97/22.12 apply (zenon_L1268_); trivial. % 21.97/22.12 (* end of lemma zenon_L1336_ *) % 21.97/22.12 assert (zenon_L1337_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.12 do 0 intro. intros zenon_H141 zenon_H5c zenon_H109 zenon_H9d zenon_H10c zenon_Hf0 zenon_H191 zenon_H183 zenon_H18a zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H162 zenon_H6e zenon_H192 zenon_H72 zenon_H163 zenon_H7f zenon_He4 zenon_H234 zenon_Hfe zenon_H140 zenon_H195 zenon_H48 zenon_H1f1 zenon_H77 zenon_H65 zenon_H13f zenon_H61 zenon_H196 zenon_H38. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.12 apply (zenon_L27_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.12 apply (zenon_L1335_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.12 apply (zenon_L1336_); trivial. % 21.97/22.12 apply (zenon_L1162_); trivial. % 21.97/22.12 (* end of lemma zenon_L1337_ *) % 21.97/22.12 assert (zenon_L1338_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H1c3 zenon_H68 zenon_H38 zenon_H77 zenon_H5c zenon_H189 zenon_H6d zenon_H102 zenon_H18a. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.97/22.12 apply (zenon_L165_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.97/22.12 apply (zenon_L206_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.97/22.12 apply (zenon_L439_); trivial. % 21.97/22.12 apply (zenon_L268_); trivial. % 21.97/22.12 (* end of lemma zenon_L1338_ *) % 21.97/22.12 assert (zenon_L1339_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 21.97/22.12 do 0 intro. intros zenon_Hb2 zenon_Hc4 zenon_H1a3 zenon_H10c zenon_H11a zenon_H33 zenon_H121 zenon_H77 zenon_H5c zenon_H18a zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H129 zenon_H1bb zenon_H6e zenon_H25 zenon_Hfa zenon_Ha9 zenon_H102. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.97/22.12 apply (zenon_L538_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.97/22.12 apply (zenon_L116_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.97/22.12 apply (zenon_L171_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.97/22.12 apply (zenon_L226_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.12 apply (zenon_L43_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.12 apply (zenon_L1338_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.12 apply (zenon_L87_); trivial. % 21.97/22.12 apply (zenon_L1236_); trivial. % 21.97/22.12 apply (zenon_L206_); trivial. % 21.97/22.12 apply (zenon_L91_); trivial. % 21.97/22.12 (* end of lemma zenon_L1339_ *) % 21.97/22.12 assert (zenon_L1340_ : (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (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 (e2) (e0)) = (op (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) (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H68 zenon_Ha9 zenon_H125 zenon_H61 zenon_H13f zenon_H1f1 zenon_H140 zenon_H234 zenon_He4 zenon_H162 zenon_H183 zenon_H191 zenon_Hf0 zenon_H109 zenon_H141 zenon_Hb2 zenon_H77 zenon_H18a zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H25 zenon_Hfa zenon_H7f zenon_H192 zenon_Ha0 zenon_H38 zenon_Hb6 zenon_H10c zenon_H173 zenon_H121 zenon_H33 zenon_H11a zenon_H1a3 zenon_Hc4 zenon_H13a zenon_H5c zenon_Hf5. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.12 apply (zenon_L251_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.97/22.12 apply (zenon_L251_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.97/22.12 apply (zenon_L171_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.97/22.12 apply (zenon_L253_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.97/22.12 apply (zenon_L110_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 21.97/22.12 apply (zenon_L253_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 21.97/22.12 apply (zenon_L116_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 21.97/22.12 apply (zenon_L43_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.97/22.12 apply (zenon_L171_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.97/22.12 apply (zenon_L226_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.97/22.12 apply (zenon_L1337_); trivial. % 21.97/22.12 apply (zenon_L206_); trivial. % 21.97/22.12 apply (zenon_L156_); trivial. % 21.97/22.12 apply (zenon_L1339_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.12 apply (zenon_L1249_); trivial. % 21.97/22.12 apply (zenon_L165_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.97/22.12 apply (zenon_L146_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.97/22.12 apply (zenon_L1252_); trivial. % 21.97/22.12 apply (zenon_L192_); trivial. % 21.97/22.12 (* end of lemma zenon_L1340_ *) % 21.97/22.12 assert (zenon_L1341_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> False). % 21.97/22.12 do 0 intro. intros zenon_H82 zenon_H68 zenon_H38 zenon_H77 zenon_H153 zenon_H13a zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H139 zenon_H5d zenon_H61 zenon_H48 zenon_H2d zenon_H7d zenon_H7f. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.97/22.12 apply (zenon_L1284_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.97/22.12 apply (zenon_L18_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.97/22.12 apply (zenon_L217_); trivial. % 21.97/22.12 apply (zenon_L31_); trivial. % 21.97/22.12 (* end of lemma zenon_L1341_ *) % 21.97/22.12 assert (zenon_L1342_ : (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H1a3 zenon_H11a zenon_H33 zenon_H121 zenon_H77 zenon_H5c zenon_H140 zenon_H68 zenon_H195 zenon_H48 zenon_H1f1 zenon_H65 zenon_H13f zenon_H61 zenon_Hbc zenon_H34 zenon_H173 zenon_H6e zenon_H1cf zenon_Ha9 zenon_H10c zenon_H47 zenon_Hb6 zenon_H13a zenon_H4e zenon_H1ef zenon_H1c3 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_Hfa zenon_H38 zenon_Ha0. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.97/22.12 apply (zenon_L538_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.97/22.12 apply (zenon_L120_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.97/22.12 apply (zenon_L1266_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.97/22.12 apply (zenon_L226_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.97/22.12 apply (zenon_L68_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.97/22.12 apply (zenon_L62_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.97/22.12 apply (zenon_L1336_); trivial. % 21.97/22.12 apply (zenon_L328_); trivial. % 21.97/22.12 apply (zenon_L206_); trivial. % 21.97/22.12 apply (zenon_L156_); trivial. % 21.97/22.12 (* end of lemma zenon_L1342_ *) % 21.97/22.12 assert (zenon_L1343_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H19a zenon_H1b7 zenon_H7f zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H34 zenon_H18a. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 21.97/22.12 apply (zenon_L1276_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 21.97/22.12 apply (zenon_L157_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 21.97/22.12 apply (zenon_L158_); trivial. % 21.97/22.12 apply (zenon_L416_); trivial. % 21.97/22.12 (* end of lemma zenon_L1343_ *) % 21.97/22.12 assert (zenon_L1344_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((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)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (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) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H16a zenon_Ha0 zenon_Hfa zenon_H1ef zenon_H4e zenon_H13a zenon_Hb6 zenon_H47 zenon_H10c zenon_Ha9 zenon_H1cf zenon_H173 zenon_Hbc zenon_H61 zenon_H13f zenon_H1f1 zenon_H195 zenon_H140 zenon_H121 zenon_H33 zenon_H11a zenon_Hdd zenon_H1a3 zenon_H1cb zenon_H1cd zenon_H105 zenon_H231 zenon_H104 zenon_H192 zenon_H6e zenon_H1c3 zenon_H38 zenon_H1c2 zenon_H183 zenon_H19a zenon_H1b7 zenon_H7f zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H48 zenon_H68 zenon_H34 zenon_H18a. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.12 apply (zenon_L1342_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.12 apply (zenon_L54_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.12 apply (zenon_L1275_); trivial. % 21.97/22.12 apply (zenon_L1343_); trivial. % 21.97/22.12 (* end of lemma zenon_L1344_ *) % 21.97/22.12 assert (zenon_L1345_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (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) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 21.97/22.12 do 0 intro. intros zenon_H201 zenon_H191 zenon_H1a2 zenon_Hf3 zenon_H18a zenon_H34 zenon_H68 zenon_H48 zenon_H5c zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1b7 zenon_H19a zenon_H183 zenon_H1c2 zenon_H38 zenon_H1c3 zenon_H6e zenon_H192 zenon_H104 zenon_H231 zenon_H1cb zenon_H1a3 zenon_Hdd zenon_H11a zenon_H33 zenon_H121 zenon_H140 zenon_H195 zenon_H1f1 zenon_H13f zenon_H61 zenon_Hbc zenon_H173 zenon_H1cf zenon_Ha9 zenon_H10c zenon_H47 zenon_Hb6 zenon_H13a zenon_H4e zenon_H1ef zenon_Hfa zenon_Ha0 zenon_H16a zenon_H1cd zenon_H7f. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.12 apply (zenon_L1265_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.12 apply (zenon_L117_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.12 apply (zenon_L1344_); trivial. % 21.97/22.12 apply (zenon_L331_); trivial. % 21.97/22.12 (* end of lemma zenon_L1345_ *) % 21.97/22.12 assert (zenon_L1346_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H15d zenon_H68 zenon_Ha9 zenon_H141 zenon_H109 zenon_H34 zenon_Hbc zenon_H191 zenon_H1a2 zenon_H18a zenon_H18d zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1b7 zenon_H19a zenon_H183 zenon_H1c2 zenon_H1c3 zenon_H104 zenon_H231 zenon_H1cb zenon_H140 zenon_H195 zenon_H1f1 zenon_H13f zenon_H61 zenon_H1cf zenon_H4e zenon_H1ef zenon_Hfa zenon_H16a zenon_H26d zenon_H1cd zenon_H48 zenon_H186 zenon_H139 zenon_H77 zenon_H201 zenon_H196 zenon_H7f zenon_H192 zenon_Ha0 zenon_H38 zenon_Hb6 zenon_H10c zenon_H173 zenon_H121 zenon_H33 zenon_H11a zenon_H1a3 zenon_Hc4 zenon_H13a zenon_H5c zenon_Hf5. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.12 apply (zenon_L251_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.12 apply (zenon_L359_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.97/22.12 apply (zenon_L756_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.97/22.12 apply (zenon_L1345_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.97/22.12 apply (zenon_L1285_); trivial. % 21.97/22.12 apply (zenon_L328_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.12 apply (zenon_L1285_); trivial. % 21.97/22.12 apply (zenon_L1162_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.12 apply (zenon_L1249_); trivial. % 21.97/22.12 apply (zenon_L165_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.97/22.12 apply (zenon_L146_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.97/22.12 apply (zenon_L1252_); trivial. % 21.97/22.12 apply (zenon_L192_); trivial. % 21.97/22.12 (* end of lemma zenon_L1346_ *) % 21.97/22.12 assert (zenon_L1347_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((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)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((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)) = (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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H1fe zenon_Hb2 zenon_H162 zenon_He4 zenon_H234 zenon_H125 zenon_H82 zenon_H5d zenon_H7d zenon_Hf0 zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H1fb zenon_Hcc zenon_H282 zenon_Heb zenon_H117 zenon_H236 zenon_H189 zenon_H27e zenon_H25b zenon_H1c6 zenon_H13c zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H283 zenon_H15d zenon_H68 zenon_Ha9 zenon_H141 zenon_H109 zenon_Hbc zenon_H191 zenon_H1a2 zenon_H18a zenon_H18d zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1b7 zenon_H19a zenon_H183 zenon_H1c2 zenon_H1c3 zenon_H104 zenon_H231 zenon_H1cb zenon_H140 zenon_H195 zenon_H1f1 zenon_H13f zenon_H61 zenon_H1cf zenon_H4e zenon_H1ef zenon_Hfa zenon_H16a zenon_H26d zenon_H1cd zenon_H48 zenon_H186 zenon_H139 zenon_H77 zenon_H201 zenon_H196 zenon_H7f zenon_H192 zenon_Ha0 zenon_H38 zenon_Hb6 zenon_H10c zenon_H173 zenon_H121 zenon_H33 zenon_H11a zenon_H1a3 zenon_Hc4 zenon_H13a zenon_H5c zenon_Hf5. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.97/22.12 apply (zenon_L1334_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.97/22.12 apply (zenon_L1340_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.12 apply (zenon_L251_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.12 apply (zenon_L1264_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.12 apply (zenon_L1249_); trivial. % 21.97/22.12 apply (zenon_L165_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.97/22.12 apply (zenon_L146_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.97/22.12 apply (zenon_L1341_); trivial. % 21.97/22.12 apply (zenon_L246_); trivial. % 21.97/22.12 apply (zenon_L1346_); trivial. % 21.97/22.12 (* end of lemma zenon_L1347_ *) % 21.97/22.12 assert (zenon_L1348_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.12 do 0 intro. intros zenon_H23b zenon_H173 zenon_H10c zenon_Ha9 zenon_H66 zenon_Ha0 zenon_H13a zenon_H38. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 21.97/22.12 exact (zenon_H238 zenon_H38). % 21.97/22.12 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.97/22.12 exact (zenon_Ha4 zenon_H9f). % 21.97/22.12 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.97/22.12 apply (zenon_L120_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.97/22.12 apply (zenon_L193_); trivial. % 21.97/22.12 apply (zenon_L156_); trivial. % 21.97/22.12 (* end of lemma zenon_L1348_ *) % 21.97/22.12 assert (zenon_L1349_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.12 do 0 intro. intros zenon_H63 zenon_H173 zenon_H10c zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H38. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 21.97/22.12 apply (zenon_L1348_); trivial. % 21.97/22.12 (* end of lemma zenon_L1349_ *) % 21.97/22.12 assert (zenon_L1350_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> False). % 21.97/22.12 do 0 intro. intros zenon_H15c zenon_H10c zenon_H5c. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 21.97/22.12 exact (zenon_Hec zenon_H5c). % 21.97/22.12 exact (zenon_H159 zenon_H10c). % 21.97/22.12 (* end of lemma zenon_L1350_ *) % 21.97/22.12 assert (zenon_L1351_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> False). % 21.97/22.12 do 0 intro. intros zenon_H87 zenon_H10c zenon_H5c. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 21.97/22.12 apply (zenon_L1350_); trivial. % 21.97/22.12 (* end of lemma zenon_L1351_ *) % 21.97/22.12 assert (zenon_L1352_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H99 zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H1cb. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 21.97/22.12 apply (zenon_L1260_); trivial. % 21.97/22.12 (* end of lemma zenon_L1352_ *) % 21.97/22.12 assert (zenon_L1353_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H9b zenon_H38 zenon_Ha0. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 21.97/22.12 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 21.97/22.12 apply (zenon_L156_); trivial. % 21.97/22.12 (* end of lemma zenon_L1353_ *) % 21.97/22.12 assert (zenon_L1354_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 21.97/22.12 do 0 intro. intros zenon_Hb1 zenon_H10c zenon_H11a. % 21.97/22.12 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 21.97/22.12 apply (zenon_L79_); trivial. % 21.97/22.12 (* end of lemma zenon_L1354_ *) % 21.97/22.12 assert (zenon_L1355_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H13a zenon_Ha0 zenon_H1e zenon_H173 zenon_H10c zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.97/22.12 apply (zenon_L41_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.97/22.12 apply (zenon_L120_); trivial. % 21.97/22.12 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.97/22.12 apply (zenon_L178_); trivial. % 21.97/22.12 apply (zenon_L154_); trivial. % 21.97/22.12 (* end of lemma zenon_L1355_ *) % 21.97/22.12 assert (zenon_L1356_ : ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 21.97/22.12 do 0 intro. intros zenon_H54 zenon_H1ba zenon_H8b zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H5c zenon_H129 zenon_H1bb. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.13 apply (zenon_L30_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.13 exact (zenon_H1ba zenon_H6d). % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.13 exact (zenon_H8b zenon_H8a). % 21.97/22.13 apply (zenon_L1236_); trivial. % 21.97/22.13 (* end of lemma zenon_L1356_ *) % 21.97/22.13 assert (zenon_L1357_ : (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 21.97/22.13 do 0 intro. intros zenon_H7b zenon_H53 zenon_H8b zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H5c zenon_H129 zenon_H1bb. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.13 exact (zenon_H7b zenon_H65). % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.13 apply (zenon_L56_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.13 exact (zenon_H8b zenon_H8a). % 21.97/22.13 apply (zenon_L1236_); trivial. % 21.97/22.13 (* end of lemma zenon_L1357_ *) % 21.97/22.13 assert (zenon_L1358_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.97/22.13 do 0 intro. intros zenon_H13f zenon_H1ba zenon_H1bb zenon_H129 zenon_H20f zenon_H38 zenon_H1b4 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H8b zenon_H7b zenon_H48 zenon_H14c zenon_H195 zenon_H5c. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.97/22.13 apply (zenon_L1356_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.97/22.13 apply (zenon_L1357_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.97/22.13 apply (zenon_L255_); trivial. % 21.97/22.13 apply (zenon_L149_); trivial. % 21.97/22.13 (* end of lemma zenon_L1358_ *) % 21.97/22.13 assert (zenon_L1359_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 21.97/22.13 do 0 intro. intros zenon_H140 zenon_H25 zenon_H5c zenon_H195 zenon_H48 zenon_H7b zenon_H8b zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H129 zenon_H1bb zenon_H1ba zenon_H13f zenon_Ha0 zenon_Hbb. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.97/22.13 apply (zenon_L756_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.97/22.13 apply (zenon_L274_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.97/22.13 apply (zenon_L1358_); trivial. % 21.97/22.13 apply (zenon_L80_); trivial. % 21.97/22.13 (* end of lemma zenon_L1359_ *) % 21.97/22.13 assert (zenon_L1360_ : (((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)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.97/22.13 do 0 intro. intros zenon_H16a zenon_H68 zenon_H2d zenon_H1ba zenon_H8b zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H5c zenon_H129 zenon_Hc4. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.13 apply (zenon_L27_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.13 exact (zenon_H1ba zenon_H6d). % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.13 exact (zenon_H8b zenon_H8a). % 21.97/22.13 apply (zenon_L413_); trivial. % 21.97/22.13 (* end of lemma zenon_L1360_ *) % 21.97/22.13 assert (zenon_L1361_ : (((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)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.97/22.13 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_H173 zenon_H10c zenon_H177 zenon_Hbb zenon_H38 zenon_Ha0. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.97/22.13 apply (zenon_L253_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.97/22.13 apply (zenon_L120_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.97/22.13 apply (zenon_L178_); trivial. % 21.97/22.13 apply (zenon_L156_); trivial. % 21.97/22.13 (* end of lemma zenon_L1361_ *) % 21.97/22.13 assert (zenon_L1362_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.97/22.13 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha9 zenon_H6e zenon_H177 zenon_Hbb zenon_H38 zenon_Ha0. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.97/22.13 apply (zenon_L253_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.97/22.13 apply (zenon_L110_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.97/22.13 apply (zenon_L178_); trivial. % 21.97/22.13 apply (zenon_L156_); trivial. % 21.97/22.13 (* end of lemma zenon_L1362_ *) % 21.97/22.13 assert (zenon_L1363_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.97/22.13 do 0 intro. intros zenon_H139 zenon_H77 zenon_Hbb zenon_H177 zenon_Ha0 zenon_Ha9 zenon_H3d zenon_Hb6 zenon_H47 zenon_H13a zenon_H38 zenon_H68. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.13 apply (zenon_L251_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.13 apply (zenon_L1362_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.13 apply (zenon_L1148_); trivial. % 21.97/22.13 apply (zenon_L165_); trivial. % 21.97/22.13 (* end of lemma zenon_L1363_ *) % 21.97/22.13 assert (zenon_L1364_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (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 (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.97/22.13 do 0 intro. intros zenon_H82 zenon_H3d zenon_H177 zenon_Hbb zenon_H1bb zenon_H129 zenon_H5c zenon_H20f zenon_H38 zenon_H1b4 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H8b zenon_H1ba zenon_H34 zenon_H48. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.97/22.13 apply (zenon_L1363_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.97/22.13 apply (zenon_L17_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.97/22.13 apply (zenon_L1356_); trivial. % 21.97/22.13 apply (zenon_L456_); trivial. % 21.97/22.13 (* end of lemma zenon_L1364_ *) % 21.97/22.13 assert (zenon_L1365_ : (((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)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 21.97/22.13 do 0 intro. intros zenon_H16a zenon_H7b zenon_H6f zenon_H6e zenon_H8b zenon_H17c zenon_H129. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.13 exact (zenon_H7b zenon_H65). % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.13 apply (zenon_L21_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.13 exact (zenon_H8b zenon_H8a). % 21.97/22.13 apply (zenon_L126_); trivial. % 21.97/22.13 (* end of lemma zenon_L1365_ *) % 21.97/22.13 assert (zenon_L1366_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((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)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 21.97/22.13 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H153 zenon_H234 zenon_H55 zenon_H54 zenon_H183 zenon_H34 zenon_H1cb zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H5c zenon_Hc4 zenon_H77 zenon_H68 zenon_H1c3 zenon_H288 zenon_He7 zenon_H192 zenon_H129 zenon_H8b zenon_H6f zenon_H7b zenon_H16a zenon_H10c zenon_H173. % 21.97/22.13 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.97/22.13 apply (zenon_L738_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.97/22.13 apply (zenon_L484_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.97/22.13 apply (zenon_L15_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.97/22.13 apply (zenon_L291_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.97/22.13 apply (zenon_L169_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.97/22.13 apply (zenon_L1260_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H2a | zenon_intro zenon_H289 ]. % 21.97/22.13 apply (zenon_L272_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H3d | zenon_intro zenon_H28a ]. % 21.97/22.13 apply (zenon_L146_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H6e | zenon_intro zenon_Hdb ]. % 21.97/22.13 apply (zenon_L1365_); trivial. % 21.97/22.13 apply (zenon_L120_); trivial. % 21.97/22.13 (* end of lemma zenon_L1366_ *) % 21.97/22.13 assert (zenon_L1367_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.13 do 0 intro. intros zenon_H1cf zenon_H1d5 zenon_H67 zenon_H4e zenon_H76 zenon_H8b zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H1cb. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.97/22.13 apply (zenon_L252_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.97/22.13 apply (zenon_L83_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.97/22.13 exact (zenon_H8b zenon_H8a). % 21.97/22.13 apply (zenon_L1260_); trivial. % 21.97/22.13 (* end of lemma zenon_L1367_ *) % 21.97/22.13 assert (zenon_L1368_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (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 (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.97/22.13 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H153 zenon_H234 zenon_H55 zenon_H54 zenon_Hfa zenon_H1cb zenon_H38 zenon_H1c3 zenon_H4e zenon_H67 zenon_H1d5 zenon_H1cf zenon_H18a zenon_H34 zenon_H48 zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1b7 zenon_H19a zenon_H8b zenon_Hf0 zenon_H7b zenon_H16a zenon_Hf3 zenon_H68 zenon_H5c zenon_H77. % 21.97/22.13 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.97/22.13 apply (zenon_L738_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.97/22.13 apply (zenon_L484_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.97/22.13 apply (zenon_L15_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.97/22.13 apply (zenon_L1367_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.13 exact (zenon_H7b zenon_H65). % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.13 apply (zenon_L61_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.13 exact (zenon_H8b zenon_H8a). % 21.97/22.13 apply (zenon_L1343_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.97/22.13 apply (zenon_L62_); trivial. % 21.97/22.13 apply (zenon_L206_); trivial. % 21.97/22.13 (* end of lemma zenon_L1368_ *) % 21.97/22.13 assert (zenon_L1369_ : (((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) (e1)) = (e3)) -> (~((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.97/22.13 do 0 intro. intros zenon_H13b zenon_H179 zenon_H173 zenon_H10c zenon_H6f zenon_H192 zenon_H288 zenon_H183 zenon_H77 zenon_H68 zenon_H16a zenon_H7b zenon_Hf0 zenon_H8b zenon_H19a zenon_H1b7 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H34 zenon_H18a zenon_H1cf zenon_H1d5 zenon_H67 zenon_H4e zenon_H1c3 zenon_H38 zenon_H1cb zenon_Hfa zenon_H54 zenon_H55 zenon_H234 zenon_H153 zenon_H1d8 zenon_He4 zenon_H48 zenon_H5c. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.97/22.13 apply (zenon_L297_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.97/22.13 apply (zenon_L1366_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.97/22.13 apply (zenon_L1368_); trivial. % 21.97/22.13 apply (zenon_L157_); trivial. % 21.97/22.13 (* end of lemma zenon_L1369_ *) % 21.97/22.13 assert (zenon_L1370_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (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)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.97/22.13 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H153 zenon_H234 zenon_H55 zenon_H54 zenon_H16a zenon_H7b zenon_H6f zenon_H6e zenon_H8b zenon_H19a zenon_H1b7 zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H48 zenon_H68 zenon_H34 zenon_H18a. % 21.97/22.13 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.97/22.13 apply (zenon_L738_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.97/22.13 apply (zenon_L484_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.97/22.13 apply (zenon_L15_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.13 exact (zenon_H7b zenon_H65). % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.13 apply (zenon_L21_); trivial. % 21.97/22.13 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.13 exact (zenon_H8b zenon_H8a). % 21.97/22.13 apply (zenon_L1343_); trivial. % 21.97/22.13 (* end of lemma zenon_L1370_ *) % 21.97/22.13 assert (zenon_L1371_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (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)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.97/22.14 do 0 intro. intros zenon_H82 zenon_H13a zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H5d zenon_H68 zenon_H38 zenon_H77 zenon_H153 zenon_He4 zenon_H1d8 zenon_H234 zenon_H55 zenon_H16a zenon_H7b zenon_H6f zenon_H8b zenon_H19a zenon_H1b7 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H18a zenon_H13b zenon_H179 zenon_H173 zenon_H10c zenon_H192 zenon_H288 zenon_H183 zenon_Hf0 zenon_H1cf zenon_H1d5 zenon_H4e zenon_H1c3 zenon_H1cb zenon_Hfa zenon_H139 zenon_H34 zenon_H48. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.97/22.14 apply (zenon_L1284_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.97/22.14 apply (zenon_L17_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.14 apply (zenon_L1369_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.14 apply (zenon_L1370_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.14 apply (zenon_L94_); trivial. % 21.97/22.14 apply (zenon_L165_); trivial. % 21.97/22.14 apply (zenon_L456_); trivial. % 21.97/22.14 (* end of lemma zenon_L1371_ *) % 21.97/22.14 assert (zenon_L1372_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e2) (e3)) = (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 (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (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) (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) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.97/22.14 do 0 intro. intros zenon_H1fe zenon_Hb9 zenon_H13f zenon_H140 zenon_H1ba zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H196 zenon_H13c zenon_H1ef zenon_H266 zenon_H190 zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H283 zenon_Hbb zenon_H177 zenon_H139 zenon_Hfa zenon_H1cb zenon_H1c3 zenon_H4e zenon_H1d5 zenon_H1cf zenon_Hf0 zenon_H183 zenon_H288 zenon_H192 zenon_H10c zenon_H173 zenon_H179 zenon_H13b zenon_H18a zenon_H5c zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1b7 zenon_H19a zenon_H8b zenon_H6f zenon_H7b zenon_H16a zenon_H55 zenon_H234 zenon_H1d8 zenon_He4 zenon_H77 zenon_H68 zenon_H5d zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H82 zenon_H38 zenon_H48. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.97/22.14 apply (zenon_L1355_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.97/22.14 apply (zenon_L1359_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.97/22.14 apply (zenon_L1360_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.97/22.14 apply (zenon_L1361_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.97/22.14 apply (zenon_L1364_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.97/22.14 apply (zenon_L1371_); trivial. % 21.97/22.14 apply (zenon_L246_); trivial. % 21.97/22.14 (* end of lemma zenon_L1372_ *) % 21.97/22.14 assert (zenon_L1373_ : (((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) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.97/22.14 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H5c zenon_H129 zenon_Hc4. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.14 exact (zenon_H7b zenon_H65). % 21.97/22.14 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.14 apply (zenon_L61_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.14 exact (zenon_H8b zenon_H8a). % 21.97/22.14 apply (zenon_L413_); trivial. % 21.97/22.14 (* end of lemma zenon_L1373_ *) % 21.97/22.14 assert (zenon_L1374_ : (((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)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.97/22.14 do 0 intro. intros zenon_H16a zenon_H7b zenon_H6f zenon_H6e zenon_H8b zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H7f zenon_H1b7. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.14 exact (zenon_H7b zenon_H65). % 21.97/22.14 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.14 apply (zenon_L21_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.14 exact (zenon_H8b zenon_H8a). % 21.97/22.14 apply (zenon_L1276_); trivial. % 21.97/22.14 (* end of lemma zenon_L1374_ *) % 21.97/22.14 assert (zenon_L1375_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.97/22.14 do 0 intro. intros zenon_H212 zenon_He0 zenon_H7f zenon_H7d zenon_H18a zenon_H17c zenon_Hbb zenon_Hbc. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H34 | zenon_intro zenon_H213 ]. % 21.97/22.14 apply (zenon_L802_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H7e | zenon_intro zenon_H214 ]. % 21.97/22.14 apply (zenon_L31_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H102 | zenon_intro zenon_H9d ]. % 21.97/22.14 apply (zenon_L268_); trivial. % 21.97/22.14 apply (zenon_L48_); trivial. % 21.97/22.14 (* end of lemma zenon_L1375_ *) % 21.97/22.14 assert (zenon_L1376_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((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) (e1)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 21.97/22.14 do 0 intro. intros zenon_H183 zenon_H6d zenon_H189 zenon_H5c zenon_H38 zenon_H68 zenon_H1c3 zenon_H77 zenon_H72 zenon_H163 zenon_H212 zenon_He0 zenon_H7f zenon_H7d zenon_H18a zenon_Hbb zenon_Hbc. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.97/22.14 apply (zenon_L1338_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.97/22.14 apply (zenon_L169_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.97/22.14 apply (zenon_L227_); trivial. % 21.97/22.14 apply (zenon_L1375_); trivial. % 21.97/22.14 (* end of lemma zenon_L1376_ *) % 21.97/22.14 assert (zenon_L1377_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (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) (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 (e1) (e1)) = (e3)) -> (~((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.14 do 0 intro. intros zenon_H164 zenon_H48 zenon_He4 zenon_H1d8 zenon_H153 zenon_H234 zenon_H55 zenon_H54 zenon_Hfa zenon_H1cb zenon_H4e zenon_H67 zenon_H1d5 zenon_H1cf zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1bb zenon_H1b7 zenon_H19a zenon_H8b zenon_Hf0 zenon_H7b zenon_H16a zenon_H288 zenon_H192 zenon_H6f zenon_H10c zenon_H173 zenon_H179 zenon_H13b zenon_Hbc zenon_H18a zenon_H7d zenon_H7f zenon_H212 zenon_H163 zenon_H72 zenon_H77 zenon_H1c3 zenon_H68 zenon_H5c zenon_H189 zenon_H6d zenon_H183 zenon_Hbb zenon_Ha0 zenon_H1b4 zenon_H38. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 21.97/22.14 apply (zenon_L1369_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 21.97/22.14 apply (zenon_L1376_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 21.97/22.14 apply (zenon_L80_); trivial. % 21.97/22.14 apply (zenon_L411_); trivial. % 21.97/22.14 (* end of lemma zenon_L1377_ *) % 21.97/22.14 assert (zenon_L1378_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (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) (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 (e1) (e1)) = (e3)) -> (~((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.97/22.14 do 0 intro. intros zenon_H164 zenon_H48 zenon_He4 zenon_H1d8 zenon_H153 zenon_H234 zenon_H55 zenon_H54 zenon_Hfa zenon_H1cb zenon_H4e zenon_H67 zenon_H1d5 zenon_H1cf zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1bb zenon_H1b7 zenon_H19a zenon_H8b zenon_Hf0 zenon_H7b zenon_H16a zenon_H288 zenon_H192 zenon_H6f zenon_H10c zenon_H173 zenon_H179 zenon_H13b zenon_Hbc zenon_H18a zenon_H7d zenon_H212 zenon_H163 zenon_H1c3 zenon_H68 zenon_H189 zenon_H183 zenon_Hbb zenon_Ha0 zenon_H1b4 zenon_H38 zenon_H156 zenon_H1a8 zenon_H5c zenon_H77. % 21.97/22.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.97/22.14 apply (zenon_L738_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.97/22.14 apply (zenon_L484_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.97/22.14 apply (zenon_L15_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.97/22.14 apply (zenon_L1367_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.97/22.14 apply (zenon_L1373_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.97/22.14 apply (zenon_L1374_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.97/22.14 apply (zenon_L100_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.97/22.14 apply (zenon_L1377_); trivial. % 21.97/22.14 apply (zenon_L169_); trivial. % 21.97/22.14 apply (zenon_L206_); trivial. % 21.97/22.14 (* end of lemma zenon_L1378_ *) % 21.97/22.14 assert (zenon_L1379_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((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)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (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 (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 (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 21.97/22.14 do 0 intro. intros zenon_H13f zenon_Hbb zenon_H72 zenon_H164 zenon_He4 zenon_H1d8 zenon_H234 zenon_Hfa zenon_H67 zenon_H1d5 zenon_Hc4 zenon_Hf0 zenon_H288 zenon_H192 zenon_H10c zenon_H179 zenon_H13b zenon_Hbc zenon_H18a zenon_H7d zenon_H212 zenon_H183 zenon_H1a8 zenon_H201 zenon_H1bb zenon_H129 zenon_H5c zenon_H20f zenon_H38 zenon_H1b4 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H8b zenon_H7b zenon_H1bf zenon_Hb6 zenon_Hb9. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.14 apply (zenon_L1378_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.14 apply (zenon_L59_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.14 exact (zenon_H1bf zenon_H105). % 21.97/22.14 apply (zenon_L363_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.97/22.14 apply (zenon_L1357_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.97/22.14 exact (zenon_H1bf zenon_H105). % 21.97/22.14 apply (zenon_L182_); trivial. % 21.97/22.14 (* end of lemma zenon_L1379_ *) % 21.97/22.14 assert (zenon_L1380_ : ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (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 (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((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)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.97/22.14 do 0 intro. intros zenon_Hb9 zenon_Hb6 zenon_H1bf zenon_H7b zenon_H8b zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H129 zenon_H1bb zenon_H201 zenon_H1a8 zenon_H183 zenon_H212 zenon_H7d zenon_H18a zenon_Hbc zenon_H13b zenon_H179 zenon_H10c zenon_H192 zenon_H288 zenon_Hf0 zenon_Hc4 zenon_H1d5 zenon_H67 zenon_Hfa zenon_H234 zenon_H1d8 zenon_He4 zenon_H164 zenon_Hbb zenon_H13f zenon_H5c zenon_H77. % 21.97/22.14 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.97/22.14 apply (zenon_L1367_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.97/22.14 apply (zenon_L1373_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.97/22.14 apply (zenon_L1379_); trivial. % 21.97/22.14 apply (zenon_L206_); trivial. % 21.97/22.14 (* end of lemma zenon_L1380_ *) % 21.97/22.14 assert (zenon_L1381_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (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 (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (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)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.97/22.14 do 0 intro. intros zenon_He4 zenon_H234 zenon_H5c zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H196 zenon_H1cb zenon_H1a2 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H16a zenon_H7b zenon_H6f zenon_H6e zenon_H8b zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1b7. % 21.97/22.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.97/22.14 apply (zenon_L214_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.97/22.14 apply (zenon_L484_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.97/22.14 apply (zenon_L1357_); trivial. % 21.97/22.14 apply (zenon_L1374_); trivial. % 21.97/22.14 (* end of lemma zenon_L1381_ *) % 21.97/22.14 assert (zenon_L1382_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 21.97/22.14 do 0 intro. intros zenon_H201 zenon_H66 zenon_H77 zenon_H186 zenon_H5c zenon_H1bf zenon_Hb6 zenon_Hbb. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.14 apply (zenon_L94_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.14 apply (zenon_L138_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.14 exact (zenon_H1bf zenon_H105). % 21.97/22.14 apply (zenon_L363_); trivial. % 21.97/22.14 (* end of lemma zenon_L1382_ *) % 21.97/22.14 assert (zenon_L1383_ : (((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))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (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) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (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)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.97/22.14 do 0 intro. intros zenon_H13f zenon_H164 zenon_H1d8 zenon_Hfa zenon_H1d5 zenon_Hf0 zenon_H288 zenon_H192 zenon_H10c zenon_H179 zenon_H13b zenon_Hbc zenon_H18a zenon_H7d zenon_H212 zenon_H183 zenon_H1a8 zenon_Hb9 zenon_H1b7 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H8b zenon_H6f zenon_H7b zenon_H16a zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H1cb zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H234 zenon_He4 zenon_Hbb zenon_Hb6 zenon_H1bf zenon_H5c zenon_H186 zenon_H77 zenon_H201 zenon_H38 zenon_H68. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.14 apply (zenon_L1380_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.14 apply (zenon_L1381_); trivial. % 21.97/22.14 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.14 apply (zenon_L1382_); trivial. % 21.97/22.14 apply (zenon_L165_); trivial. % 21.97/22.15 (* end of lemma zenon_L1383_ *) % 21.97/22.15 assert (zenon_L1384_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (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) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> False). % 21.97/22.15 do 0 intro. intros zenon_H89 zenon_H201 zenon_Hb6 zenon_H1bf zenon_H1d8 zenon_H234 zenon_H55 zenon_H48 zenon_H1b7 zenon_H18d zenon_H6f zenon_H156 zenon_H164 zenon_Ha0 zenon_H189 zenon_H163 zenon_H212 zenon_Hbb zenon_Hbc zenon_H7d zenon_H179 zenon_He4 zenon_H288 zenon_H10c zenon_H192 zenon_H173 zenon_H183 zenon_H18a zenon_H19a zenon_Hfa zenon_H13b zenon_H1a8 zenon_H283 zenon_H131 zenon_H73 zenon_H1ec zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H190 zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H196 zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_Hb9 zenon_H13f zenon_H7b zenon_Hf0 zenon_H16a zenon_H1d5 zenon_H4e zenon_H1c3 zenon_H1cb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H1bb zenon_H5c zenon_H77 zenon_H38 zenon_H68 zenon_H1cf. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.97/22.15 apply (zenon_L1383_); trivial. % 21.97/22.15 apply (zenon_L1383_); trivial. % 21.97/22.15 (* end of lemma zenon_L1384_ *) % 21.97/22.15 assert (zenon_L1385_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 21.97/22.15 do 0 intro. intros zenon_H140 zenon_H26d zenon_H38 zenon_H25 zenon_H4e zenon_H13d zenon_Ha0 zenon_Hbb. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 21.97/22.15 apply (zenon_L756_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 21.97/22.15 apply (zenon_L274_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 21.97/22.15 exact (zenon_H13d zenon_H14c). % 21.97/22.15 apply (zenon_L80_); trivial. % 21.97/22.15 (* end of lemma zenon_L1385_ *) % 21.97/22.15 assert (zenon_L1386_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 21.97/22.15 do 0 intro. intros zenon_H16a zenon_H195 zenon_H111 zenon_H153 zenon_Hdd zenon_H13f zenon_H1ba zenon_H8b zenon_H19a zenon_H1b7 zenon_H7f zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H48 zenon_H68 zenon_H34 zenon_H18a. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.15 apply (zenon_L150_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.15 exact (zenon_H1ba zenon_H6d). % 21.97/22.15 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.15 exact (zenon_H8b zenon_H8a). % 21.97/22.15 apply (zenon_L1343_); trivial. % 21.97/22.15 (* end of lemma zenon_L1386_ *) % 21.97/22.15 assert (zenon_L1387_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (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) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 21.97/22.15 do 0 intro. intros zenon_H141 zenon_H54 zenon_H18a zenon_H34 zenon_H68 zenon_H48 zenon_H5c zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H7f zenon_H1b7 zenon_H19a zenon_H8b zenon_H1ba zenon_H13f zenon_H153 zenon_H111 zenon_H195 zenon_H16a zenon_H13d zenon_Ha0 zenon_Hb9. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.15 apply (zenon_L217_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.15 apply (zenon_L1386_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.15 exact (zenon_H13d zenon_H14c). % 21.97/22.15 apply (zenon_L77_); trivial. % 21.97/22.15 (* end of lemma zenon_L1387_ *) % 21.97/22.15 assert (zenon_L1388_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e1)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (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) (e1)) = (op (e2) (e2)))) -> (((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) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (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) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (((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). % 21.97/22.15 do 0 intro. intros zenon_H1fe zenon_H140 zenon_H10c zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H1cb zenon_H196 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_Hbb zenon_H177 zenon_H48 zenon_He4 zenon_H1d8 zenon_H234 zenon_H55 zenon_H141 zenon_H18a zenon_H68 zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1b7 zenon_H19a zenon_H8b zenon_H1ba zenon_H13f zenon_H111 zenon_H195 zenon_H16a zenon_H13d zenon_Ha0 zenon_Hb9 zenon_H5d zenon_H139 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H38 zenon_H82 zenon_H5c zenon_Hf5. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 21.97/22.15 apply (zenon_L1355_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 21.97/22.15 apply (zenon_L1385_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 21.97/22.15 apply (zenon_L1360_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.97/22.15 apply (zenon_L1361_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.97/22.15 apply (zenon_L1364_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.97/22.15 apply (zenon_L1284_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.97/22.15 apply (zenon_L17_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.97/22.15 apply (zenon_L738_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.97/22.15 apply (zenon_L484_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.97/22.15 apply (zenon_L15_); trivial. % 21.97/22.15 apply (zenon_L1387_); trivial. % 21.97/22.15 apply (zenon_L456_); trivial. % 21.97/22.15 apply (zenon_L192_); trivial. % 21.97/22.15 (* end of lemma zenon_L1388_ *) % 21.97/22.15 assert (zenon_L1389_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 21.97/22.15 do 0 intro. intros zenon_H89 zenon_H13d zenon_H1bf zenon_H191 zenon_H13e. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.97/22.15 apply (zenon_L382_); trivial. % 21.97/22.15 apply (zenon_L382_); trivial. % 21.97/22.15 (* end of lemma zenon_L1389_ *) % 21.97/22.15 assert (zenon_L1390_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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 (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (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 (e2) (e2)) = (op (e2) (e3)))) -> (~((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)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (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)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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))))) -> (~((e2) = (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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 21.97/22.15 do 0 intro. intros zenon_H2c zenon_H26a zenon_H23c zenon_H24e zenon_H12e zenon_H121 zenon_H33 zenon_H125 zenon_Hb2 zenon_H1f1 zenon_H109 zenon_H1cd zenon_H231 zenon_H104 zenon_H1c2 zenon_H11a zenon_H1a8 zenon_H7d zenon_Hbc zenon_H212 zenon_H164 zenon_H201 zenon_H1fe zenon_H82 zenon_H13b zenon_Hfa zenon_Hf0 zenon_H18a zenon_H1d5 zenon_H1d8 zenon_H234 zenon_H183 zenon_H192 zenon_H288 zenon_He4 zenon_H179 zenon_Hc4 zenon_H26d zenon_H38 zenon_H4e zenon_H13f zenon_H77 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_Ha9 zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H5c zenon_H129 zenon_H1bb zenon_H140 zenon_Ha0 zenon_H173 zenon_H10c zenon_H177 zenon_H196 zenon_H13a zenon_H191 zenon_H141 zenon_H111. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 21.97/22.15 apply (zenon_L2_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 21.97/22.15 apply (zenon_L1146_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 21.97/22.15 apply (zenon_L1147_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 21.97/22.15 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 21.97/22.15 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 21.97/22.15 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.97/22.15 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.97/22.15 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.97/22.15 apply (zenon_L1333_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 21.97/22.15 apply (zenon_L1206_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 21.97/22.15 apply (zenon_L11_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 21.97/22.15 apply (zenon_L1207_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 21.97/22.15 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 21.97/22.15 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 21.97/22.15 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 21.97/22.15 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 21.97/22.15 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.97/22.15 apply (zenon_L1250_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.97/22.15 apply (zenon_L146_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.97/22.15 apply (zenon_L1252_); trivial. % 21.97/22.15 apply (zenon_L192_); trivial. % 21.97/22.15 apply (zenon_L414_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.97/22.15 apply (zenon_L1347_); trivial. % 21.97/22.15 apply (zenon_L414_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 21.97/22.15 apply (zenon_L1349_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 21.97/22.15 apply (zenon_L1351_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 21.97/22.15 apply (zenon_L37_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 21.97/22.15 apply (zenon_L1352_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 21.97/22.15 apply (zenon_L1353_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 21.97/22.15 apply (zenon_L1354_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 21.97/22.15 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 21.97/22.15 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 21.97/22.15 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 21.97/22.15 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 21.97/22.15 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.97/22.15 apply (zenon_L1372_); trivial. % 21.97/22.15 apply (zenon_L1372_); trivial. % 21.97/22.15 apply (zenon_L1384_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 21.97/22.15 apply (zenon_L1388_); trivial. % 21.97/22.15 apply (zenon_L1388_); trivial. % 21.97/22.15 apply (zenon_L1389_); trivial. % 21.97/22.15 apply (zenon_L51_); trivial. % 21.97/22.15 (* end of lemma zenon_L1390_ *) % 21.97/22.15 assert (zenon_L1391_ : ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (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)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (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) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (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) (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (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)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e3)) -> False). % 21.97/22.15 do 0 intro. intros zenon_H38 zenon_H1fb zenon_H26d zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H1c3 zenon_H139 zenon_H68 zenon_H173 zenon_Hb6 zenon_Ha9 zenon_H121 zenon_H177 zenon_H11a zenon_Ha0 zenon_H13a zenon_H77 zenon_H33 zenon_H48 zenon_H15d zenon_H1d5 zenon_H2c zenon_H1d8 zenon_H111 zenon_H26a zenon_H23c zenon_H82 zenon_H234 zenon_H141 zenon_H186 zenon_H1c2 zenon_H183 zenon_H1f1 zenon_H24e zenon_H1cd zenon_H7d zenon_H12e zenon_H192 zenon_H19a zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_Hcc zenon_H282 zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H18a zenon_H201 zenon_H109 zenon_H104 zenon_H231 zenon_He4 zenon_Hbc zenon_H140 zenon_Hfa zenon_Hf0 zenon_H13f zenon_H125 zenon_Hb2 zenon_H1fe zenon_H1a8 zenon_H212 zenon_H164 zenon_H13b zenon_H288 zenon_H179 zenon_H10c. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H159 | zenon_intro zenon_H5c ]. % 21.97/22.15 exact (zenon_H159 zenon_H10c). % 21.97/22.15 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H191 | zenon_intro zenon_H93 ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 21.97/22.15 apply (zenon_L1390_); trivial. % 21.97/22.15 apply (zenon_L1235_); trivial. % 21.97/22.15 apply (zenon_L1236_); trivial. % 21.97/22.15 (* end of lemma zenon_L1391_ *) % 21.97/22.15 assert (zenon_L1392_ : ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 21.97/22.15 do 0 intro. intros zenon_H54 zenon_Hf0 zenon_Hef zenon_H66 zenon_H111 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H5c zenon_H129 zenon_H1bb. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.15 apply (zenon_L30_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.15 apply (zenon_L61_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.15 apply (zenon_L258_); trivial. % 21.97/22.15 apply (zenon_L1236_); trivial. % 21.97/22.15 (* end of lemma zenon_L1392_ *) % 21.97/22.15 assert (zenon_L1393_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.15 do 0 intro. intros zenon_H141 zenon_H48 zenon_H68 zenon_H195 zenon_Ha5 zenon_Ha0 zenon_H6d zenon_Ha9 zenon_H54 zenon_Hb6 zenon_H117 zenon_H196 zenon_H38. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.15 apply (zenon_L217_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.15 apply (zenon_L54_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.15 apply (zenon_L1090_); trivial. % 21.97/22.15 apply (zenon_L1162_); trivial. % 21.97/22.15 (* end of lemma zenon_L1393_ *) % 21.97/22.15 assert (zenon_L1394_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.97/22.15 do 0 intro. intros zenon_H117 zenon_Ha0 zenon_H2d zenon_Ha9 zenon_H6d zenon_Hb6 zenon_H105 zenon_Ha5 zenon_H195. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.97/22.15 apply (zenon_L67_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.97/22.15 apply (zenon_L289_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.97/22.15 apply (zenon_L400_); trivial. % 21.97/22.15 apply (zenon_L172_); trivial. % 21.97/22.15 (* end of lemma zenon_L1394_ *) % 21.97/22.15 assert (zenon_L1395_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((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)) = (e1)) -> False). % 21.97/22.15 do 0 intro. intros zenon_H13f zenon_H38 zenon_H196 zenon_H68 zenon_H48 zenon_H141 zenon_H77 zenon_Ha5 zenon_Hb6 zenon_H6d zenon_Ha9 zenon_H2d zenon_Ha0 zenon_H117 zenon_H195 zenon_H5c. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.97/22.15 apply (zenon_L1393_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.97/22.15 apply (zenon_L56_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.97/22.15 apply (zenon_L1394_); trivial. % 21.97/22.15 apply (zenon_L149_); trivial. % 21.97/22.15 (* end of lemma zenon_L1395_ *) % 21.97/22.15 assert (zenon_L1396_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 21.97/22.15 do 0 intro. intros zenon_H13f zenon_Ha5 zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H117 zenon_H6d zenon_H77 zenon_H48 zenon_H14c zenon_H195 zenon_H5c. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.97/22.15 apply (zenon_L1090_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.97/22.15 apply (zenon_L56_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.97/22.15 apply (zenon_L255_); trivial. % 21.97/22.15 apply (zenon_L149_); trivial. % 21.97/22.15 (* end of lemma zenon_L1396_ *) % 21.97/22.15 assert (zenon_L1397_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (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). % 21.97/22.15 do 0 intro. intros zenon_H141 zenon_H68 zenon_H5c zenon_H195 zenon_H48 zenon_H77 zenon_H6d zenon_H117 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_Ha5 zenon_H13f zenon_H196 zenon_H38. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.15 apply (zenon_L1395_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.15 apply (zenon_L54_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.15 apply (zenon_L1396_); trivial. % 21.97/22.15 apply (zenon_L1162_); trivial. % 21.97/22.15 (* end of lemma zenon_L1397_ *) % 21.97/22.15 assert (zenon_L1398_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((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) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 21.97/22.15 do 0 intro. intros zenon_H1a8 zenon_H3d zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_H66 zenon_Hf0 zenon_H54 zenon_H38 zenon_H196 zenon_H13f zenon_Ha5 zenon_Ha0 zenon_Hb6 zenon_H117 zenon_H77 zenon_H48 zenon_H195 zenon_H5c zenon_H68 zenon_H141 zenon_Ha9 zenon_Hac. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.97/22.15 apply (zenon_L214_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.97/22.15 apply (zenon_L1392_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.97/22.15 apply (zenon_L1397_); trivial. % 21.97/22.15 apply (zenon_L371_); trivial. % 21.97/22.15 (* end of lemma zenon_L1398_ *) % 21.97/22.15 assert (zenon_L1399_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e2) (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) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (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 (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((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) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 21.97/22.15 do 0 intro. intros zenon_H179 zenon_H288 zenon_H13b zenon_H164 zenon_H212 zenon_H1fe zenon_Hb2 zenon_H125 zenon_Hfa zenon_H140 zenon_Hbc zenon_He4 zenon_H231 zenon_H104 zenon_H109 zenon_H201 zenon_H18a zenon_H192 zenon_H12e zenon_H7d zenon_H1cd zenon_H24e zenon_H1f1 zenon_H183 zenon_H1c2 zenon_H234 zenon_H82 zenon_H23c zenon_H26a zenon_H1d8 zenon_H2c zenon_H1d5 zenon_H33 zenon_H11a zenon_H177 zenon_H121 zenon_H1a3 zenon_H1a8 zenon_H3d zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_H66 zenon_Hf0 zenon_H54 zenon_H38 zenon_H196 zenon_H13f zenon_Ha5 zenon_Ha0 zenon_Hb6 zenon_H117 zenon_H77 zenon_H48 zenon_H195 zenon_H5c zenon_H68 zenon_H141 zenon_Ha9. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.97/22.15 apply (zenon_L55_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.97/22.15 apply (zenon_L1391_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.97/22.15 apply (zenon_L1173_); trivial. % 21.97/22.15 apply (zenon_L1398_); trivial. % 21.97/22.15 (* end of lemma zenon_L1399_ *) % 21.97/22.15 assert (zenon_L1400_ : ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e2) (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) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (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 (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((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))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 21.97/22.15 do 0 intro. intros zenon_H9f zenon_H24 zenon_Hc4 zenon_Hf3 zenon_H179 zenon_H288 zenon_H13b zenon_H164 zenon_H212 zenon_H1fe zenon_Hb2 zenon_H125 zenon_Hfa zenon_H140 zenon_Hbc zenon_He4 zenon_H231 zenon_H104 zenon_H109 zenon_H201 zenon_H18a zenon_H192 zenon_H12e zenon_H7d zenon_H1cd zenon_H24e zenon_H1f1 zenon_H183 zenon_H1c2 zenon_H234 zenon_H82 zenon_H23c zenon_H26a zenon_H1d8 zenon_H2c zenon_H1d5 zenon_H33 zenon_H11a zenon_H177 zenon_H121 zenon_H1a3 zenon_H1a8 zenon_H3d zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_H66 zenon_Hf0 zenon_H54 zenon_H38 zenon_H196 zenon_H13f zenon_Ha0 zenon_Hb6 zenon_H117 zenon_H77 zenon_H48 zenon_H195 zenon_H5c zenon_H68 zenon_H141 zenon_Ha9. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.15 apply (zenon_L900_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.15 apply (zenon_L1248_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.15 apply (zenon_L162_); trivial. % 21.97/22.15 apply (zenon_L1399_); trivial. % 21.97/22.15 (* end of lemma zenon_L1400_ *) % 21.97/22.15 assert (zenon_L1401_ : (((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)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.97/22.15 do 0 intro. intros zenon_H121 zenon_H33 zenon_H9f zenon_He0 zenon_Ha0 zenon_H1a3 zenon_Hc4. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.97/22.15 apply (zenon_L245_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.97/22.15 apply (zenon_L107_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.97/22.15 exact (zenon_H1a3 zenon_Hbb). % 21.97/22.15 exact (zenon_Hc4 zenon_Hc3). % 21.97/22.15 (* end of lemma zenon_L1401_ *) % 21.97/22.15 assert (zenon_L1402_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e2) (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) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((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))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((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)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 21.97/22.15 do 0 intro. intros zenon_H36 zenon_H100 zenon_H68 zenon_H34 zenon_H94 zenon_Hc4 zenon_H1a3 zenon_Ha0 zenon_H9f zenon_H33 zenon_H121 zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_H1c7 zenon_H24 zenon_H179 zenon_H288 zenon_H13b zenon_H164 zenon_H212 zenon_H1fe zenon_Hb2 zenon_H125 zenon_Hfa zenon_H140 zenon_Hbc zenon_He4 zenon_H231 zenon_H104 zenon_H109 zenon_H201 zenon_H18a zenon_H192 zenon_H12e zenon_H7d zenon_H1cd zenon_H24e zenon_H1f1 zenon_H183 zenon_H1c2 zenon_H234 zenon_H82 zenon_H23c zenon_H26a zenon_H1d8 zenon_H2c zenon_H1d5 zenon_H11a zenon_H177 zenon_H1a8 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_Hf0 zenon_H54 zenon_H13f zenon_H117 zenon_H77 zenon_H48 zenon_H195 zenon_H141 zenon_Ha9 zenon_He2 zenon_Hf5 zenon_H38 zenon_H93 zenon_H196. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.97/22.15 apply (zenon_L297_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.97/22.15 apply (zenon_L1237_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.97/22.15 apply (zenon_L1243_); trivial. % 21.97/22.15 apply (zenon_L663_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.15 apply (zenon_L214_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 21.97/22.15 apply (zenon_L252_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.97/22.15 apply (zenon_L171_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.97/22.15 apply (zenon_L214_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.97/22.15 apply (zenon_L1245_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.97/22.15 apply (zenon_L439_); trivial. % 21.97/22.15 apply (zenon_L1246_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.97/22.15 apply (zenon_L65_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.97/22.15 apply (zenon_L1247_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.97/22.15 apply (zenon_L1240_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.97/22.15 apply (zenon_L117_); trivial. % 21.97/22.15 apply (zenon_L1400_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.97/22.15 apply (zenon_L1242_); trivial. % 21.97/22.15 apply (zenon_L1401_); trivial. % 21.97/22.15 apply (zenon_L663_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 21.97/22.15 apply (zenon_L38_); trivial. % 21.97/22.15 apply (zenon_L291_); trivial. % 21.97/22.15 apply (zenon_L167_); trivial. % 21.97/22.15 (* end of lemma zenon_L1402_ *) % 21.97/22.15 assert (zenon_L1403_ : (((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)))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.97/22.15 do 0 intro. intros zenon_H117 zenon_H9f zenon_H2c zenon_Hb6 zenon_H53 zenon_H14c zenon_Ha0 zenon_Ha5 zenon_H195. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.97/22.15 apply (zenon_L1065_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.97/22.15 apply (zenon_L113_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.97/22.15 apply (zenon_L278_); trivial. % 21.97/22.15 apply (zenon_L172_); trivial. % 21.97/22.15 (* end of lemma zenon_L1403_ *) % 21.97/22.15 assert (zenon_L1404_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.15 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_H48 zenon_H195 zenon_Ha5 zenon_Ha0 zenon_H53 zenon_Hb6 zenon_H2c zenon_H9f zenon_H117 zenon_H196 zenon_H38. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.15 apply (zenon_L359_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.15 apply (zenon_L111_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.15 apply (zenon_L1403_); trivial. % 21.97/22.15 apply (zenon_L1162_); trivial. % 21.97/22.15 (* end of lemma zenon_L1404_ *) % 21.97/22.15 assert (zenon_L1405_ : (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.15 do 0 intro. intros zenon_H13c zenon_H24 zenon_H159 zenon_Hef zenon_H141 zenon_H34 zenon_H109 zenon_H48 zenon_H195 zenon_Ha0 zenon_H53 zenon_Hb6 zenon_H2c zenon_H9f zenon_H117 zenon_H196 zenon_H38. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.15 apply (zenon_L900_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.15 exact (zenon_H159 zenon_H10c). % 21.97/22.15 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.15 apply (zenon_L359_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.15 apply (zenon_L111_); trivial. % 21.97/22.15 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.16 apply (zenon_L265_); trivial. % 21.97/22.16 apply (zenon_L1162_); trivial. % 21.97/22.16 apply (zenon_L1404_); trivial. % 21.97/22.16 (* end of lemma zenon_L1405_ *) % 21.97/22.16 assert (zenon_L1406_ : ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (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) (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 (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (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) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (((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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (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)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (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)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.97/22.16 do 0 intro. intros zenon_H93 zenon_H68 zenon_Hf5 zenon_He2 zenon_Ha9 zenon_H13f zenon_Hf0 zenon_H111 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H139 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H1a8 zenon_H177 zenon_H11a zenon_H1d5 zenon_H1d8 zenon_H26a zenon_H23c zenon_H82 zenon_H234 zenon_H1c2 zenon_H183 zenon_H1f1 zenon_H24e zenon_H1cd zenon_H7d zenon_H12e zenon_H192 zenon_H18a zenon_H201 zenon_H104 zenon_H231 zenon_He4 zenon_Hbc zenon_H140 zenon_Hfa zenon_H125 zenon_Hb2 zenon_H1fe zenon_H212 zenon_H164 zenon_H13b zenon_H288 zenon_H179 zenon_H3d zenon_H1c6 zenon_H121 zenon_H33 zenon_H1a3 zenon_Hc4 zenon_H94 zenon_H100 zenon_H36 zenon_H38 zenon_H196 zenon_H117 zenon_H9f zenon_H2c zenon_Hb6 zenon_Ha0 zenon_H195 zenon_H109 zenon_H34 zenon_H141 zenon_Hef zenon_H159 zenon_H24 zenon_H13c zenon_H48 zenon_H77 zenon_H1c7. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.97/22.16 apply (zenon_L55_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.97/22.16 exact (zenon_H159 zenon_H10c). % 21.97/22.16 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.16 apply (zenon_L359_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.16 apply (zenon_L152_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 21.97/22.16 apply (zenon_L1402_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 21.97/22.16 apply (zenon_L1405_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 21.97/22.16 apply (zenon_L255_); trivial. % 21.97/22.16 apply (zenon_L218_); trivial. % 21.97/22.16 apply (zenon_L158_); trivial. % 21.97/22.16 exact (zenon_H1c7 zenon_Hac). % 21.97/22.16 (* end of lemma zenon_L1406_ *) % 21.97/22.16 assert (zenon_L1407_ : ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (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) (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 (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (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) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (((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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (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)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (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)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.97/22.16 do 0 intro. intros zenon_H38 zenon_H196 zenon_H67 zenon_He7 zenon_H68 zenon_Hf5 zenon_He2 zenon_Ha9 zenon_H13f zenon_Hf0 zenon_H111 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H139 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H1a8 zenon_H177 zenon_H11a zenon_H1d5 zenon_H1d8 zenon_H26a zenon_H23c zenon_H82 zenon_H234 zenon_H1c2 zenon_H183 zenon_H1f1 zenon_H24e zenon_H1cd zenon_H7d zenon_H12e zenon_H192 zenon_H18a zenon_H201 zenon_H104 zenon_H231 zenon_He4 zenon_Hbc zenon_H140 zenon_Hfa zenon_H125 zenon_Hb2 zenon_H1fe zenon_H212 zenon_H164 zenon_H13b zenon_H288 zenon_H179 zenon_H3d zenon_H1c6 zenon_H121 zenon_H33 zenon_H1a3 zenon_Hc4 zenon_H94 zenon_H100 zenon_H36 zenon_H117 zenon_H9f zenon_H2c zenon_Hb6 zenon_Ha0 zenon_H195 zenon_H109 zenon_H34 zenon_H141 zenon_Hef zenon_H159 zenon_H24 zenon_H13c zenon_H48 zenon_H77 zenon_H1c7. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.97/22.16 apply (zenon_L55_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.97/22.16 exact (zenon_H159 zenon_H10c). % 21.97/22.16 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.16 apply (zenon_L359_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.16 apply (zenon_L152_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.16 apply (zenon_L180_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.16 apply (zenon_L61_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.16 apply (zenon_L1169_); trivial. % 21.97/22.16 apply (zenon_L1406_); trivial. % 21.97/22.16 apply (zenon_L1162_); trivial. % 21.97/22.16 exact (zenon_H1c7 zenon_Hac). % 21.97/22.16 (* end of lemma zenon_L1407_ *) % 21.97/22.16 assert (zenon_L1408_ : (((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)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 21.97/22.16 do 0 intro. intros zenon_H13a zenon_H33 zenon_H9d zenon_Ha9 zenon_H6e zenon_Hb6 zenon_H153 zenon_H38 zenon_Ha0. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 21.97/22.16 apply (zenon_L245_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 21.97/22.16 apply (zenon_L110_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 21.97/22.16 apply (zenon_L95_); trivial. % 21.97/22.16 apply (zenon_L156_); trivial. % 21.97/22.16 (* end of lemma zenon_L1408_ *) % 21.97/22.16 assert (zenon_L1409_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((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 (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.97/22.16 do 0 intro. intros zenon_H121 zenon_Ha0 zenon_H38 zenon_H153 zenon_Hb6 zenon_H6e zenon_Ha9 zenon_H33 zenon_H13a zenon_H1c7 zenon_H1a3 zenon_Hc4. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.97/22.16 apply (zenon_L1408_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.97/22.16 exact (zenon_H1c7 zenon_Hac). % 21.97/22.16 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.97/22.16 exact (zenon_H1a3 zenon_Hbb). % 21.97/22.16 exact (zenon_Hc4 zenon_Hc3). % 21.97/22.16 (* end of lemma zenon_L1409_ *) % 21.97/22.16 assert (zenon_L1410_ : (((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)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((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)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 21.97/22.16 do 0 intro. intros zenon_H139 zenon_H2c zenon_H65 zenon_Hc4 zenon_H1a3 zenon_H1c7 zenon_H13a zenon_H33 zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H121 zenon_H153 zenon_H77 zenon_H38 zenon_H68. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.16 apply (zenon_L180_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.16 apply (zenon_L1409_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.16 apply (zenon_L94_); trivial. % 21.97/22.16 apply (zenon_L165_); trivial. % 21.97/22.16 (* end of lemma zenon_L1410_ *) % 21.97/22.16 assert (zenon_L1411_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (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 (e0) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> False). % 21.97/22.16 do 0 intro. intros zenon_H12e zenon_H48 zenon_H212 zenon_H1cb zenon_H1cd zenon_Hbc zenon_H231 zenon_H18a zenon_H7d zenon_H104 zenon_H14c zenon_H1c2 zenon_H8a zenon_H121 zenon_H33 zenon_H9f zenon_H20f zenon_H77 zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_Hc4 zenon_H38 zenon_H1c3 zenon_He7 zenon_H171. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 21.97/22.16 apply (zenon_L456_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 21.97/22.16 apply (zenon_L1168_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 21.97/22.16 apply (zenon_L1158_); trivial. % 21.97/22.16 apply (zenon_L964_); trivial. % 21.97/22.16 (* end of lemma zenon_L1411_ *) % 21.97/22.16 assert (zenon_L1412_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e0) (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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.16 do 0 intro. intros zenon_H141 zenon_H77 zenon_H111 zenon_H3f zenon_Hf0 zenon_H48 zenon_H13f zenon_H10d zenon_H1cd zenon_H171 zenon_H1c2 zenon_H93 zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Ha9 zenon_Ha0 zenon_H1a3 zenon_H67 zenon_H1d5 zenon_H1cf zenon_H196 zenon_H38. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.16 apply (zenon_L219_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.16 apply (zenon_L152_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.16 apply (zenon_L1171_); trivial. % 21.97/22.16 apply (zenon_L1162_); trivial. % 21.97/22.16 (* end of lemma zenon_L1412_ *) % 21.97/22.16 assert (zenon_L1413_ : (((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))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (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) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((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))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((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 (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e0) (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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.16 do 0 intro. intros zenon_H16a zenon_H13a zenon_H1c7 zenon_H2c zenon_H139 zenon_He7 zenon_H1c3 zenon_Hc4 zenon_H183 zenon_H68 zenon_H34 zenon_H20f zenon_H9f zenon_H33 zenon_H121 zenon_H14c zenon_H104 zenon_H7d zenon_H18a zenon_H231 zenon_Hbc zenon_H1cb zenon_H212 zenon_H12e zenon_H141 zenon_H77 zenon_H111 zenon_H3f zenon_Hf0 zenon_H48 zenon_H13f zenon_H10d zenon_H1cd zenon_H171 zenon_H1c2 zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Ha9 zenon_Ha0 zenon_H1a3 zenon_H67 zenon_H1d5 zenon_H1cf zenon_H196 zenon_H38. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.16 apply (zenon_L1410_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.16 apply (zenon_L289_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.16 apply (zenon_L1411_); trivial. % 21.97/22.16 apply (zenon_L1412_); trivial. % 21.97/22.16 (* end of lemma zenon_L1413_ *) % 21.97/22.16 assert (zenon_L1414_ : (((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 (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.97/22.16 do 0 intro. intros zenon_H121 zenon_H33 zenon_H9f zenon_H1c7 zenon_H106 zenon_Hb6 zenon_Hc4. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.97/22.16 apply (zenon_L245_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.97/22.16 exact (zenon_H1c7 zenon_Hac). % 21.97/22.16 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.97/22.16 apply (zenon_L363_); trivial. % 21.97/22.16 exact (zenon_Hc4 zenon_Hc3). % 21.97/22.16 (* end of lemma zenon_L1414_ *) % 21.97/22.16 assert (zenon_L1415_ : (((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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((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) (e1)) = (op (e3) (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) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (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 (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 21.97/22.16 do 0 intro. intros zenon_H13c zenon_H24 zenon_H195 zenon_H117 zenon_H36 zenon_H100 zenon_H94 zenon_H179 zenon_H288 zenon_H13b zenon_H164 zenon_H1fe zenon_Hb2 zenon_H125 zenon_Hfa zenon_H140 zenon_He4 zenon_H24e zenon_H1f1 zenon_H234 zenon_H82 zenon_H23c zenon_H26a zenon_H1d8 zenon_H11a zenon_H177 zenon_H1a8 zenon_H1bb zenon_H129 zenon_H1b4 zenon_H283 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H1b7 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_He2 zenon_Hf5 zenon_H1c6 zenon_H159 zenon_H38 zenon_H196 zenon_H201 zenon_H1cf zenon_H1d5 zenon_H67 zenon_H1a3 zenon_Ha0 zenon_Ha9 zenon_H1a2 zenon_H1c2 zenon_H1cd zenon_H13f zenon_Hf0 zenon_H3f zenon_H111 zenon_H77 zenon_H141 zenon_H212 zenon_H1cb zenon_Hbc zenon_H231 zenon_H18a zenon_H7d zenon_H104 zenon_H20f zenon_H68 zenon_H183 zenon_H1c3 zenon_H139 zenon_H2c zenon_H13a zenon_H16a zenon_He7 zenon_H163 zenon_H192 zenon_H3d zenon_H34 zenon_H12e zenon_H48 zenon_H121 zenon_H33 zenon_H9f zenon_Hb6 zenon_Hc4 zenon_H109 zenon_H1c7. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.97/22.16 apply (zenon_L214_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.97/22.16 apply (zenon_L1407_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.97/22.16 apply (zenon_L1164_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.97/22.16 apply (zenon_L55_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.97/22.16 exact (zenon_H159 zenon_H10c). % 21.97/22.16 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.16 apply (zenon_L359_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.16 apply (zenon_L152_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.16 apply (zenon_L1413_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.16 apply (zenon_L965_); trivial. % 21.97/22.16 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.16 apply (zenon_L255_); trivial. % 21.97/22.16 apply (zenon_L1414_); trivial. % 21.97/22.16 apply (zenon_L1162_); trivial. % 21.97/22.16 exact (zenon_H1c7 zenon_Hac). % 21.97/22.16 (* end of lemma zenon_L1415_ *) % 21.97/22.16 assert (zenon_L1416_ : (~((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 (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)))) -> (~((e0) = (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) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (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 (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e2) (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) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((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 (e1) (e1)) = (e0)) -> False). % 21.97/22.17 do 0 intro. intros zenon_H77 zenon_H13c zenon_H24 zenon_H141 zenon_H109 zenon_H195 zenon_Ha0 zenon_H2c zenon_H9f zenon_H117 zenon_H36 zenon_H100 zenon_H94 zenon_Hc4 zenon_H1a3 zenon_H33 zenon_H121 zenon_H179 zenon_H288 zenon_H13b zenon_H164 zenon_H212 zenon_H1fe zenon_Hb2 zenon_H125 zenon_Hfa zenon_H140 zenon_Hbc zenon_He4 zenon_H231 zenon_H104 zenon_H201 zenon_H18a zenon_H7d zenon_H1cd zenon_H24e zenon_H1f1 zenon_H183 zenon_H1c2 zenon_H234 zenon_H82 zenon_H23c zenon_H26a zenon_H1d8 zenon_H1d5 zenon_H11a zenon_H177 zenon_H1a8 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H139 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_Hf0 zenon_H13f zenon_He2 zenon_Hf5 zenon_H68 zenon_H67 zenon_H196 zenon_H38 zenon_H1c7 zenon_Ha9 zenon_H159 zenon_Hb6 zenon_H1c6 zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H4d zenon_H163 zenon_He7. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.97/22.17 apply (zenon_L214_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.97/22.17 apply (zenon_L1407_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.97/22.17 apply (zenon_L1164_); trivial. % 21.97/22.17 apply (zenon_L965_); trivial. % 21.97/22.17 (* end of lemma zenon_L1416_ *) % 21.97/22.17 assert (zenon_L1417_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H1a2 zenon_Hb6 zenon_H153 zenon_H186 zenon_Ha5 zenon_H14c zenon_Ha0 zenon_H1a3. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.97/22.17 apply (zenon_L95_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.97/22.17 apply (zenon_L308_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.97/22.17 apply (zenon_L278_); trivial. % 21.97/22.17 exact (zenon_H1a3 zenon_Hbb). % 21.97/22.17 (* end of lemma zenon_L1417_ *) % 21.97/22.17 assert (zenon_L1418_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H183 zenon_H18a zenon_H1c2 zenon_H8a zenon_H68 zenon_H1c3 zenon_Hef zenon_H11a zenon_H106 zenon_H77 zenon_H27e zenon_H38 zenon_H196 zenon_H5c zenon_H129 zenon_Ha5 zenon_H195. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.97/22.17 apply (zenon_L1259_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.97/22.17 apply (zenon_L119_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.97/22.17 apply (zenon_L367_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H115 | zenon_intro zenon_H27f ]. % 21.97/22.17 apply (zenon_L1162_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H128 | zenon_intro zenon_H280 ]. % 21.97/22.17 apply (zenon_L149_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H93 | zenon_intro zenon_Hb9 ]. % 21.97/22.17 apply (zenon_L126_); trivial. % 21.97/22.17 apply (zenon_L172_); trivial. % 21.97/22.17 (* end of lemma zenon_L1418_ *) % 21.97/22.17 assert (zenon_L1419_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (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 (e1) (e3)) = (e3)) -> ((op (e1) (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 (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H16a zenon_Ha0 zenon_H14c zenon_Ha9 zenon_H54 zenon_Hb6 zenon_H117 zenon_H195 zenon_Ha5 zenon_H5c zenon_H196 zenon_H27e zenon_H11a zenon_Hef zenon_H1c3 zenon_H68 zenon_H1c2 zenon_H18a zenon_H183 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H106 zenon_H1cb. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.17 apply (zenon_L30_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.17 apply (zenon_L1090_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.17 apply (zenon_L1418_); trivial. % 21.97/22.17 apply (zenon_L1159_); trivial. % 21.97/22.17 (* end of lemma zenon_L1419_ *) % 21.97/22.17 assert (zenon_L1420_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (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 (e1) (e3)) = (e3)) -> ((op (e1) (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 (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H201 zenon_H1a3 zenon_H1a2 zenon_H186 zenon_H16a zenon_Ha0 zenon_H14c zenon_Ha9 zenon_H54 zenon_Hb6 zenon_H117 zenon_H195 zenon_Ha5 zenon_H5c zenon_H196 zenon_H27e zenon_H11a zenon_Hef zenon_H1c3 zenon_H68 zenon_H1c2 zenon_H18a zenon_H183 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.17 apply (zenon_L1417_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.17 apply (zenon_L138_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.17 apply (zenon_L255_); trivial. % 21.97/22.17 apply (zenon_L1419_); trivial. % 21.97/22.17 (* end of lemma zenon_L1420_ *) % 21.97/22.17 assert (zenon_L1421_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((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)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.17 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H183 zenon_H18a zenon_H1c2 zenon_H68 zenon_H1c3 zenon_Hef zenon_H11a zenon_H27e zenon_H5c zenon_Ha5 zenon_H195 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_Ha0 zenon_H16a zenon_H186 zenon_H1a2 zenon_H1a3 zenon_H201 zenon_H196 zenon_H38. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.17 apply (zenon_L359_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.17 apply (zenon_L929_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.17 apply (zenon_L1420_); trivial. % 21.97/22.17 apply (zenon_L1162_); trivial. % 21.97/22.17 (* end of lemma zenon_L1421_ *) % 21.97/22.17 assert (zenon_L1422_ : (((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 (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 (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((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)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.17 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H13a zenon_H33 zenon_H121 zenon_H173 zenon_H177 zenon_H209 zenon_H139 zenon_H15d zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H183 zenon_H18a zenon_H1c2 zenon_H68 zenon_H1c3 zenon_Hef zenon_H11a zenon_H27e zenon_H5c zenon_H195 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_Ha0 zenon_H16a zenon_H186 zenon_H1a2 zenon_H1a3 zenon_H201 zenon_H196 zenon_H38. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.17 apply (zenon_L900_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.17 apply (zenon_L1253_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.17 apply (zenon_L1244_); trivial. % 21.97/22.17 apply (zenon_L1421_); trivial. % 21.97/22.17 (* end of lemma zenon_L1422_ *) % 21.97/22.17 assert (zenon_L1423_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H1cf zenon_H1a3 zenon_Ha0 zenon_H14c zenon_Ha9 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H190 zenon_H6d zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H1cb. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.97/22.17 apply (zenon_L94_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.97/22.17 apply (zenon_L1170_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.97/22.17 apply (zenon_L366_); trivial. % 21.97/22.17 apply (zenon_L1260_); trivial. % 21.97/22.17 (* end of lemma zenon_L1423_ *) % 21.97/22.17 assert (zenon_L1424_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (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 (e2) (e1)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H16a zenon_H5c zenon_H195 zenon_Hb6 zenon_H13f zenon_H10d zenon_H14c zenon_H1c2 zenon_H121 zenon_H33 zenon_H9f zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_H1c3 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H106 zenon_H1cb. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.17 apply (zenon_L256_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.17 apply (zenon_L289_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.17 apply (zenon_L1158_); trivial. % 21.97/22.17 apply (zenon_L1159_); trivial. % 21.97/22.17 (* end of lemma zenon_L1424_ *) % 21.97/22.17 assert (zenon_L1425_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (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 (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 (e3) (e2)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> False). % 21.97/22.17 do 0 intro. intros zenon_H117 zenon_H54 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_Hc4 zenon_H48 zenon_H18d zenon_H1a3 zenon_H34 zenon_H1c2 zenon_H13f zenon_H195 zenon_H16a zenon_H191 zenon_H183 zenon_H18a zenon_H6d zenon_H189 zenon_H5c zenon_H77 zenon_H38 zenon_H68 zenon_H1c3 zenon_H129 zenon_Hb6 zenon_Ha9 zenon_H9f zenon_H33 zenon_H121 zenon_H66 zenon_H177 zenon_H14c zenon_H106. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 21.97/22.17 apply (zenon_L151_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 21.97/22.17 apply (zenon_L1424_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 21.97/22.17 exact (zenon_H191 zenon_H110). % 21.97/22.17 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.97/22.17 apply (zenon_L1338_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.97/22.17 apply (zenon_L493_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.97/22.17 apply (zenon_L122_); trivial. % 21.97/22.17 apply (zenon_L1157_); trivial. % 21.97/22.17 (* end of lemma zenon_L1425_ *) % 21.97/22.17 assert (zenon_L1426_ : (((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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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 (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (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). % 21.97/22.17 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H13a zenon_Hc4 zenon_H1a3 zenon_H11a zenon_H33 zenon_H121 zenon_H173 zenon_H177 zenon_H209 zenon_H139 zenon_H15d zenon_H72 zenon_H141 zenon_H68 zenon_H5c zenon_H195 zenon_H48 zenon_H77 zenon_H6d zenon_H117 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H13f zenon_H196 zenon_H38. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.17 apply (zenon_L900_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.17 apply (zenon_L1253_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.17 apply (zenon_L436_); trivial. % 21.97/22.17 apply (zenon_L1397_); trivial. % 21.97/22.17 (* end of lemma zenon_L1426_ *) % 21.97/22.17 assert (zenon_L1427_ : (((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H183 zenon_H6e zenon_H192 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H5c zenon_H129 zenon_Hc4 zenon_H77 zenon_H68 zenon_H1c3 zenon_H231 zenon_H34 zenon_Hbc zenon_H7f zenon_H1cd zenon_H1cb zenon_H1a3. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 21.97/22.17 apply (zenon_L291_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 21.97/22.17 apply (zenon_L1128_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 21.97/22.17 apply (zenon_L1260_); trivial. % 21.97/22.17 apply (zenon_L1165_); trivial. % 21.97/22.17 (* end of lemma zenon_L1427_ *) % 21.97/22.17 assert (zenon_L1428_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (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 (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((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 (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((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). % 21.97/22.17 do 0 intro. intros zenon_H141 zenon_H48 zenon_H54 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H5c zenon_H129 zenon_Hc4 zenon_H77 zenon_H68 zenon_H1c3 zenon_H6d zenon_H190 zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Ha9 zenon_Ha0 zenon_H1a3 zenon_H1cf zenon_H196 zenon_H38. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.17 apply (zenon_L217_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.17 apply (zenon_L54_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.17 apply (zenon_L1423_); trivial. % 21.97/22.17 apply (zenon_L1162_); trivial. % 21.97/22.17 (* end of lemma zenon_L1428_ *) % 21.97/22.17 assert (zenon_L1429_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H1a8 zenon_H1cd zenon_H231 zenon_H192 zenon_H183 zenon_H34 zenon_Hbc zenon_H191 zenon_H140 zenon_H38 zenon_H196 zenon_H1cf zenon_H1a3 zenon_Ha0 zenon_Ha9 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H190 zenon_H1c3 zenon_H68 zenon_Hc4 zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H54 zenon_H48 zenon_H141 zenon_H7f zenon_H77. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.97/22.17 apply (zenon_L1427_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.97/22.17 apply (zenon_L1316_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.97/22.17 apply (zenon_L1428_); trivial. % 21.97/22.17 apply (zenon_L169_); trivial. % 21.97/22.17 (* end of lemma zenon_L1429_ *) % 21.97/22.17 assert (zenon_L1430_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> False). % 21.97/22.17 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H234 zenon_H55 zenon_H1a8 zenon_H1cd zenon_H231 zenon_H192 zenon_H183 zenon_H34 zenon_Hbc zenon_H191 zenon_H140 zenon_H38 zenon_H196 zenon_H1cf zenon_H1a3 zenon_Ha0 zenon_Ha9 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H190 zenon_H1c3 zenon_H68 zenon_Hc4 zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H54 zenon_H48 zenon_H141 zenon_H77. % 21.97/22.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 21.97/22.17 apply (zenon_L738_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 21.97/22.17 apply (zenon_L484_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 21.97/22.17 apply (zenon_L15_); trivial. % 21.97/22.17 apply (zenon_L1429_); trivial. % 21.97/22.17 (* end of lemma zenon_L1430_ *) % 21.97/22.17 assert (zenon_L1431_ : (((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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 (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((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)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H82 zenon_H13a zenon_H139 zenon_H5d zenon_H77 zenon_H141 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H5c zenon_H129 zenon_Hc4 zenon_H68 zenon_H1c3 zenon_H190 zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Ha9 zenon_Ha0 zenon_H1a3 zenon_H1cf zenon_H196 zenon_H38 zenon_H140 zenon_H191 zenon_Hbc zenon_H183 zenon_H192 zenon_H231 zenon_H1cd zenon_H1a8 zenon_H55 zenon_H234 zenon_H1d8 zenon_He4 zenon_H34 zenon_H48. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.97/22.17 apply (zenon_L1284_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.97/22.17 apply (zenon_L17_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.97/22.17 apply (zenon_L1430_); trivial. % 21.97/22.17 apply (zenon_L456_); trivial. % 21.97/22.17 (* end of lemma zenon_L1431_ *) % 21.97/22.17 assert (zenon_L1432_ : ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (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)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e3)) -> (((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (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 (e2) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.17 do 0 intro. intros zenon_H54 zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H1c3 zenon_H1a3 zenon_H183 zenon_H68 zenon_H34 zenon_Ha9 zenon_H9f zenon_H33 zenon_H121 zenon_H1c2 zenon_H10d zenon_H13f zenon_Hb6 zenon_H195 zenon_H5c zenon_H16a zenon_H133 zenon_H82 zenon_H13a zenon_H139 zenon_H5d zenon_H141 zenon_H190 zenon_H1a2 zenon_Ha0 zenon_H1cf zenon_H140 zenon_H191 zenon_Hbc zenon_H192 zenon_H231 zenon_H1cd zenon_H1a8 zenon_H55 zenon_H234 zenon_H1d8 zenon_He4 zenon_H201 zenon_H196 zenon_H38. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.17 apply (zenon_L217_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.17 apply (zenon_L152_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.17 apply (zenon_L1431_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.17 apply (zenon_L124_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.17 apply (zenon_L255_); trivial. % 21.97/22.17 apply (zenon_L1424_); trivial. % 21.97/22.17 apply (zenon_L1162_); trivial. % 21.97/22.17 (* end of lemma zenon_L1432_ *) % 21.97/22.17 assert (zenon_L1433_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.17 do 0 intro. intros zenon_H141 zenon_H48 zenon_H54 zenon_H10d zenon_H1a3 zenon_Ha0 zenon_Ha5 zenon_H186 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H196 zenon_H38. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.17 apply (zenon_L217_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.17 apply (zenon_L152_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.17 apply (zenon_L1417_); trivial. % 21.97/22.17 apply (zenon_L1162_); trivial. % 21.97/22.17 (* end of lemma zenon_L1433_ *) % 21.97/22.17 assert (zenon_L1434_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H16a zenon_H10d zenon_H5c zenon_H195 zenon_H117 zenon_Hb6 zenon_Ha0 zenon_Ha5 zenon_H13f zenon_H14c zenon_H1c2 zenon_H121 zenon_H33 zenon_H9f zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_H1c3 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H106 zenon_H1cb. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.17 apply (zenon_L256_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.17 apply (zenon_L1396_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.17 apply (zenon_L1158_); trivial. % 21.97/22.17 apply (zenon_L1159_); trivial. % 21.97/22.17 (* end of lemma zenon_L1434_ *) % 21.97/22.17 assert (zenon_L1435_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((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 (e1) (e3)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.17 do 0 intro. intros zenon_H109 zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H1c3 zenon_H1a3 zenon_H183 zenon_H68 zenon_H34 zenon_Ha9 zenon_H9f zenon_H33 zenon_H121 zenon_H1c2 zenon_H13f zenon_Ha5 zenon_Ha0 zenon_Hb6 zenon_H117 zenon_H195 zenon_H5c zenon_H10d zenon_H16a zenon_H186 zenon_H141 zenon_H54 zenon_H1a2 zenon_H201 zenon_H196 zenon_H38. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.17 apply (zenon_L359_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.17 apply (zenon_L152_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.17 apply (zenon_L1433_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.17 apply (zenon_L138_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.17 apply (zenon_L255_); trivial. % 21.97/22.17 apply (zenon_L1434_); trivial. % 21.97/22.17 apply (zenon_L1162_); trivial. % 21.97/22.17 (* end of lemma zenon_L1435_ *) % 21.97/22.17 assert (zenon_L1436_ : (((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 (e3) (e0)) = (op (e3) (e3)))) -> (~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (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 (e2) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((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)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (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 (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H27e zenon_Hf0 zenon_He7 zenon_H18a zenon_H189 zenon_H13c zenon_H24 zenon_H82 zenon_H139 zenon_H5d zenon_H190 zenon_H1cf zenon_H140 zenon_H191 zenon_Hbc zenon_H192 zenon_H231 zenon_H1cd zenon_H1a8 zenon_H55 zenon_H234 zenon_H1d8 zenon_He4 zenon_H15d zenon_H173 zenon_H1c6 zenon_H209 zenon_H11a zenon_H177 zenon_H3d zenon_H13a zenon_H38 zenon_H196 zenon_H201 zenon_H1a2 zenon_H54 zenon_H141 zenon_H186 zenon_H16a zenon_H5c zenon_H195 zenon_H117 zenon_Hb6 zenon_Ha0 zenon_H13f zenon_H1c2 zenon_H121 zenon_H33 zenon_H9f zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_H1c3 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1cb zenon_H109 zenon_Ha9. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.97/22.17 apply (zenon_L214_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.97/22.17 apply (zenon_L1422_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.17 apply (zenon_L900_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.17 apply (zenon_L1251_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.17 apply (zenon_L217_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.17 apply (zenon_L54_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.17 apply (zenon_L1423_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.17 apply (zenon_L124_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.17 apply (zenon_L255_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.97/22.17 apply (zenon_L1425_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.97/22.17 apply (zenon_L1426_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.97/22.17 apply (zenon_L1158_); trivial. % 21.97/22.17 apply (zenon_L367_); trivial. % 21.97/22.17 apply (zenon_L1162_); trivial. % 21.97/22.17 apply (zenon_L1397_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.17 apply (zenon_L900_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.17 apply (zenon_L1253_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.97/22.17 apply (zenon_L55_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.97/22.17 apply (zenon_L1253_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.97/22.17 apply (zenon_L1432_); trivial. % 21.97/22.17 apply (zenon_L371_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.97/22.17 apply (zenon_L55_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.97/22.17 apply (zenon_L1251_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.97/22.17 apply (zenon_L1435_); trivial. % 21.97/22.17 apply (zenon_L371_); trivial. % 21.97/22.17 (* end of lemma zenon_L1436_ *) % 21.97/22.17 assert (zenon_L1437_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((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 (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H1cf zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Hf3 zenon_Ha9 zenon_H1a2 zenon_H4e zenon_H76 zenon_H1ef zenon_H65 zenon_H1bb zenon_H18a zenon_H34 zenon_H106 zenon_H1cb zenon_Hc4. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 21.97/22.17 apply (zenon_L364_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 21.97/22.17 apply (zenon_L83_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 21.97/22.17 apply (zenon_L533_); trivial. % 21.97/22.17 apply (zenon_L847_); trivial. % 21.97/22.17 (* end of lemma zenon_L1437_ *) % 21.97/22.17 assert (zenon_L1438_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.17 do 0 intro. intros zenon_H141 zenon_H109 zenon_H10d zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H1c3 zenon_H1a3 zenon_H183 zenon_H68 zenon_H34 zenon_Ha9 zenon_H9f zenon_H33 zenon_H121 zenon_H1c2 zenon_H1cf zenon_Hb6 zenon_Ha0 zenon_Hf3 zenon_H1a2 zenon_H201 zenon_H4e zenon_H76 zenon_H190 zenon_H1ef zenon_H18a zenon_H16a zenon_H186 zenon_Ha5 zenon_H196 zenon_H38. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.17 apply (zenon_L359_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.17 apply (zenon_L152_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.17 apply (zenon_L1417_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.17 apply (zenon_L117_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.17 apply (zenon_L255_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.17 apply (zenon_L1437_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.17 apply (zenon_L368_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.17 apply (zenon_L1158_); trivial. % 21.97/22.17 apply (zenon_L1159_); trivial. % 21.97/22.17 apply (zenon_L1162_); trivial. % 21.97/22.17 (* end of lemma zenon_L1438_ *) % 21.97/22.17 assert (zenon_L1439_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H1a2 zenon_Hb6 zenon_H153 zenon_H186 zenon_Ha5 zenon_H191 zenon_Hac zenon_H1cd. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.97/22.17 apply (zenon_L95_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.97/22.17 apply (zenon_L308_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.97/22.17 exact (zenon_H191 zenon_H110). % 21.97/22.17 apply (zenon_L360_); trivial. % 21.97/22.17 (* end of lemma zenon_L1439_ *) % 21.97/22.17 assert (zenon_L1440_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H1a2 zenon_H67 zenon_H105 zenon_H186 zenon_Ha5 zenon_H191 zenon_Hac zenon_H1cd. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 21.97/22.17 apply (zenon_L446_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 21.97/22.17 apply (zenon_L308_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 21.97/22.17 exact (zenon_H191 zenon_H110). % 21.97/22.17 apply (zenon_L360_); trivial. % 21.97/22.17 (* end of lemma zenon_L1440_ *) % 21.97/22.17 assert (zenon_L1441_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (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 (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 21.97/22.17 do 0 intro. intros zenon_H16a zenon_H196 zenon_H13f zenon_H5c zenon_H68 zenon_H141 zenon_H195 zenon_Ha5 zenon_Ha9 zenon_Hdd zenon_Ha0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H106 zenon_H1cb. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 21.97/22.17 apply (zenon_L30_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 21.97/22.17 apply (zenon_L1397_); trivial. % 21.97/22.17 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 21.97/22.17 apply (zenon_L173_); trivial. % 21.97/22.18 apply (zenon_L1159_); trivial. % 21.97/22.18 (* end of lemma zenon_L1441_ *) % 21.97/22.18 assert (zenon_L1442_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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 (e2) (e0)) = (op (e3) (e0)))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (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 (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (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) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((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 (e3) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (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) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((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) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 21.97/22.18 do 0 intro. intros zenon_Hcb zenon_Hb6 zenon_H9f zenon_H13b zenon_Hf5 zenon_H1fb zenon_Hfa zenon_H4e zenon_H1ef zenon_He2 zenon_H13c zenon_H109 zenon_H201 zenon_H117 zenon_H195 zenon_H183 zenon_H129 zenon_H27e zenon_H1c2 zenon_H18a zenon_H1c3 zenon_H18d zenon_H1cb zenon_H1b4 zenon_H20f zenon_H1bb zenon_H16a zenon_H186 zenon_H1a2 zenon_Hf0 zenon_H196 zenon_H141 zenon_H173 zenon_H121 zenon_Hc4 zenon_H177 zenon_H11a zenon_H209 zenon_H33 zenon_H48 zenon_H15d zenon_H24 zenon_H189 zenon_H191 zenon_H13f zenon_H190 zenon_H1cf zenon_H82 zenon_H1d8 zenon_H234 zenon_H55 zenon_H1a8 zenon_H140 zenon_H192 zenon_H231 zenon_H1cd zenon_Hbc zenon_He4 zenon_H1c6 zenon_H34 zenon_H179 zenon_H288 zenon_H164 zenon_H212 zenon_H1fe zenon_Hb2 zenon_H125 zenon_H104 zenon_H12e zenon_H7d zenon_H24e zenon_H1f1 zenon_H23c zenon_H26a zenon_H2c zenon_H1d5 zenon_H111 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H26d zenon_Hcc zenon_H282 zenon_Heb zenon_H236 zenon_H25b zenon_H1b7 zenon_H266 zenon_H6f zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H283 zenon_H5c zenon_H5d zenon_H77 zenon_H13a zenon_H38 zenon_Ha0 zenon_Ha9 zenon_H68 zenon_H139. % 21.97/22.18 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 21.97/22.18 apply (zenon_L253_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 21.97/22.18 apply (zenon_L1149_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 21.97/22.18 apply (zenon_L17_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 21.97/22.18 apply (zenon_L297_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 21.97/22.18 apply (zenon_L1436_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.97/22.18 apply (zenon_L316_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.97/22.18 apply (zenon_L214_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.97/22.18 apply (zenon_L1422_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.18 apply (zenon_L900_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.18 apply (zenon_L1253_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.18 apply (zenon_L162_); trivial. % 21.97/22.18 apply (zenon_L1397_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.18 apply (zenon_L900_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.18 apply (zenon_L1251_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.18 apply (zenon_L162_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.97/22.18 apply (zenon_L55_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.97/22.18 apply (zenon_L1251_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.97/22.18 apply (zenon_L1438_); trivial. % 21.97/22.18 apply (zenon_L371_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.97/22.18 apply (zenon_L1422_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.97/22.18 apply (zenon_L62_); trivial. % 21.97/22.18 apply (zenon_L206_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.18 apply (zenon_L900_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.18 apply (zenon_L1251_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.18 apply (zenon_L162_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.97/22.18 apply (zenon_L55_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.97/22.18 apply (zenon_L1251_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.97/22.18 apply (zenon_L1435_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.18 apply (zenon_L1439_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.18 apply (zenon_L117_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.18 apply (zenon_L1440_); trivial. % 21.97/22.18 apply (zenon_L1441_); trivial. % 21.97/22.18 apply (zenon_L543_); trivial. % 21.97/22.18 apply (zenon_L663_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 21.97/22.18 apply (zenon_L214_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 21.97/22.18 apply (zenon_L214_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 21.97/22.18 apply (zenon_L1392_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.18 apply (zenon_L900_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.18 apply (zenon_L1253_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.97/22.18 apply (zenon_L55_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.97/22.18 apply (zenon_L1253_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.97/22.18 apply (zenon_L1432_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.18 apply (zenon_L359_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.18 apply (zenon_L54_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.18 apply (zenon_L1423_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.18 apply (zenon_L379_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.18 apply (zenon_L255_); trivial. % 21.97/22.18 apply (zenon_L1425_); trivial. % 21.97/22.18 apply (zenon_L1162_); trivial. % 21.97/22.18 apply (zenon_L1393_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.18 apply (zenon_L900_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.18 apply (zenon_L1248_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.97/22.18 apply (zenon_L55_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.97/22.18 apply (zenon_L1248_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.97/22.18 apply (zenon_L1432_); trivial. % 21.97/22.18 apply (zenon_L371_); trivial. % 21.97/22.18 apply (zenon_L1399_); trivial. % 21.97/22.18 apply (zenon_L165_); trivial. % 21.97/22.18 apply (zenon_L456_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 21.97/22.18 apply (zenon_L1431_); trivial. % 21.97/22.18 apply (zenon_L192_); trivial. % 21.97/22.18 apply (zenon_L414_); trivial. % 21.97/22.18 (* end of lemma zenon_L1442_ *) % 21.97/22.18 assert (zenon_L1443_ : ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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 (e2) (e0)) = (op (e3) (e0)))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (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 (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (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) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((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 (e3) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (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) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((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) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 21.97/22.18 do 0 intro. intros zenon_H54 zenon_He7 zenon_H3d zenon_H159 zenon_H1c7 zenon_H67 zenon_H1a3 zenon_H100 zenon_H36 zenon_Hcb zenon_Hb6 zenon_H9f zenon_H13b zenon_Hf5 zenon_H1fb zenon_Hfa zenon_H4e zenon_H1ef zenon_He2 zenon_H13c zenon_H109 zenon_H201 zenon_H117 zenon_H195 zenon_H183 zenon_H129 zenon_H27e zenon_H1c2 zenon_H18a zenon_H1c3 zenon_H18d zenon_H1cb zenon_H1b4 zenon_H20f zenon_H1bb zenon_H16a zenon_H186 zenon_H1a2 zenon_Hf0 zenon_H196 zenon_H141 zenon_H173 zenon_H121 zenon_Hc4 zenon_H177 zenon_H11a zenon_H209 zenon_H33 zenon_H48 zenon_H15d zenon_H24 zenon_H189 zenon_H191 zenon_H13f zenon_H190 zenon_H1cf zenon_H82 zenon_H1d8 zenon_H234 zenon_H55 zenon_H1a8 zenon_H140 zenon_H192 zenon_H231 zenon_H1cd zenon_Hbc zenon_He4 zenon_H1c6 zenon_H34 zenon_H179 zenon_H288 zenon_H164 zenon_H212 zenon_H1fe zenon_Hb2 zenon_H125 zenon_H104 zenon_H12e zenon_H7d zenon_H24e zenon_H1f1 zenon_H23c zenon_H26a zenon_H2c zenon_H1d5 zenon_H111 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H26d zenon_Hcc zenon_H282 zenon_Heb zenon_H236 zenon_H25b zenon_H1b7 zenon_H266 zenon_H6f zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H283 zenon_H5d zenon_H77 zenon_H13a zenon_H38 zenon_Ha0 zenon_Ha9 zenon_H68 zenon_H139. % 21.97/22.18 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 21.97/22.18 apply (zenon_L69_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 21.97/22.18 apply (zenon_L1415_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 21.97/22.18 apply (zenon_L1416_); trivial. % 21.97/22.18 apply (zenon_L1442_); trivial. % 21.97/22.18 (* end of lemma zenon_L1443_ *) % 21.97/22.18 assert (zenon_L1444_ : (((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)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 21.97/22.18 do 0 intro. intros zenon_H1c3 zenon_H68 zenon_H38 zenon_Ha5 zenon_Ha9 zenon_H128 zenon_H77 zenon_H171 zenon_H1b7. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 21.97/22.18 apply (zenon_L165_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 21.97/22.18 apply (zenon_L299_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 21.97/22.18 apply (zenon_L218_); trivial. % 21.97/22.18 apply (zenon_L188_); trivial. % 21.97/22.18 (* end of lemma zenon_L1444_ *) % 21.97/22.18 assert (zenon_L1445_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.97/22.18 do 0 intro. intros zenon_H121 zenon_H209 zenon_H20f zenon_Hf7 zenon_H77 zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H106 zenon_Hb6 zenon_Hc4. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 21.97/22.18 exact (zenon_H209 zenon_H9d). % 21.97/22.18 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 21.97/22.18 apply (zenon_L1153_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 21.97/22.18 apply (zenon_L363_); trivial. % 21.97/22.18 exact (zenon_Hc4 zenon_Hc3). % 21.97/22.18 (* end of lemma zenon_L1445_ *) % 21.97/22.18 assert (zenon_L1446_ : (((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)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 21.97/22.18 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H1c7 zenon_H141 zenon_H109 zenon_Ha0 zenon_Hc4 zenon_Hb6 zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H20f zenon_H209 zenon_H121 zenon_H48 zenon_H3d zenon_H1d8 zenon_H201 zenon_H196 zenon_H38 zenon_H159 zenon_H1c6 zenon_Ha9 zenon_Hf7. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.18 apply (zenon_L900_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.18 exact (zenon_H159 zenon_H10c). % 21.97/22.18 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 21.97/22.18 apply (zenon_L55_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 21.97/22.18 exact (zenon_H159 zenon_H10c). % 21.97/22.18 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.18 apply (zenon_L359_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.18 apply (zenon_L152_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 21.97/22.18 apply (zenon_L738_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 21.97/22.18 apply (zenon_L124_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 21.97/22.18 apply (zenon_L255_); trivial. % 21.97/22.18 apply (zenon_L1445_); trivial. % 21.97/22.18 apply (zenon_L1162_); trivial. % 21.97/22.18 exact (zenon_H1c7 zenon_Hac). % 21.97/22.18 apply (zenon_L299_); trivial. % 21.97/22.18 (* end of lemma zenon_L1446_ *) % 21.97/22.18 assert (zenon_L1447_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 21.97/22.18 do 0 intro. intros zenon_H13c zenon_Hb6 zenon_H3c zenon_H159 zenon_Ha0 zenon_Hf3 zenon_Ha9 zenon_Hf7. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 21.97/22.18 apply (zenon_L46_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 21.97/22.18 exact (zenon_H159 zenon_H10c). % 21.97/22.18 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 21.97/22.18 apply (zenon_L162_); trivial. % 21.97/22.18 apply (zenon_L299_); trivial. % 21.97/22.18 (* end of lemma zenon_L1447_ *) % 21.97/22.18 assert (zenon_L1448_ : (~((op (e3) (e1)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((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 (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e2) (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) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 21.97/22.18 do 0 intro. intros zenon_H1c7 zenon_H77 zenon_H48 zenon_H24 zenon_H141 zenon_H34 zenon_H109 zenon_H195 zenon_H2c zenon_H9f zenon_H117 zenon_H36 zenon_H100 zenon_H94 zenon_Hc4 zenon_H1a3 zenon_H33 zenon_H121 zenon_H1c6 zenon_H3d zenon_H179 zenon_H288 zenon_H13b zenon_H164 zenon_H212 zenon_H1fe zenon_Hb2 zenon_H125 zenon_Hfa zenon_H140 zenon_Hbc zenon_He4 zenon_H231 zenon_H104 zenon_H201 zenon_H18a zenon_H192 zenon_H12e zenon_H7d zenon_H1cd zenon_H24e zenon_H1f1 zenon_H183 zenon_H1c2 zenon_H234 zenon_H82 zenon_H23c zenon_H26a zenon_H1d8 zenon_H1d5 zenon_H11a zenon_H177 zenon_H1a8 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H139 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_Hf0 zenon_H13f zenon_He2 zenon_Hf5 zenon_He7 zenon_H67 zenon_H196 zenon_H38 zenon_H68 zenon_H13c zenon_Hb6 zenon_H3c zenon_H159 zenon_Ha0 zenon_Hf3 zenon_Ha9. % 21.97/22.18 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 21.97/22.18 apply (zenon_L24_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 21.97/22.18 apply (zenon_L1407_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 21.97/22.18 apply (zenon_L62_); trivial. % 21.97/22.18 apply (zenon_L1447_); trivial. % 21.97/22.18 (* end of lemma zenon_L1448_ *) % 21.97/22.18 assert (zenon_L1449_ : (~((e2) = (e3))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (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) (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 (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (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) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((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 (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 21.97/22.18 do 0 intro. intros zenon_Ha9 zenon_Hf3 zenon_H3c zenon_H13c zenon_H68 zenon_H38 zenon_H196 zenon_H67 zenon_Hf5 zenon_He2 zenon_H13f zenon_Hf0 zenon_H111 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H139 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H1a8 zenon_H177 zenon_H11a zenon_H1d5 zenon_H1d8 zenon_H26a zenon_H23c zenon_H82 zenon_H234 zenon_H1c2 zenon_H183 zenon_H1f1 zenon_H24e zenon_H1cd zenon_H7d zenon_H12e zenon_H192 zenon_H18a zenon_H201 zenon_H104 zenon_H231 zenon_He4 zenon_Hbc zenon_H140 zenon_Hfa zenon_H125 zenon_Hb2 zenon_H1fe zenon_H212 zenon_H164 zenon_H13b zenon_H288 zenon_H179 zenon_H94 zenon_H100 zenon_H36 zenon_H117 zenon_H2c zenon_H195 zenon_H109 zenon_H34 zenon_H141 zenon_H24 zenon_H48 zenon_H77 zenon_H1c7 zenon_H159 zenon_H3d zenon_Hb6 zenon_H1c6 zenon_H121 zenon_H33 zenon_H9f zenon_Ha0 zenon_H1a3 zenon_Hc4. % 21.97/22.18 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 21.97/22.18 apply (zenon_L65_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 21.97/22.18 apply (zenon_L1448_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 21.97/22.18 apply (zenon_L1242_); trivial. % 21.97/22.18 apply (zenon_L1401_); trivial. % 21.97/22.18 (* end of lemma zenon_L1449_ *) % 21.97/22.18 assert (zenon_L1450_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 21.97/22.18 do 0 intro. intros zenon_H141 zenon_H68 zenon_H65 zenon_He7 zenon_Hf0 zenon_Hef zenon_H133 zenon_H196 zenon_H38. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 21.97/22.18 apply (zenon_L27_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 21.97/22.18 apply (zenon_L929_); trivial. % 21.97/22.18 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 21.97/22.18 apply (zenon_L265_); trivial. % 21.97/22.18 apply (zenon_L1162_); trivial. % 21.97/22.18 (* end of lemma zenon_L1450_ *) % 21.97/22.18 assert (zenon_L1451_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 21.97/22.18 do 0 intro. intros zenon_H117 zenon_H65 zenon_H1a3 zenon_H190 zenon_H186 zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H14c zenon_Ha0 zenon_Ha5 zenon_H195. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.08/22.19 apply (zenon_L43_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.08/22.19 apply (zenon_L1173_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.08/22.19 apply (zenon_L278_); trivial. % 22.08/22.19 apply (zenon_L172_); trivial. % 22.08/22.19 (* end of lemma zenon_L1451_ *) % 22.08/22.19 assert (zenon_L1452_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.08/22.19 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H195 zenon_Ha5 zenon_Ha0 zenon_H1a2 zenon_Ha9 zenon_H66 zenon_H186 zenon_H190 zenon_H1a3 zenon_H65 zenon_H117 zenon_H196 zenon_H38. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.08/22.19 apply (zenon_L359_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.08/22.19 apply (zenon_L929_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.08/22.19 apply (zenon_L1451_); trivial. % 22.08/22.19 apply (zenon_L1162_); trivial. % 22.08/22.19 (* end of lemma zenon_L1452_ *) % 22.08/22.19 assert (zenon_L1453_ : (((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)) = (e3))) -> (~((op (e1) (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 (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.08/22.19 do 0 intro. intros zenon_H13c zenon_Hb6 zenon_H3c zenon_Hc4 zenon_H11a zenon_H9f zenon_H33 zenon_H121 zenon_Hef zenon_H68 zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H195 zenon_Ha0 zenon_H1a2 zenon_Ha9 zenon_H66 zenon_H186 zenon_H190 zenon_H1a3 zenon_H65 zenon_H117 zenon_H196 zenon_H38. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.08/22.19 apply (zenon_L46_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.08/22.19 apply (zenon_L538_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.08/22.19 apply (zenon_L1450_); trivial. % 22.08/22.19 apply (zenon_L1452_); trivial. % 22.08/22.19 (* end of lemma zenon_L1453_ *) % 22.08/22.19 assert (zenon_L1454_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.08/22.19 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_Hef zenon_H133 zenon_H196 zenon_H38. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.08/22.19 apply (zenon_L359_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.08/22.19 apply (zenon_L929_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.08/22.19 apply (zenon_L265_); trivial. % 22.08/22.19 apply (zenon_L1162_); trivial. % 22.08/22.19 (* end of lemma zenon_L1454_ *) % 22.08/22.19 assert (zenon_L1455_ : (((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 (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 22.08/22.19 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_H38 zenon_H196 zenon_Hef zenon_Hf0 zenon_He7 zenon_H109 zenon_H34 zenon_H141 zenon_Ha9 zenon_Hf7. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.08/22.19 apply (zenon_L900_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.08/22.19 apply (zenon_L1454_); trivial. % 22.08/22.19 apply (zenon_L299_); trivial. % 22.08/22.19 (* end of lemma zenon_L1455_ *) % 22.08/22.19 assert (zenon_L1456_ : (((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))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 22.08/22.19 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_Hb6 zenon_H4d zenon_Ha9 zenon_Hf7. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.08/22.19 apply (zenon_L900_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.08/22.19 apply (zenon_L124_); trivial. % 22.08/22.19 apply (zenon_L299_); trivial. % 22.08/22.19 (* end of lemma zenon_L1456_ *) % 22.08/22.19 assert (zenon_L1457_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((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))))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H201 zenon_H66 zenon_H159 zenon_H24 zenon_H9f zenon_H13c zenon_H48 zenon_H14c zenon_H121 zenon_H209 zenon_H20f zenon_Hf7 zenon_H77 zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_Hb6 zenon_Hc4. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.08/22.19 apply (zenon_L94_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.08/22.19 apply (zenon_L1456_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.08/22.19 apply (zenon_L255_); trivial. % 22.08/22.19 apply (zenon_L1445_); trivial. % 22.08/22.19 (* end of lemma zenon_L1457_ *) % 22.08/22.19 assert (zenon_L1458_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((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))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H1a8 zenon_H109 zenon_He7 zenon_Hf0 zenon_H55 zenon_H1c6 zenon_H3d zenon_H38 zenon_H196 zenon_H201 zenon_H66 zenon_H159 zenon_H24 zenon_H9f zenon_H13c zenon_H48 zenon_H121 zenon_H209 zenon_H20f zenon_Hf7 zenon_H77 zenon_H34 zenon_H68 zenon_H183 zenon_Hb6 zenon_Hc4 zenon_Ha0 zenon_H65 zenon_H141 zenon_Ha9. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.08/22.19 apply (zenon_L214_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.08/22.19 apply (zenon_L1455_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.08/22.19 apply (zenon_L34_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.08/22.19 apply (zenon_L55_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.08/22.19 apply (zenon_L27_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.08/22.19 apply (zenon_L152_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.08/22.19 apply (zenon_L1457_); trivial. % 22.08/22.19 apply (zenon_L1162_); trivial. % 22.08/22.19 apply (zenon_L371_); trivial. % 22.08/22.19 (* end of lemma zenon_L1458_ *) % 22.08/22.19 assert (zenon_L1459_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H65 zenon_Ha0 zenon_Hdd zenon_H191 zenon_Ha5 zenon_H195. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.08/22.19 apply (zenon_L43_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.08/22.19 apply (zenon_L152_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.08/22.19 exact (zenon_H191 zenon_H110). % 22.08/22.19 apply (zenon_L172_); trivial. % 22.08/22.19 (* end of lemma zenon_L1459_ *) % 22.08/22.19 assert (zenon_L1460_ : (((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)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_Hf3 zenon_H117 zenon_Ha9 zenon_H65 zenon_Ha0 zenon_Hdd zenon_H191 zenon_H195. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.08/22.19 apply (zenon_L900_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.08/22.19 apply (zenon_L162_); trivial. % 22.08/22.19 apply (zenon_L1459_); trivial. % 22.08/22.19 (* end of lemma zenon_L1460_ *) % 22.08/22.19 assert (zenon_L1461_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (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)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H125 zenon_H1d5 zenon_H38 zenon_Hf5 zenon_He2 zenon_H1fb zenon_H36 zenon_H3c zenon_Hb6 zenon_H11a zenon_H33 zenon_H141 zenon_H109 zenon_Hf0 zenon_H1a2 zenon_H66 zenon_H186 zenon_H190 zenon_H196 zenon_H77 zenon_Hfa zenon_H195 zenon_H191 zenon_Ha9 zenon_H117 zenon_H159 zenon_H24 zenon_H9f zenon_H13c zenon_H121 zenon_H209 zenon_Ha0 zenon_H1a3 zenon_Hc4 zenon_H73 zenon_H1a8 zenon_H55 zenon_H1c6 zenon_H3d zenon_H201 zenon_H48 zenon_H20f zenon_H183 zenon_H179 zenon_H13b zenon_H34 zenon_H68. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.08/22.19 apply (zenon_L252_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.08/22.19 apply (zenon_L24_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.08/22.19 apply (zenon_L297_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.08/22.19 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.08/22.19 apply (zenon_L24_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.08/22.19 apply (zenon_L1453_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.08/22.19 apply (zenon_L22_); trivial. % 22.08/22.19 apply (zenon_L1458_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.08/22.19 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.08/22.19 apply (zenon_L317_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.08/22.19 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.08/22.19 apply (zenon_L24_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.08/22.19 apply (zenon_L1453_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.08/22.19 apply (zenon_L62_); trivial. % 22.08/22.19 apply (zenon_L1447_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.08/22.19 apply (zenon_L1460_); trivial. % 22.08/22.19 apply (zenon_L543_); trivial. % 22.08/22.19 apply (zenon_L663_); trivial. % 22.08/22.19 apply (zenon_L291_); trivial. % 22.08/22.19 (* end of lemma zenon_L1461_ *) % 22.08/22.19 assert (zenon_L1462_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H1c6 zenon_Ha9 zenon_H6e zenon_H159 zenon_Ha0 zenon_Hdd zenon_H1c7. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.08/22.19 apply (zenon_L110_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.08/22.19 apply (zenon_L152_); trivial. % 22.08/22.19 exact (zenon_H1c7 zenon_Hac). % 22.08/22.19 (* end of lemma zenon_L1462_ *) % 22.08/22.19 assert (zenon_L1463_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H1cf zenon_H1d5 zenon_H67 zenon_H4e zenon_H76 zenon_H195 zenon_Ha5 zenon_Ha9 zenon_Hdd zenon_Ha0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H171 zenon_H1cd. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.08/22.19 apply (zenon_L252_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.08/22.19 apply (zenon_L83_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.08/22.19 apply (zenon_L173_); trivial. % 22.08/22.19 apply (zenon_L240_); trivial. % 22.08/22.19 (* end of lemma zenon_L1463_ *) % 22.08/22.19 assert (zenon_L1464_ : (((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)) = (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) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_Hf3 zenon_H1cf zenon_H1d5 zenon_H67 zenon_H4e zenon_H76 zenon_H195 zenon_Ha9 zenon_Hdd zenon_Ha0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H171 zenon_H1cd. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.08/22.19 apply (zenon_L900_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.08/22.19 apply (zenon_L162_); trivial. % 22.08/22.19 apply (zenon_L1463_); trivial. % 22.08/22.19 (* end of lemma zenon_L1464_ *) % 22.08/22.19 assert (zenon_L1465_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e2))) -> (((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)) = (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) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H1a8 zenon_H1c7 zenon_H1c6 zenon_H77 zenon_H3f zenon_H68 zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_Hf3 zenon_H1cf zenon_H1d5 zenon_H67 zenon_H4e zenon_H76 zenon_H195 zenon_Ha9 zenon_Hdd zenon_Ha0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H1cd. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.08/22.19 apply (zenon_L1462_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.08/22.19 apply (zenon_L186_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.08/22.19 apply (zenon_L54_); trivial. % 22.08/22.19 apply (zenon_L1464_); trivial. % 22.08/22.19 (* end of lemma zenon_L1465_ *) % 22.08/22.19 assert (zenon_L1466_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H117 zenon_Hb6 zenon_H54 zenon_Hdb zenon_H6f zenon_H14c zenon_Ha0 zenon_Ha5 zenon_H195. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.08/22.19 apply (zenon_L151_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.08/22.19 apply (zenon_L205_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.08/22.19 apply (zenon_L278_); trivial. % 22.08/22.19 apply (zenon_L172_); trivial. % 22.08/22.19 (* end of lemma zenon_L1466_ *) % 22.08/22.19 assert (zenon_L1467_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (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 (e1) (e2)) = (e0)) -> (~((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))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.08/22.19 do 0 intro. intros zenon_H141 zenon_H48 zenon_H1cd zenon_Ha9 zenon_H76 zenon_H4e zenon_H67 zenon_H1d5 zenon_H1cf zenon_Hf3 zenon_H159 zenon_H24 zenon_H9f zenon_H13c zenon_H68 zenon_H3f zenon_H77 zenon_H1c6 zenon_H1c7 zenon_H1a8 zenon_H195 zenon_Ha5 zenon_Ha0 zenon_H6f zenon_Hdb zenon_H54 zenon_Hb6 zenon_H117 zenon_H196 zenon_H38. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.08/22.19 apply (zenon_L217_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.08/22.19 apply (zenon_L1465_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.08/22.19 apply (zenon_L1466_); trivial. % 22.08/22.19 apply (zenon_L1162_); trivial. % 22.08/22.19 (* end of lemma zenon_L1467_ *) % 22.08/22.19 assert (zenon_L1468_ : (((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))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 22.08/22.19 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_Ha0 zenon_Hf3 zenon_Ha9 zenon_Hf7. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.08/22.19 apply (zenon_L900_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.08/22.19 apply (zenon_L162_); trivial. % 22.08/22.19 apply (zenon_L299_); trivial. % 22.08/22.19 (* end of lemma zenon_L1468_ *) % 22.08/22.19 assert (zenon_L1469_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((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 (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((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)) = (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) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e2))) -> (((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))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 22.08/22.19 do 0 intro. intros zenon_Hfa zenon_H1c7 zenon_H141 zenon_H109 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H1c3 zenon_H1a3 zenon_H183 zenon_H34 zenon_H33 zenon_H121 zenon_H1c2 zenon_H1cf zenon_Hb6 zenon_H1a2 zenon_H201 zenon_H4e zenon_H190 zenon_H1ef zenon_H18a zenon_H16a zenon_H186 zenon_H196 zenon_H38 zenon_H1cd zenon_H67 zenon_H1d5 zenon_H1c6 zenon_H1a8 zenon_H195 zenon_H6f zenon_H54 zenon_H117 zenon_H77 zenon_H3f zenon_H68 zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_Ha0 zenon_Hf3 zenon_Ha9. % 22.08/22.19 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.08/22.19 apply (zenon_L900_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.08/22.19 apply (zenon_L162_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.08/22.19 apply (zenon_L1467_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.08/22.19 apply (zenon_L1438_); trivial. % 22.08/22.19 exact (zenon_H1c7 zenon_Hac). % 22.08/22.19 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.08/22.19 apply (zenon_L186_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.08/22.19 apply (zenon_L62_); trivial. % 22.08/22.19 apply (zenon_L1468_); trivial. % 22.08/22.19 (* end of lemma zenon_L1469_ *) % 22.08/22.19 assert (zenon_L1470_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H201 zenon_H66 zenon_H77 zenon_H133 zenon_H48 zenon_H14c zenon_H121 zenon_H33 zenon_H9f zenon_H1c7 zenon_Hb6 zenon_Hc4. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.08/22.19 apply (zenon_L94_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.08/22.19 apply (zenon_L124_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.08/22.19 apply (zenon_L255_); trivial. % 22.08/22.19 apply (zenon_L1414_); trivial. % 22.08/22.19 (* end of lemma zenon_L1470_ *) % 22.08/22.19 assert (zenon_L1471_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H1c6 zenon_H3d zenon_H159 zenon_H38 zenon_H196 zenon_H201 zenon_H66 zenon_H77 zenon_H133 zenon_H48 zenon_H121 zenon_H33 zenon_H9f zenon_Hb6 zenon_Hc4 zenon_Ha0 zenon_H54 zenon_H141 zenon_H1c7. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.08/22.19 apply (zenon_L55_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.08/22.19 apply (zenon_L217_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.08/22.19 apply (zenon_L152_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.08/22.19 apply (zenon_L1470_); trivial. % 22.08/22.19 apply (zenon_L1162_); trivial. % 22.08/22.19 exact (zenon_H1c7 zenon_Hac). % 22.08/22.19 (* end of lemma zenon_L1471_ *) % 22.08/22.19 assert (zenon_L1472_ : (((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)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (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))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H13c zenon_H24 zenon_H141 zenon_H54 zenon_Ha0 zenon_Hc4 zenon_H9f zenon_H33 zenon_H121 zenon_H48 zenon_H77 zenon_H201 zenon_H196 zenon_H38 zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_H1a3 zenon_H190 zenon_H186 zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H1c7. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.08/22.19 apply (zenon_L900_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.08/22.19 apply (zenon_L1471_); trivial. % 22.08/22.19 apply (zenon_L1174_); trivial. % 22.08/22.19 (* end of lemma zenon_L1472_ *) % 22.08/22.19 assert (zenon_L1473_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.08/22.19 do 0 intro. intros zenon_H13c zenon_H3c zenon_H159 zenon_Ha9 zenon_H72 zenon_H141 zenon_H34 zenon_H109 zenon_H48 zenon_H195 zenon_Ha0 zenon_H53 zenon_Hb6 zenon_H2c zenon_H9f zenon_H117 zenon_H196 zenon_H38. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.08/22.19 apply (zenon_L46_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.08/22.19 apply (zenon_L436_); trivial. % 22.08/22.19 apply (zenon_L1404_); trivial. % 22.08/22.19 (* end of lemma zenon_L1473_ *) % 22.08/22.19 assert (zenon_L1474_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H1c6 zenon_Ha9 zenon_H6e zenon_H159 zenon_Hb6 zenon_H53 zenon_H1c7. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.08/22.19 apply (zenon_L110_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.08/22.19 apply (zenon_L113_); trivial. % 22.08/22.19 exact (zenon_H1c7 zenon_Hac). % 22.08/22.19 (* end of lemma zenon_L1474_ *) % 22.08/22.19 assert (zenon_L1475_ : ((op (e1) (e0)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H3c zenon_H47 zenon_H24. % 22.08/22.19 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H28b | zenon_intro zenon_H101 ]. % 22.08/22.19 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e0) (e0)) = (op (e1) (e0)))). % 22.08/22.19 intro zenon_D_pnotp. % 22.08/22.19 apply zenon_H24. % 22.08/22.19 rewrite <- zenon_D_pnotp. % 22.08/22.19 exact zenon_H28b. % 22.08/22.19 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H101]. % 22.08/22.19 cut (((op (e1) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28c]. % 22.08/22.19 congruence. % 22.08/22.19 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e0) (e0)))). % 22.08/22.19 intro zenon_D_pnotp. % 22.08/22.19 apply zenon_H28c. % 22.08/22.19 rewrite <- zenon_D_pnotp. % 22.08/22.19 exact zenon_H3c. % 22.08/22.19 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 22.08/22.19 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H101]. % 22.08/22.19 congruence. % 22.08/22.19 apply zenon_H101. apply refl_equal. % 22.08/22.19 apply zenon_H28d. apply sym_equal. exact zenon_H47. % 22.08/22.19 apply zenon_H101. apply refl_equal. % 22.08/22.19 apply zenon_H101. apply refl_equal. % 22.08/22.19 (* end of lemma zenon_L1475_ *) % 22.08/22.19 assert (zenon_L1476_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((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 (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (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)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H15d zenon_H24 zenon_H1d8 zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H1a2 zenon_H186 zenon_H190 zenon_H26a zenon_H1c3 zenon_H1cf zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H1b7 zenon_H117 zenon_H109 zenon_H6f zenon_H14c zenon_H1ef zenon_H18a zenon_H34 zenon_H1bb zenon_H1b4 zenon_H129 zenon_H183 zenon_H111 zenon_H104 zenon_H18d zenon_H5d zenon_H3c zenon_H1cb zenon_H68 zenon_H77 zenon_H121 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H33 zenon_H13a zenon_H1c7 zenon_H1a3 zenon_Hc4 zenon_H65 zenon_H2c zenon_H139 zenon_H38 zenon_H48. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.08/22.19 apply (zenon_L1475_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.08/22.19 apply (zenon_L1301_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.08/22.19 apply (zenon_L1410_); trivial. % 22.08/22.19 apply (zenon_L246_); trivial. % 22.08/22.19 (* end of lemma zenon_L1476_ *) % 22.08/22.19 assert (zenon_L1477_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.08/22.19 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H1a3 zenon_Ha0 zenon_Ha5 zenon_H186 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H196 zenon_H38. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.08/22.19 apply (zenon_L359_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.08/22.19 apply (zenon_L929_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.08/22.19 apply (zenon_L1417_); trivial. % 22.08/22.19 apply (zenon_L1162_); trivial. % 22.08/22.19 (* end of lemma zenon_L1477_ *) % 22.08/22.19 assert (zenon_L1478_ : (((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))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.08/22.19 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_Ha9 zenon_H72 zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H1a3 zenon_Ha0 zenon_H186 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H196 zenon_H38. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.08/22.19 apply (zenon_L900_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.08/22.19 apply (zenon_L436_); trivial. % 22.08/22.19 apply (zenon_L1477_); trivial. % 22.08/22.19 (* end of lemma zenon_L1478_ *) % 22.08/22.19 assert (zenon_L1479_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.08/22.19 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_H6d zenon_H68 zenon_H1a3 zenon_Ha0 zenon_H72 zenon_Ha9 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H196 zenon_H38. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.08/22.19 apply (zenon_L359_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.08/22.19 apply (zenon_L54_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.08/22.19 apply (zenon_L1170_); trivial. % 22.08/22.19 apply (zenon_L1162_); trivial. % 22.08/22.19 (* end of lemma zenon_L1479_ *) % 22.08/22.19 assert (zenon_L1480_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H12e zenon_H48 zenon_H3f zenon_H11a zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H160 zenon_H1c7. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.08/22.19 apply (zenon_L456_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.08/22.19 apply (zenon_L552_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.08/22.19 apply (zenon_L847_); trivial. % 22.08/22.19 apply (zenon_L848_); trivial. % 22.08/22.19 (* end of lemma zenon_L1480_ *) % 22.08/22.19 assert (zenon_L1481_ : (((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)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.08/22.19 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_H72 zenon_H141 zenon_H48 zenon_H68 zenon_H195 zenon_Ha0 zenon_H6d zenon_Ha9 zenon_H54 zenon_Hb6 zenon_H117 zenon_H196 zenon_H38. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.08/22.19 apply (zenon_L900_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.08/22.19 exact (zenon_H159 zenon_H10c). % 22.08/22.19 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.08/22.19 apply (zenon_L436_); trivial. % 22.08/22.19 apply (zenon_L1393_); trivial. % 22.08/22.19 (* end of lemma zenon_L1481_ *) % 22.08/22.19 assert (zenon_L1482_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (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)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((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 (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.08/22.19 do 0 intro. intros zenon_H1cf zenon_H1d5 zenon_H67 zenon_H38 zenon_H196 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_Ha0 zenon_H195 zenon_H68 zenon_H48 zenon_H141 zenon_H159 zenon_H24 zenon_H9f zenon_H13c zenon_H190 zenon_H6d zenon_H171 zenon_H1cd. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.08/22.19 apply (zenon_L252_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.08/22.19 apply (zenon_L1481_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.08/22.19 apply (zenon_L366_); trivial. % 22.08/22.19 apply (zenon_L240_); trivial. % 22.08/22.19 (* end of lemma zenon_L1482_ *) % 22.08/22.19 assert (zenon_L1483_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((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)) = (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) (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 (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)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> False). % 22.08/22.19 do 0 intro. intros zenon_Heb zenon_H100 zenon_H16a zenon_H13a zenon_H1c7 zenon_H2c zenon_H139 zenon_H13c zenon_H24 zenon_H159 zenon_H195 zenon_H117 zenon_He7 zenon_H9f zenon_H33 zenon_H121 zenon_H104 zenon_H7d zenon_H18a zenon_H212 zenon_H12e zenon_H1d5 zenon_H67 zenon_H1c2 zenon_Hf0 zenon_H109 zenon_H11a zenon_H24e zenon_H1b7 zenon_H73 zenon_He4 zenon_H1d8 zenon_H234 zenon_H55 zenon_H1a8 zenon_H1cd zenon_H231 zenon_H192 zenon_H183 zenon_H34 zenon_Hbc zenon_H191 zenon_H140 zenon_H38 zenon_H196 zenon_H1cf zenon_H1a3 zenon_Ha0 zenon_Ha9 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H190 zenon_H1c3 zenon_H68 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H54 zenon_H48 zenon_H141 zenon_H77. % 22.08/22.19 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.08/22.19 apply (zenon_L69_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.08/22.19 apply (zenon_L1409_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.08/22.19 apply (zenon_L186_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.08/22.19 apply (zenon_L252_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.08/22.19 apply (zenon_L1479_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.08/22.19 apply (zenon_L366_); trivial. % 22.08/22.19 apply (zenon_L1480_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.08/22.19 apply (zenon_L217_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.08/22.19 apply (zenon_L929_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.08/22.19 apply (zenon_L1410_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.08/22.19 apply (zenon_L1482_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.08/22.19 apply (zenon_L1411_); trivial. % 22.08/22.19 apply (zenon_L1171_); trivial. % 22.08/22.19 apply (zenon_L1162_); trivial. % 22.08/22.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.08/22.19 apply (zenon_L184_); trivial. % 22.08/22.19 apply (zenon_L1430_); trivial. % 22.08/22.19 (* end of lemma zenon_L1483_ *) % 22.08/22.19 assert (zenon_L1484_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (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 (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (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 (e3) (e0)) = (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)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((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 (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((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)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.10/22.20 do 0 intro. intros zenon_Hfa zenon_H3c zenon_H186 zenon_H38 zenon_H196 zenon_H13f zenon_H141 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H68 zenon_H1c3 zenon_H190 zenon_H1a2 zenon_H153 zenon_Ha0 zenon_H1a3 zenon_H1cf zenon_H140 zenon_Hbc zenon_H34 zenon_H183 zenon_H192 zenon_H231 zenon_H1cd zenon_H1a8 zenon_H55 zenon_H234 zenon_H1d8 zenon_He4 zenon_H73 zenon_H1b7 zenon_H24e zenon_H11a zenon_H109 zenon_Hf0 zenon_H1c2 zenon_H67 zenon_H1d5 zenon_H12e zenon_H212 zenon_H18a zenon_H7d zenon_H104 zenon_H121 zenon_H33 zenon_He7 zenon_H195 zenon_H159 zenon_H24 zenon_H13c zenon_H139 zenon_H1c7 zenon_H13a zenon_H16a zenon_H100 zenon_Heb zenon_H1f1 zenon_H48 zenon_H117 zenon_H9f zenon_H2c zenon_Ha9 zenon_H191 zenon_Hb6 zenon_H7f zenon_H77. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.10/22.20 apply (zenon_L24_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.10/22.20 apply (zenon_L1316_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.10/22.20 apply (zenon_L1478_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.10/22.20 apply (zenon_L1409_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.10/22.20 apply (zenon_L1455_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.10/22.20 apply (zenon_L359_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.10/22.20 apply (zenon_L54_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.10/22.20 apply (zenon_L1483_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.10/22.20 apply (zenon_L284_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.10/22.20 apply (zenon_L255_); trivial. % 22.10/22.20 apply (zenon_L1066_); trivial. % 22.10/22.20 apply (zenon_L1162_); trivial. % 22.10/22.20 apply (zenon_L169_); trivial. % 22.10/22.20 (* end of lemma zenon_L1484_ *) % 22.10/22.20 assert (zenon_L1485_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (e0) (e0)) = (op (e2) (e0)))) -> (((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)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((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)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.10/22.20 do 0 intro. intros zenon_Hf5 zenon_H1a2 zenon_H191 zenon_Heb zenon_H100 zenon_H16a zenon_H2c zenon_H139 zenon_H13c zenon_H24 zenon_H159 zenon_H195 zenon_H117 zenon_H9f zenon_H104 zenon_H7d zenon_H18a zenon_H212 zenon_H12e zenon_H1d5 zenon_H1c2 zenon_Hf0 zenon_H109 zenon_H11a zenon_H24e zenon_H1b7 zenon_H73 zenon_He4 zenon_H1d8 zenon_H234 zenon_H55 zenon_H1a8 zenon_H1cd zenon_H231 zenon_H192 zenon_H183 zenon_H34 zenon_Hbc zenon_H140 zenon_H196 zenon_H1cf zenon_H190 zenon_H1c3 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H54 zenon_H48 zenon_H141 zenon_H179 zenon_H13b zenon_Hc4 zenon_H1a3 zenon_H1c7 zenon_H13a zenon_H33 zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H121 zenon_H153 zenon_H77 zenon_H38 zenon_H68. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.10/22.20 apply (zenon_L297_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.10/22.20 apply (zenon_L1483_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.10/22.20 apply (zenon_L1265_); trivial. % 22.10/22.20 apply (zenon_L663_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.10/22.20 apply (zenon_L1409_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.10/22.20 apply (zenon_L94_); trivial. % 22.10/22.20 apply (zenon_L165_); trivial. % 22.10/22.20 (* end of lemma zenon_L1485_ *) % 22.10/22.20 assert (zenon_L1486_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e3))) -> (~((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 (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> False). % 22.10/22.20 do 0 intro. intros zenon_H16a zenon_H67 zenon_Hb6 zenon_H191 zenon_Ha9 zenon_H2c zenon_H9f zenon_H117 zenon_H181 zenon_H104 zenon_H7f zenon_H34 zenon_H68 zenon_H183 zenon_H77 zenon_H128. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.10/22.20 apply (zenon_L180_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.10/22.20 apply (zenon_L1066_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.10/22.20 apply (zenon_L420_); trivial. % 22.10/22.20 apply (zenon_L218_); trivial. % 22.10/22.20 (* end of lemma zenon_L1486_ *) % 22.10/22.20 assert (zenon_L1487_ : (((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)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e3))) -> (~((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 (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H13f zenon_H3c zenon_H100 zenon_H195 zenon_Ha5 zenon_Ha0 zenon_H48 zenon_H14c zenon_H16a zenon_H67 zenon_Hb6 zenon_H191 zenon_Ha9 zenon_H2c zenon_H9f zenon_H117 zenon_H181 zenon_H104 zenon_H7f zenon_H34 zenon_H68 zenon_H183 zenon_H77. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.10/22.20 apply (zenon_L69_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.10/22.20 apply (zenon_L1403_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.10/22.20 apply (zenon_L255_); trivial. % 22.10/22.20 apply (zenon_L1486_); trivial. % 22.10/22.20 (* end of lemma zenon_L1487_ *) % 22.10/22.20 assert (zenon_L1488_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.10/22.20 do 0 intro. intros zenon_H141 zenon_H109 zenon_He7 zenon_Hf0 zenon_H77 zenon_H183 zenon_H68 zenon_H34 zenon_H7f zenon_H104 zenon_H181 zenon_H117 zenon_H9f zenon_H2c zenon_Ha9 zenon_H191 zenon_Hb6 zenon_H67 zenon_H16a zenon_H48 zenon_Ha0 zenon_Ha5 zenon_H195 zenon_H100 zenon_H3c zenon_H13f zenon_H196 zenon_H38. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.10/22.20 apply (zenon_L359_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.10/22.20 apply (zenon_L929_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.10/22.20 apply (zenon_L1487_); trivial. % 22.10/22.20 apply (zenon_L1162_); trivial. % 22.10/22.20 (* end of lemma zenon_L1488_ *) % 22.10/22.20 assert (zenon_L1489_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e1)) = (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e0) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.10/22.20 do 0 intro. intros zenon_H13c zenon_H159 zenon_Hef zenon_H141 zenon_H109 zenon_He7 zenon_Hf0 zenon_H77 zenon_H183 zenon_H68 zenon_H34 zenon_H7f zenon_H104 zenon_H181 zenon_H117 zenon_H9f zenon_H2c zenon_Ha9 zenon_H191 zenon_Hb6 zenon_H67 zenon_H16a zenon_H48 zenon_Ha0 zenon_H195 zenon_H100 zenon_H3c zenon_H13f zenon_H196 zenon_H38. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.10/22.20 apply (zenon_L46_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.10/22.20 exact (zenon_H159 zenon_H10c). % 22.10/22.20 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.10/22.20 apply (zenon_L1454_); trivial. % 22.10/22.20 apply (zenon_L1488_); trivial. % 22.10/22.20 (* end of lemma zenon_L1489_ *) % 22.10/22.20 assert (zenon_L1490_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (((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)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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)) = (e3))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H26a zenon_Ha0 zenon_H1cd zenon_Hac zenon_H191 zenon_H186 zenon_H153 zenon_H1a2 zenon_H1b7 zenon_H7f zenon_Hb6 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_Hc4. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H9e | zenon_intro zenon_H26b ]. % 22.10/22.20 apply (zenon_L156_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H26c ]. % 22.10/22.20 apply (zenon_L1439_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc3 ]. % 22.10/22.20 apply (zenon_L1290_); trivial. % 22.10/22.20 exact (zenon_Hc4 zenon_Hc3). % 22.10/22.20 (* end of lemma zenon_L1490_ *) % 22.10/22.20 assert (zenon_L1491_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (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) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H121 zenon_H209 zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_Hb6 zenon_H7f zenon_H1b7 zenon_H1a2 zenon_H153 zenon_H186 zenon_H191 zenon_H1cd zenon_Ha0 zenon_H26a zenon_H163 zenon_H133 zenon_Hc4. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 22.10/22.20 exact (zenon_H209 zenon_H9d). % 22.10/22.20 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 22.10/22.20 apply (zenon_L1490_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 22.10/22.20 apply (zenon_L617_); trivial. % 22.10/22.20 exact (zenon_Hc4 zenon_Hc3). % 22.10/22.20 (* end of lemma zenon_L1491_ *) % 22.10/22.20 assert (zenon_L1492_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (((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)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 22.10/22.20 do 0 intro. intros zenon_H13c zenon_H159 zenon_Hc4 zenon_H163 zenon_H26a zenon_Ha0 zenon_H1cd zenon_H191 zenon_H186 zenon_H153 zenon_H1a2 zenon_H1b7 zenon_H7f zenon_Hb6 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_H209 zenon_H121 zenon_Ha9 zenon_Hf7. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.10/22.20 apply (zenon_L46_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.10/22.20 exact (zenon_H159 zenon_H10c). % 22.10/22.20 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.10/22.20 apply (zenon_L1491_); trivial. % 22.10/22.20 apply (zenon_L299_); trivial. % 22.10/22.20 (* end of lemma zenon_L1492_ *) % 22.10/22.20 assert (zenon_L1493_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((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) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (((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)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 22.10/22.20 do 0 intro. intros zenon_Hfa zenon_H196 zenon_H13f zenon_H100 zenon_H195 zenon_H16a zenon_H67 zenon_H2c zenon_H9f zenon_H117 zenon_H181 zenon_H104 zenon_H34 zenon_H68 zenon_H183 zenon_H77 zenon_Hf0 zenon_He7 zenon_H109 zenon_H141 zenon_H24 zenon_H13c zenon_H159 zenon_Hc4 zenon_H163 zenon_H26a zenon_Ha0 zenon_H1cd zenon_H191 zenon_H186 zenon_H153 zenon_H1a2 zenon_H1b7 zenon_H7f zenon_Hb6 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_H209 zenon_H121 zenon_Ha9. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.10/22.20 apply (zenon_L24_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.10/22.20 apply (zenon_L1489_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.10/22.20 apply (zenon_L900_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.10/22.20 exact (zenon_H159 zenon_H10c). % 22.10/22.20 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.10/22.20 apply (zenon_L436_); trivial. % 22.10/22.20 apply (zenon_L1488_); trivial. % 22.10/22.20 apply (zenon_L1492_); trivial. % 22.10/22.20 (* end of lemma zenon_L1493_ *) % 22.10/22.20 assert (zenon_L1494_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (((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) (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) (e3)) = (op (e2) (e3)))) -> (((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) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 22.10/22.20 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H23c zenon_H1c7 zenon_H6e zenon_H1c6 zenon_Hfa zenon_H196 zenon_H13f zenon_H100 zenon_H195 zenon_H16a zenon_H67 zenon_H2c zenon_H9f zenon_H117 zenon_H181 zenon_H104 zenon_H34 zenon_H68 zenon_H183 zenon_H77 zenon_Hf0 zenon_He7 zenon_H109 zenon_H141 zenon_H24 zenon_H13c zenon_H159 zenon_Hc4 zenon_H163 zenon_H26a zenon_Ha0 zenon_H1cd zenon_H191 zenon_H186 zenon_H153 zenon_H1a2 zenon_H1b7 zenon_Hb6 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_H209 zenon_H121 zenon_Ha9. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.10/22.20 apply (zenon_L738_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.10/22.20 apply (zenon_L492_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.10/22.20 apply (zenon_L1474_); trivial. % 22.10/22.20 apply (zenon_L1493_); trivial. % 22.10/22.20 (* end of lemma zenon_L1494_ *) % 22.10/22.20 assert (zenon_L1495_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> False). % 22.10/22.20 do 0 intro. intros zenon_H12e zenon_H48 zenon_H181 zenon_H104 zenon_H8a zenon_H77 zenon_H34 zenon_H68 zenon_H183 zenon_H153 zenon_H177 zenon_He7 zenon_H171. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.10/22.20 apply (zenon_L456_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.10/22.20 apply (zenon_L420_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.10/22.20 apply (zenon_L566_); trivial. % 22.10/22.20 apply (zenon_L964_); trivial. % 22.10/22.20 (* end of lemma zenon_L1495_ *) % 22.10/22.20 assert (zenon_L1496_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (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)))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((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). % 22.10/22.20 do 0 intro. intros zenon_Hfa zenon_H77 zenon_H24 zenon_H38 zenon_H196 zenon_H117 zenon_H9f zenon_H2c zenon_Hb6 zenon_H53 zenon_Ha0 zenon_H48 zenon_H109 zenon_H34 zenon_H141 zenon_Ha9 zenon_H159 zenon_H3c zenon_H13c zenon_H93 zenon_H195. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.10/22.20 apply (zenon_L24_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.10/22.20 apply (zenon_L1405_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.10/22.20 apply (zenon_L1473_); trivial. % 22.10/22.20 apply (zenon_L228_); trivial. % 22.10/22.20 (* end of lemma zenon_L1496_ *) % 22.10/22.20 assert (zenon_L1497_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (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) (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((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) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H12e zenon_H177 zenon_He4 zenon_H1d8 zenon_H23c zenon_H1c7 zenon_H1c6 zenon_H1a8 zenon_Hfa zenon_H196 zenon_H13f zenon_H100 zenon_H195 zenon_H16a zenon_H67 zenon_H2c zenon_H9f zenon_H117 zenon_H181 zenon_H104 zenon_H34 zenon_H68 zenon_H183 zenon_H77 zenon_Hf0 zenon_He7 zenon_H109 zenon_H141 zenon_H24 zenon_H13c zenon_H159 zenon_Hc4 zenon_H163 zenon_H26a zenon_Ha0 zenon_H1cd zenon_H191 zenon_H186 zenon_H153 zenon_H1a2 zenon_H1b7 zenon_Hb6 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_H209 zenon_H121 zenon_Ha9. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.10/22.20 apply (zenon_L738_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.10/22.20 apply (zenon_L492_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.10/22.20 apply (zenon_L24_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.10/22.20 apply (zenon_L1405_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.10/22.20 apply (zenon_L1473_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.10/22.20 apply (zenon_L1494_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.10/22.20 apply (zenon_L1455_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.10/22.20 apply (zenon_L56_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.10/22.20 apply (zenon_L180_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.10/22.20 apply (zenon_L56_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.10/22.20 apply (zenon_L1495_); trivial. % 22.10/22.20 apply (zenon_L1496_); trivial. % 22.10/22.20 apply (zenon_L1493_); trivial. % 22.10/22.20 (* end of lemma zenon_L1497_ *) % 22.10/22.20 assert (zenon_L1498_ : (((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)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.10/22.20 do 0 intro. intros zenon_H13c zenon_H3c zenon_H159 zenon_Hf3 zenon_H141 zenon_H34 zenon_H109 zenon_H48 zenon_H195 zenon_Ha0 zenon_H53 zenon_Hb6 zenon_H2c zenon_H9f zenon_H117 zenon_H196 zenon_H38. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.10/22.20 apply (zenon_L46_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.10/22.20 exact (zenon_H159 zenon_H10c). % 22.10/22.20 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.10/22.20 apply (zenon_L162_); trivial. % 22.10/22.20 apply (zenon_L1404_); trivial. % 22.10/22.20 (* end of lemma zenon_L1498_ *) % 22.10/22.20 assert (zenon_L1499_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((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 (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)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e3))) -> (~((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 (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((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))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 22.10/22.20 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H153 zenon_H23c zenon_Hfa zenon_H38 zenon_H196 zenon_H13f zenon_H3c zenon_H100 zenon_H195 zenon_H48 zenon_H16a zenon_H67 zenon_Hb6 zenon_H191 zenon_H2c zenon_H117 zenon_H181 zenon_H104 zenon_H34 zenon_H183 zenon_H77 zenon_Hf0 zenon_He7 zenon_H109 zenon_H141 zenon_H68 zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_Ha0 zenon_Hf3 zenon_Ha9. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.10/22.20 apply (zenon_L738_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.10/22.20 apply (zenon_L492_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.10/22.20 apply (zenon_L1498_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.10/22.20 apply (zenon_L24_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.10/22.20 apply (zenon_L1489_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.10/22.20 apply (zenon_L62_); trivial. % 22.10/22.20 apply (zenon_L1468_); trivial. % 22.10/22.20 (* end of lemma zenon_L1499_ *) % 22.10/22.20 assert (zenon_L1500_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((e0) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((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 (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.10/22.20 do 0 intro. intros zenon_Heb zenon_H100 zenon_Ha9 zenon_Ha0 zenon_H159 zenon_H24 zenon_H9f zenon_H13c zenon_H1a8 zenon_H1c7 zenon_H1c6 zenon_H1cf zenon_H1d5 zenon_H67 zenon_H4e zenon_H195 zenon_Hdd zenon_H54 zenon_Hb6 zenon_H117 zenon_H1cd zenon_Hfa zenon_Hf3 zenon_H48 zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H181. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.10/22.20 apply (zenon_L69_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.10/22.20 apply (zenon_L1465_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.10/22.20 apply (zenon_L186_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.10/22.20 apply (zenon_L62_); trivial. % 22.10/22.20 apply (zenon_L1468_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.10/22.20 apply (zenon_L117_); trivial. % 22.10/22.20 apply (zenon_L414_); trivial. % 22.10/22.20 (* end of lemma zenon_L1500_ *) % 22.10/22.20 assert (zenon_L1501_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (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)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((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 (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (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))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 22.10/22.20 do 0 intro. intros zenon_He2 zenon_H1fb zenon_H36 zenon_Hf0 zenon_H1d8 zenon_H77 zenon_H183 zenon_H68 zenon_H104 zenon_H181 zenon_H117 zenon_H9f zenon_H2c zenon_Ha9 zenon_H191 zenon_Hb6 zenon_H67 zenon_H16a zenon_H111 zenon_H153 zenon_H141 zenon_H109 zenon_H48 zenon_H195 zenon_Ha0 zenon_H196 zenon_H38 zenon_Heb zenon_H100 zenon_H159 zenon_H24 zenon_H13c zenon_H1a8 zenon_H1c7 zenon_H1c6 zenon_H1cf zenon_H1d5 zenon_H4e zenon_H1cd zenon_Hfa zenon_Hf3 zenon_H1c3 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H13f zenon_H121 zenon_H209 zenon_H18d zenon_H5d zenon_H3c zenon_H1b7 zenon_H1a2 zenon_H186 zenon_H26a zenon_H163 zenon_H23c zenon_He4 zenon_H7d zenon_H34. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.10/22.20 apply (zenon_L317_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.10/22.20 apply (zenon_L1499_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.10/22.20 apply (zenon_L1242_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.10/22.20 apply (zenon_L492_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.10/22.20 apply (zenon_L111_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.10/22.20 apply (zenon_L46_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.10/22.20 exact (zenon_H159 zenon_H10c). % 22.10/22.20 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.10/22.20 apply (zenon_L1491_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.10/22.20 apply (zenon_L1500_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.10/22.20 apply (zenon_L1404_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.10/22.20 apply (zenon_L148_); trivial. % 22.10/22.20 apply (zenon_L1486_); trivial. % 22.10/22.20 apply (zenon_L802_); trivial. % 22.10/22.20 (* end of lemma zenon_L1501_ *) % 22.10/22.20 assert (zenon_L1502_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H121 zenon_H1cb zenon_H34 zenon_H18a zenon_H1bb zenon_H65 zenon_H1ef zenon_H186 zenon_Hf7 zenon_H13a zenon_H33 zenon_H14c zenon_H6f zenon_H109 zenon_H117 zenon_H18d zenon_H48 zenon_H5d zenon_H3c zenon_H1b7 zenon_H1f1 zenon_H77 zenon_H13f zenon_H201 zenon_H4e zenon_H190 zenon_H23c zenon_He4 zenon_Ha9 zenon_H38 zenon_Ha0 zenon_H1cf zenon_H1c7 zenon_H106 zenon_Hb6 zenon_Hc4. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 22.10/22.20 apply (zenon_L1295_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 22.10/22.20 exact (zenon_H1c7 zenon_Hac). % 22.10/22.20 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 22.10/22.20 apply (zenon_L363_); trivial. % 22.10/22.20 exact (zenon_Hc4 zenon_Hc3). % 22.10/22.20 (* end of lemma zenon_L1502_ *) % 22.10/22.20 assert (zenon_L1503_ : (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H1d8 zenon_H3d zenon_H133 zenon_H121 zenon_H1cb zenon_H34 zenon_H18a zenon_H1bb zenon_H65 zenon_H1ef zenon_H186 zenon_Hf7 zenon_H13a zenon_H33 zenon_H14c zenon_H6f zenon_H109 zenon_H117 zenon_H18d zenon_H48 zenon_H5d zenon_H3c zenon_H1b7 zenon_H1f1 zenon_H77 zenon_H13f zenon_H201 zenon_H4e zenon_H190 zenon_H23c zenon_He4 zenon_Ha9 zenon_H38 zenon_Ha0 zenon_H1cf zenon_H1c7 zenon_Hb6 zenon_Hc4. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.10/22.20 apply (zenon_L738_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.10/22.20 apply (zenon_L124_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.10/22.20 apply (zenon_L255_); trivial. % 22.10/22.20 apply (zenon_L1502_); trivial. % 22.10/22.20 (* end of lemma zenon_L1503_ *) % 22.10/22.20 assert (zenon_L1504_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e3)) = (e2))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H1c3 zenon_H68 zenon_Hb6 zenon_H1c7 zenon_H1cf zenon_Ha0 zenon_Ha9 zenon_He4 zenon_H23c zenon_H190 zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H1b7 zenon_H3c zenon_H5d zenon_H117 zenon_H109 zenon_H6f zenon_H14c zenon_H33 zenon_H13a zenon_H186 zenon_H1ef zenon_H65 zenon_H18a zenon_H34 zenon_H121 zenon_H133 zenon_H3d zenon_H1d8 zenon_H1cb zenon_H106 zenon_H77 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H181. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 22.10/22.20 apply (zenon_L165_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 22.10/22.20 apply (zenon_L1503_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 22.10/22.20 apply (zenon_L1159_); trivial. % 22.10/22.20 exact (zenon_H181 zenon_H17c). % 22.10/22.20 (* end of lemma zenon_L1504_ *) % 22.10/22.20 assert (zenon_L1505_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H190 zenon_H1c3 zenon_H68 zenon_H1cf zenon_Ha0 zenon_Ha9 zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H1b7 zenon_H117 zenon_H109 zenon_H6f zenon_H14c zenon_H13a zenon_H186 zenon_H1ef zenon_H65 zenon_H18a zenon_H34 zenon_H3d zenon_H1d8 zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_H181 zenon_H66 zenon_H1a2 zenon_Hc4 zenon_H104 zenon_H1c7 zenon_H9f zenon_H33 zenon_H121 zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_Hb6 zenon_H1cb. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.10/22.20 apply (zenon_L94_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.10/22.20 apply (zenon_L14_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.10/22.20 apply (zenon_L255_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.10/22.20 apply (zenon_L43_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.10/22.20 apply (zenon_L193_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.10/22.20 apply (zenon_L1504_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.10/22.20 apply (zenon_L163_); trivial. % 22.10/22.20 apply (zenon_L363_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.10/22.20 apply (zenon_L819_); trivial. % 22.10/22.20 apply (zenon_L1151_); trivial. % 22.10/22.20 (* end of lemma zenon_L1505_ *) % 22.10/22.20 assert (zenon_L1506_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((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) (e3)) = (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (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))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H196 zenon_H190 zenon_H1c3 zenon_H68 zenon_H1cf zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H1b7 zenon_H117 zenon_H109 zenon_H6f zenon_H13a zenon_H186 zenon_H1ef zenon_H65 zenon_H18a zenon_H34 zenon_H1d8 zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_H181 zenon_H1a2 zenon_Hc4 zenon_H104 zenon_H1c7 zenon_H33 zenon_H121 zenon_H18d zenon_H48 zenon_H5d zenon_H3c zenon_H1cb zenon_Hf0 zenon_He7 zenon_H141 zenon_Hb6 zenon_H3d zenon_Ha9 zenon_H66 zenon_H38 zenon_Ha0. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.10/22.20 apply (zenon_L359_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.10/22.20 apply (zenon_L929_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.10/22.20 apply (zenon_L1505_); trivial. % 22.10/22.20 apply (zenon_L1162_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.10/22.20 apply (zenon_L55_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.10/22.20 apply (zenon_L193_); trivial. % 22.10/22.20 apply (zenon_L156_); trivial. % 22.10/22.20 (* end of lemma zenon_L1506_ *) % 22.10/22.20 assert (zenon_L1507_ : (((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 (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H183 zenon_H68 zenon_H6e zenon_H192 zenon_Hc4 zenon_H1cb zenon_H106 zenon_H34 zenon_H18a zenon_H1bb zenon_H181. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.10/22.20 apply (zenon_L291_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.10/22.20 apply (zenon_L1128_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.10/22.20 apply (zenon_L847_); trivial. % 22.10/22.20 exact (zenon_H181 zenon_H17c). % 22.10/22.20 (* end of lemma zenon_L1507_ *) % 22.10/22.20 assert (zenon_L1508_ : (((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 (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H183 zenon_H68 zenon_H6e zenon_H192 zenon_H1c7 zenon_H1cd zenon_H11f zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H181. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.10/22.20 apply (zenon_L291_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.10/22.20 apply (zenon_L1128_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.10/22.20 apply (zenon_L848_); trivial. % 22.10/22.20 exact (zenon_H181 zenon_H17c). % 22.10/22.20 (* end of lemma zenon_L1508_ *) % 22.10/22.20 assert (zenon_L1509_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((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 (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H12e zenon_H48 zenon_H104 zenon_H8a zenon_H77 zenon_H1bb zenon_H18a zenon_H1cb zenon_Hc4 zenon_H183 zenon_H68 zenon_H6e zenon_H192 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H181. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.10/22.20 apply (zenon_L456_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.10/22.20 apply (zenon_L420_); trivial. % 22.10/22.20 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.10/22.20 apply (zenon_L1507_); trivial. % 22.10/22.20 apply (zenon_L1508_); trivial. % 22.10/22.20 (* end of lemma zenon_L1509_ *) % 22.10/22.20 assert (zenon_L1510_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.10/22.20 do 0 intro. intros zenon_H12e zenon_H77 zenon_H93 zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H160 zenon_H1c7. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.10/22.21 apply (zenon_L456_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.10/22.21 apply (zenon_L1276_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.10/22.21 apply (zenon_L847_); trivial. % 22.10/22.21 apply (zenon_L848_); trivial. % 22.10/22.21 (* end of lemma zenon_L1510_ *) % 22.10/22.21 assert (zenon_L1511_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e3)) = (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 (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.10/22.21 do 0 intro. intros zenon_H1cf zenon_H153 zenon_Ha9 zenon_H133 zenon_H181 zenon_H192 zenon_H6e zenon_H68 zenon_H183 zenon_H104 zenon_H12e zenon_H77 zenon_H93 zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.10/22.21 apply (zenon_L94_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.10/22.21 apply (zenon_L436_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.10/22.21 apply (zenon_L1509_); trivial. % 22.10/22.21 apply (zenon_L1510_); trivial. % 22.10/22.21 (* end of lemma zenon_L1511_ *) % 22.10/22.21 assert (zenon_L1512_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.10/22.21 do 0 intro. intros zenon_H141 zenon_H93 zenon_H77 zenon_H111 zenon_H153 zenon_H3f zenon_H48 zenon_H13f zenon_He7 zenon_Hf0 zenon_H195 zenon_Ha5 zenon_Ha0 zenon_H6f zenon_Hdb zenon_H54 zenon_Hb6 zenon_H117 zenon_H196 zenon_H38. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.10/22.21 apply (zenon_L219_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.10/22.21 apply (zenon_L929_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.10/22.21 apply (zenon_L1466_); trivial. % 22.10/22.21 apply (zenon_L1162_); trivial. % 22.10/22.21 (* end of lemma zenon_L1512_ *) % 22.10/22.21 assert (zenon_L1513_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 22.10/22.21 do 0 intro. intros zenon_H231 zenon_Hbc zenon_H11f zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H1bb zenon_H18a zenon_H1cb zenon_Hc4 zenon_H18d zenon_H48 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H93 zenon_H77 zenon_H12e zenon_H110 zenon_H104. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H11d | zenon_intro zenon_H232 ]. % 22.10/22.21 apply (zenon_L328_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H106 | zenon_intro zenon_H233 ]. % 22.10/22.21 apply (zenon_L846_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H160 | zenon_intro zenon_Hbb ]. % 22.10/22.21 apply (zenon_L1510_); trivial. % 22.10/22.21 apply (zenon_L129_); trivial. % 22.10/22.21 (* end of lemma zenon_L1513_ *) % 22.10/22.21 assert (zenon_L1514_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 22.10/22.21 do 0 intro. intros zenon_Hca zenon_H48 zenon_H34 zenon_H18d zenon_H1b7 zenon_H77 zenon_H1b4 zenon_H20f zenon_H129 zenon_H93 zenon_Hc4 zenon_H1bb zenon_H38 zenon_H1cb zenon_H231 zenon_H110 zenon_H104 zenon_H18a zenon_H24e zenon_H1cd zenon_H7d zenon_H12e zenon_Hbc. % 22.10/22.21 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.10/22.21 apply (zenon_L456_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.10/22.21 apply (zenon_L1276_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.10/22.21 apply (zenon_L1159_); trivial. % 22.10/22.21 apply (zenon_L1513_); trivial. % 22.10/22.21 apply (zenon_L555_); trivial. % 22.10/22.21 (* end of lemma zenon_L1514_ *) % 22.10/22.21 assert (zenon_L1515_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 22.10/22.21 do 0 intro. intros zenon_H36 zenon_H48 zenon_H18d zenon_H1b7 zenon_H77 zenon_H1b4 zenon_H20f zenon_H129 zenon_H93 zenon_Hc4 zenon_H1bb zenon_H1cb zenon_H231 zenon_H110 zenon_H104 zenon_H18a zenon_H24e zenon_H1cd zenon_H7d zenon_H12e zenon_Hbc. % 22.10/22.21 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.10/22.21 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.10/22.21 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.10/22.21 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.10/22.21 apply (zenon_L1514_); trivial. % 22.10/22.21 (* end of lemma zenon_L1515_ *) % 22.10/22.21 assert (zenon_L1516_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.10/22.21 do 0 intro. intros zenon_H25e zenon_H1fb zenon_H2a zenon_H1b4 zenon_H11f zenon_H196 zenon_H93 zenon_Ha5 zenon_Hf5. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H38 | zenon_intro zenon_H25f ]. % 22.10/22.21 apply (zenon_L316_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H155 | zenon_intro zenon_H260 ]. % 22.10/22.21 apply (zenon_L187_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H9e ]. % 22.10/22.21 apply (zenon_L167_); trivial. % 22.10/22.21 apply (zenon_L262_); trivial. % 22.10/22.21 (* end of lemma zenon_L1516_ *) % 22.10/22.21 assert (zenon_L1517_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> False). % 22.10/22.21 do 0 intro. intros zenon_H1c3 zenon_H9f zenon_Ha9 zenon_Hf5 zenon_Ha5 zenon_H196 zenon_H1b4 zenon_H2a zenon_H1fb zenon_H25e zenon_H77 zenon_H11f. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 22.10/22.21 apply (zenon_L673_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 22.10/22.21 apply (zenon_L299_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 22.10/22.21 apply (zenon_L1516_); trivial. % 22.10/22.21 apply (zenon_L884_); trivial. % 22.10/22.21 (* end of lemma zenon_L1517_ *) % 22.10/22.21 assert (zenon_L1518_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.10/22.21 do 0 intro. intros zenon_H13a zenon_H11f zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha9 zenon_H1c3 zenon_Ha0 zenon_H2a zenon_Hb6 zenon_H153 zenon_Ha5 zenon_Hf5. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.10/22.21 apply (zenon_L1517_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.10/22.21 apply (zenon_L53_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.10/22.21 apply (zenon_L95_); trivial. % 22.10/22.21 apply (zenon_L262_); trivial. % 22.10/22.21 (* end of lemma zenon_L1518_ *) % 22.10/22.21 assert (zenon_L1519_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 22.10/22.21 do 0 intro. intros zenon_H12e zenon_H48 zenon_H3f zenon_H11a zenon_Hbb zenon_H288 zenon_Hf5 zenon_Ha5 zenon_Hb6 zenon_Ha0 zenon_H1c3 zenon_Ha9 zenon_H196 zenon_H1b4 zenon_H1fb zenon_H25e zenon_H77 zenon_H13a zenon_H1d8 zenon_H153 zenon_H181 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H192 zenon_H68 zenon_H183 zenon_H6f zenon_H10d. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.10/22.21 apply (zenon_L456_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.10/22.21 apply (zenon_L552_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.10/22.21 apply (zenon_L363_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H2a | zenon_intro zenon_H289 ]. % 22.10/22.21 apply (zenon_L1518_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H3d | zenon_intro zenon_H28a ]. % 22.10/22.21 apply (zenon_L738_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H6e | zenon_intro zenon_Hdb ]. % 22.10/22.21 apply (zenon_L1508_); trivial. % 22.10/22.21 apply (zenon_L205_); trivial. % 22.10/22.21 (* end of lemma zenon_L1519_ *) % 22.10/22.21 assert (zenon_L1520_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 22.10/22.21 do 0 intro. intros zenon_H1a2 zenon_H186 zenon_Hbc zenon_H18a zenon_H104 zenon_H231 zenon_H1cb zenon_H1bb zenon_Hc4 zenon_H93 zenon_H129 zenon_H20f zenon_H18d zenon_H36 zenon_H12e zenon_H48 zenon_H3f zenon_H11a zenon_H288 zenon_Hf5 zenon_Ha5 zenon_Hb6 zenon_Ha0 zenon_H1c3 zenon_Ha9 zenon_H196 zenon_H1b4 zenon_H1fb zenon_H25e zenon_H77 zenon_H13a zenon_H1d8 zenon_H153 zenon_H181 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H192 zenon_H68 zenon_H183 zenon_H6f zenon_H10d. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.10/22.21 apply (zenon_L95_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.10/22.21 apply (zenon_L308_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.10/22.21 apply (zenon_L1515_); trivial. % 22.10/22.21 apply (zenon_L1519_); trivial. % 22.10/22.21 (* end of lemma zenon_L1520_ *) % 22.10/22.21 assert (zenon_L1521_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.10/22.21 do 0 intro. intros zenon_H1c6 zenon_H38 zenon_H117 zenon_H54 zenon_H195 zenon_Hf0 zenon_He7 zenon_H13f zenon_H111 zenon_H141 zenon_H159 zenon_H6f zenon_H183 zenon_H68 zenon_H192 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H181 zenon_H153 zenon_H1d8 zenon_H13a zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha9 zenon_H1c3 zenon_Ha0 zenon_Hb6 zenon_Ha5 zenon_Hf5 zenon_H288 zenon_H11a zenon_H3f zenon_H48 zenon_H12e zenon_H36 zenon_H18d zenon_H20f zenon_H129 zenon_H93 zenon_Hc4 zenon_H1bb zenon_H1cb zenon_H231 zenon_H104 zenon_H18a zenon_Hbc zenon_H186 zenon_H1a2 zenon_H1c7. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.10/22.21 apply (zenon_L1512_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.10/22.21 exact (zenon_H159 zenon_H10c). % 22.10/22.21 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.10/22.21 apply (zenon_L1520_); trivial. % 22.10/22.21 exact (zenon_H1c7 zenon_Hac). % 22.10/22.21 (* end of lemma zenon_L1521_ *) % 22.10/22.21 assert (zenon_L1522_ : (((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 (e0) (e1)) = (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 (e0) (e3)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.10/22.21 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H6e zenon_H1cf zenon_H1c6 zenon_H38 zenon_H117 zenon_H54 zenon_H195 zenon_Hf0 zenon_He7 zenon_H13f zenon_H111 zenon_H141 zenon_H159 zenon_H6f zenon_H183 zenon_H68 zenon_H192 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H181 zenon_H153 zenon_H1d8 zenon_H13a zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha9 zenon_H1c3 zenon_Ha0 zenon_Hb6 zenon_Hf5 zenon_H288 zenon_H11a zenon_H3f zenon_H48 zenon_H12e zenon_H36 zenon_H18d zenon_H20f zenon_H129 zenon_H93 zenon_Hc4 zenon_H1bb zenon_H1cb zenon_H231 zenon_H104 zenon_H18a zenon_Hbc zenon_H186 zenon_H1a2 zenon_H1c7. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.10/22.21 apply (zenon_L900_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.10/22.21 exact (zenon_H159 zenon_H10c). % 22.10/22.21 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.10/22.21 apply (zenon_L1511_); trivial. % 22.10/22.21 apply (zenon_L1521_); trivial. % 22.10/22.21 (* end of lemma zenon_L1522_ *) % 22.10/22.21 assert (zenon_L1523_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((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)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((e1) = (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) (e3)) = (op (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.10/22.21 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H153 zenon_H23c zenon_H195 zenon_H13c zenon_H3c zenon_H159 zenon_Ha9 zenon_H141 zenon_H34 zenon_H109 zenon_Ha0 zenon_Hb6 zenon_H2c zenon_H9f zenon_H117 zenon_H196 zenon_H24 zenon_Hfa zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H93 zenon_H77 zenon_H1b7. % 22.10/22.21 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.10/22.21 apply (zenon_L738_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.10/22.21 apply (zenon_L492_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.10/22.21 apply (zenon_L1496_); trivial. % 22.10/22.21 apply (zenon_L1276_); trivial. % 22.10/22.21 (* end of lemma zenon_L1523_ *) % 22.10/22.21 assert (zenon_L1524_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((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)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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 (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (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 (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (((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 (e1) (e2)) = (e0)) -> (~((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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.10/22.21 do 0 intro. intros zenon_Heb zenon_Hfa zenon_H2c zenon_H109 zenon_H23c zenon_He4 zenon_H1c7 zenon_H1a2 zenon_H186 zenon_Hbc zenon_H18a zenon_H104 zenon_H231 zenon_H1cb zenon_H93 zenon_H18d zenon_H36 zenon_H12e zenon_H48 zenon_H11a zenon_H288 zenon_Hf5 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H196 zenon_H1fb zenon_H25e zenon_H13a zenon_H1d8 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H192 zenon_H183 zenon_H6f zenon_H159 zenon_H141 zenon_H111 zenon_H13f zenon_He7 zenon_Hf0 zenon_H195 zenon_H54 zenon_H117 zenon_H1c6 zenon_Hf3 zenon_H24 zenon_H9f zenon_H13c zenon_H73 zenon_H153 zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H181. % 22.10/22.21 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.10/22.21 apply (zenon_L1523_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.10/22.21 apply (zenon_L900_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.10/22.21 exact (zenon_H159 zenon_H10c). % 22.10/22.21 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.10/22.21 apply (zenon_L162_); trivial. % 22.10/22.21 apply (zenon_L1521_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.10/22.21 apply (zenon_L184_); trivial. % 22.10/22.21 apply (zenon_L414_); trivial. % 22.10/22.21 (* end of lemma zenon_L1524_ *) % 22.10/22.21 assert (zenon_L1525_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (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) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((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)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((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) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (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) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 22.10/22.21 do 0 intro. intros zenon_He2 zenon_H181 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H77 zenon_H68 zenon_H1c3 zenon_H153 zenon_H73 zenon_H13c zenon_H9f zenon_H24 zenon_Hf3 zenon_H117 zenon_H54 zenon_H195 zenon_Hf0 zenon_H13f zenon_H111 zenon_H141 zenon_H6f zenon_H183 zenon_H192 zenon_H1cd zenon_H1b7 zenon_H24e zenon_H1d8 zenon_H13a zenon_H25e zenon_H1fb zenon_H196 zenon_Hb6 zenon_Hf5 zenon_H288 zenon_H11a zenon_H48 zenon_H12e zenon_H36 zenon_H18d zenon_H93 zenon_H1cb zenon_H231 zenon_H104 zenon_H18a zenon_Hbc zenon_H186 zenon_H1a2 zenon_He4 zenon_H23c zenon_H109 zenon_H2c zenon_Hfa zenon_Heb zenon_H1c7 zenon_Ha0 zenon_H159 zenon_H6e zenon_Ha9 zenon_H1c6 zenon_H7d zenon_H34. % 22.10/22.21 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.10/22.21 apply (zenon_L147_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.10/22.21 apply (zenon_L1524_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.10/22.21 apply (zenon_L1462_); trivial. % 22.10/22.21 apply (zenon_L802_); trivial. % 22.10/22.21 (* end of lemma zenon_L1525_ *) % 22.10/22.21 assert (zenon_L1526_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (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) (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((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)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (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) (e1)) = (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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (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 (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (((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 (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.10/22.21 do 0 intro. intros zenon_H13b zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H266 zenon_H1ef zenon_H139 zenon_H16a zenon_H25b zenon_H27e zenon_H189 zenon_H236 zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H284 zenon_H76 zenon_H34 zenon_H7d zenon_H1c6 zenon_Ha9 zenon_H6e zenon_H159 zenon_Ha0 zenon_H1c7 zenon_Heb zenon_Hfa zenon_H2c zenon_H109 zenon_H23c zenon_He4 zenon_H1a2 zenon_H186 zenon_Hbc zenon_H18a zenon_H104 zenon_H231 zenon_H1cb zenon_H93 zenon_H18d zenon_H36 zenon_H12e zenon_H48 zenon_H11a zenon_H288 zenon_Hb6 zenon_H196 zenon_H1fb zenon_H25e zenon_H13a zenon_H1d8 zenon_H24e zenon_H1b7 zenon_H1cd zenon_H192 zenon_H183 zenon_H6f zenon_H141 zenon_H111 zenon_H13f zenon_Hf0 zenon_H195 zenon_H54 zenon_H117 zenon_H24 zenon_H9f zenon_H13c zenon_H73 zenon_H153 zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H181 zenon_He2 zenon_Hf5 zenon_H38. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.10/22.21 apply (zenon_L171_); trivial. % 22.10/22.21 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.10/22.21 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.12/22.21 apply (zenon_L24_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.12/22.21 apply (zenon_L1522_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.12/22.21 apply (zenon_L184_); trivial. % 22.12/22.21 apply (zenon_L1236_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.12/22.21 apply (zenon_L1525_); trivial. % 22.12/22.21 apply (zenon_L663_); trivial. % 22.12/22.21 (* end of lemma zenon_L1526_ *) % 22.12/22.21 assert (zenon_L1527_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.12/22.21 do 0 intro. intros zenon_H1cf zenon_H153 zenon_H77 zenon_Ha9 zenon_H133 zenon_H93 zenon_H1c2 zenon_H171 zenon_H1cd. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.12/22.21 apply (zenon_L94_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.12/22.21 apply (zenon_L436_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.12/22.21 apply (zenon_L207_); trivial. % 22.12/22.21 apply (zenon_L240_); trivial. % 22.12/22.21 (* end of lemma zenon_L1527_ *) % 22.12/22.21 assert (zenon_L1528_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (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 (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.12/22.21 do 0 intro. intros zenon_Hfa zenon_H1cd zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha0 zenon_Hdd zenon_Ha9 zenon_H4e zenon_H67 zenon_H1d5 zenon_H1cf zenon_H159 zenon_H24 zenon_H9f zenon_H13c zenon_H189 zenon_H1c6 zenon_H1c7 zenon_H1a8 zenon_H77 zenon_H3f zenon_Hf3 zenon_H68 zenon_H93 zenon_H195. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.21 apply (zenon_L1462_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.21 apply (zenon_L186_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.21 apply (zenon_L439_); trivial. % 22.12/22.21 apply (zenon_L1464_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.21 apply (zenon_L186_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.21 apply (zenon_L62_); trivial. % 22.12/22.21 apply (zenon_L228_); trivial. % 22.12/22.21 (* end of lemma zenon_L1528_ *) % 22.12/22.21 assert (zenon_L1529_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 22.12/22.21 do 0 intro. intros zenon_H100 zenon_Hf3 zenon_H1a8 zenon_H1c7 zenon_H9f zenon_H24 zenon_H159 zenon_H1d5 zenon_H67 zenon_Hdd zenon_H54 zenon_H1cd zenon_Hfa zenon_H153 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H129 zenon_H93 zenon_H1bb. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.12/22.21 apply (zenon_L69_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.12/22.21 apply (zenon_L1528_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.12/22.21 apply (zenon_L184_); trivial. % 22.12/22.21 apply (zenon_L1236_); trivial. % 22.12/22.21 (* end of lemma zenon_L1529_ *) % 22.12/22.21 assert (zenon_L1530_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (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 (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)) = (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 (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.21 do 0 intro. intros zenon_H179 zenon_H1c2 zenon_H13b zenon_H34 zenon_H7d zenon_H100 zenon_H1a8 zenon_H1c7 zenon_H9f zenon_H24 zenon_H159 zenon_H1d5 zenon_H67 zenon_H54 zenon_H1cd zenon_Hfa zenon_H153 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H93 zenon_H1bb zenon_H2c zenon_H109 zenon_H23c zenon_He4 zenon_Hbc zenon_H18a zenon_H104 zenon_H231 zenon_H36 zenon_H12e zenon_H11a zenon_H288 zenon_H1d8 zenon_H24e zenon_H192 zenon_H183 zenon_H141 zenon_H111 zenon_H13f zenon_Hf0 zenon_Hc4 zenon_H181 zenon_He2 zenon_Hf5 zenon_H38. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.12/22.21 apply (zenon_L297_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.12/22.21 apply (zenon_L69_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.21 apply (zenon_L1526_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.21 apply (zenon_L186_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.21 apply (zenon_L439_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.21 apply (zenon_L900_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.21 exact (zenon_H159 zenon_H10c). % 22.12/22.21 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.21 apply (zenon_L1527_); trivial. % 22.12/22.21 apply (zenon_L1521_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.21 apply (zenon_L186_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.21 apply (zenon_L900_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.21 exact (zenon_H159 zenon_H10c). % 22.12/22.21 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.21 apply (zenon_L436_); trivial. % 22.12/22.21 apply (zenon_L1521_); trivial. % 22.12/22.21 apply (zenon_L228_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.12/22.21 apply (zenon_L184_); trivial. % 22.12/22.21 apply (zenon_L1236_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.12/22.21 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.12/22.21 apply (zenon_L316_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.12/22.21 apply (zenon_L1524_); trivial. % 22.12/22.21 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.12/22.21 apply (zenon_L1529_); trivial. % 22.12/22.21 apply (zenon_L802_); trivial. % 22.12/22.21 apply (zenon_L663_); trivial. % 22.12/22.21 (* end of lemma zenon_L1530_ *) % 22.12/22.21 assert (zenon_L1531_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (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 (e0) (e2)) = (op (e2) (e2)))) -> (((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)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.12/22.22 do 0 intro. intros zenon_H201 zenon_Hf5 zenon_He2 zenon_H181 zenon_Hf0 zenon_H13f zenon_H111 zenon_H141 zenon_H183 zenon_H192 zenon_H24e zenon_H1d8 zenon_H288 zenon_H11a zenon_H12e zenon_H36 zenon_H231 zenon_H104 zenon_H18a zenon_Hbc zenon_He4 zenon_H23c zenon_H109 zenon_H2c zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H196 zenon_H16a zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_Hfa zenon_H1cd zenon_H54 zenon_H67 zenon_H1d5 zenon_H159 zenon_H24 zenon_H9f zenon_H1c7 zenon_H1a8 zenon_H100 zenon_H7d zenon_H34 zenon_H13b zenon_H1c2 zenon_H179 zenon_Hb6 zenon_H133 zenon_H14c zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H93 zenon_H77 zenon_H1cb. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.22 apply (zenon_L1530_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.22 apply (zenon_L124_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.22 apply (zenon_L255_); trivial. % 22.12/22.22 apply (zenon_L1159_); trivial. % 22.12/22.22 (* end of lemma zenon_L1531_ *) % 22.12/22.22 assert (zenon_L1532_ : ((op (e2) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (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 (e0) (e2)) = (op (e2) (e2)))) -> (((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)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.12/22.22 do 0 intro. intros zenon_H10d zenon_H171 zenon_He7 zenon_H177 zenon_H153 zenon_H201 zenon_Hf5 zenon_He2 zenon_H181 zenon_Hf0 zenon_H13f zenon_H111 zenon_H141 zenon_H183 zenon_H192 zenon_H24e zenon_H1d8 zenon_H288 zenon_H11a zenon_H12e zenon_H36 zenon_H231 zenon_H104 zenon_H18a zenon_Hbc zenon_He4 zenon_H23c zenon_H109 zenon_H2c zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H196 zenon_H16a zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_Hfa zenon_H1cd zenon_H54 zenon_H67 zenon_H1d5 zenon_H159 zenon_H24 zenon_H9f zenon_H1c7 zenon_H1a8 zenon_H100 zenon_H7d zenon_H34 zenon_H13b zenon_H1c2 zenon_H179 zenon_Hb6 zenon_H133 zenon_H14c zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.22 apply (zenon_L30_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.22 apply (zenon_L289_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.22 apply (zenon_L1495_); trivial. % 22.12/22.22 apply (zenon_L1531_); trivial. % 22.12/22.22 (* end of lemma zenon_L1532_ *) % 22.12/22.22 assert (zenon_L1533_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (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) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (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 (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 (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (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 (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)) = (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 (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (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 (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.12/22.22 do 0 intro. intros zenon_H3d zenon_H38 zenon_H196 zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_H18d zenon_H179 zenon_H1c2 zenon_H13b zenon_H34 zenon_H7d zenon_H100 zenon_H1a8 zenon_H24 zenon_H159 zenon_H1d5 zenon_H67 zenon_H54 zenon_H1cd zenon_Hfa zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H16a zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H2c zenon_H109 zenon_H23c zenon_He4 zenon_Hbc zenon_H18a zenon_H104 zenon_H231 zenon_H36 zenon_H12e zenon_H11a zenon_H288 zenon_H1d8 zenon_H24e zenon_H192 zenon_H183 zenon_H141 zenon_H111 zenon_H13f zenon_Hf0 zenon_H181 zenon_He2 zenon_Hf5 zenon_H201 zenon_H177 zenon_He7 zenon_H171 zenon_H133 zenon_H48 zenon_H121 zenon_H33 zenon_H9f zenon_Hb6 zenon_Hc4 zenon_H1c7. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.22 apply (zenon_L55_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.22 exact (zenon_H159 zenon_H10c). % 22.12/22.22 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.22 apply (zenon_L359_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.22 apply (zenon_L152_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.22 apply (zenon_L1532_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.22 apply (zenon_L124_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.22 apply (zenon_L255_); trivial. % 22.12/22.22 apply (zenon_L1414_); trivial. % 22.12/22.22 apply (zenon_L1162_); trivial. % 22.12/22.22 exact (zenon_H1c7 zenon_Hac). % 22.12/22.22 (* end of lemma zenon_L1533_ *) % 22.12/22.22 assert (zenon_L1534_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.22 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H195 zenon_Ha5 zenon_Ha0 zenon_H6f zenon_Hdb zenon_H54 zenon_Hb6 zenon_H117 zenon_H196 zenon_H38. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.22 apply (zenon_L359_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.22 apply (zenon_L929_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.22 apply (zenon_L1466_); trivial. % 22.12/22.22 apply (zenon_L1162_); trivial. % 22.12/22.22 (* end of lemma zenon_L1534_ *) % 22.12/22.22 assert (zenon_L1535_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 22.12/22.22 do 0 intro. intros zenon_H1a2 zenon_H186 zenon_H191 zenon_H12e zenon_H48 zenon_H3f zenon_H11a zenon_H288 zenon_Hf5 zenon_Ha5 zenon_Hb6 zenon_Ha0 zenon_H1c3 zenon_Ha9 zenon_H196 zenon_H1b4 zenon_H1fb zenon_H25e zenon_H77 zenon_H13a zenon_H1d8 zenon_H153 zenon_H181 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H192 zenon_H68 zenon_H183 zenon_H6f zenon_H10d. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.12/22.22 apply (zenon_L95_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.12/22.22 apply (zenon_L308_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.12/22.22 exact (zenon_H191 zenon_H110). % 22.12/22.22 apply (zenon_L1519_); trivial. % 22.12/22.22 (* end of lemma zenon_L1535_ *) % 22.12/22.22 assert (zenon_L1536_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.12/22.22 do 0 intro. intros zenon_H201 zenon_H10d zenon_H6f zenon_H183 zenon_H68 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H181 zenon_H1d8 zenon_H13a zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha9 zenon_H1c3 zenon_Ha0 zenon_Ha5 zenon_Hf5 zenon_H288 zenon_H11a zenon_H3f zenon_H191 zenon_H186 zenon_H1a2 zenon_H171 zenon_He7 zenon_H163 zenon_H192 zenon_H3d zenon_H34 zenon_H12e zenon_H48 zenon_H14c zenon_H121 zenon_H33 zenon_H9f zenon_H1c7 zenon_Hb6 zenon_Hc4. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.22 apply (zenon_L1535_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.22 apply (zenon_L965_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.22 apply (zenon_L255_); trivial. % 22.12/22.22 apply (zenon_L1414_); trivial. % 22.12/22.22 (* end of lemma zenon_L1536_ *) % 22.12/22.22 assert (zenon_L1537_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> (~((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))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.22 do 0 intro. intros zenon_H141 zenon_H54 zenon_Hc4 zenon_Hb6 zenon_H1c7 zenon_H9f zenon_H33 zenon_H121 zenon_H48 zenon_H12e zenon_H34 zenon_H3d zenon_H192 zenon_H163 zenon_He7 zenon_H171 zenon_H1a2 zenon_H186 zenon_H191 zenon_H3f zenon_H11a zenon_H288 zenon_Hf5 zenon_Ha5 zenon_Ha0 zenon_H1c3 zenon_Ha9 zenon_H1b4 zenon_H1fb zenon_H25e zenon_H77 zenon_H13a zenon_H1d8 zenon_H181 zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H68 zenon_H183 zenon_H6f zenon_H10d zenon_H201 zenon_H196 zenon_H38. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.22 apply (zenon_L217_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.22 apply (zenon_L152_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.22 apply (zenon_L1536_); trivial. % 22.12/22.22 apply (zenon_L1162_); trivial. % 22.12/22.22 (* end of lemma zenon_L1537_ *) % 22.12/22.22 assert (zenon_L1538_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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 (e3) (e3)) = (e2))) -> False). % 22.12/22.22 do 0 intro. intros zenon_H183 zenon_H68 zenon_H11f zenon_He7 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H163 zenon_H4d zenon_H192 zenon_H3d zenon_H48 zenon_H12e zenon_H181. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.12/22.22 apply (zenon_L291_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.12/22.22 apply (zenon_L964_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.12/22.22 apply (zenon_L853_); trivial. % 22.12/22.22 exact (zenon_H181 zenon_H17c). % 22.12/22.22 (* end of lemma zenon_L1538_ *) % 22.12/22.22 assert (zenon_L1539_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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 (e3) (e3)) = (e2))) -> False). % 22.12/22.22 do 0 intro. intros zenon_H183 zenon_H68 zenon_He7 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H163 zenon_H4d zenon_H192 zenon_H3d zenon_H48 zenon_H12e zenon_H181. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.12/22.22 apply (zenon_L456_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.12/22.22 apply (zenon_L146_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.12/22.22 apply (zenon_L285_); trivial. % 22.12/22.22 apply (zenon_L1538_); trivial. % 22.12/22.22 (* end of lemma zenon_L1539_ *) % 22.12/22.22 assert (zenon_L1540_ : ((op (e0) (e1)) = (e1)) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((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 (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (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 (e0) (e3)) = (op (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (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))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((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 (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (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))))) -> (~((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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((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) (e2)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.12/22.22 do 0 intro. intros zenon_H3d zenon_Hcb zenon_H11a zenon_H173 zenon_Hf0 zenon_Hfa zenon_H104 zenon_H109 zenon_H18a zenon_H283 zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H156 zenon_H158 zenon_H13e zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H1b7 zenon_H1c6 zenon_H25b zenon_Hf5 zenon_H27e zenon_H189 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H162 zenon_H19a zenon_H12e zenon_H7d zenon_H24e zenon_H1f1 zenon_H186 zenon_H23c zenon_H26a zenon_H111 zenon_H2c zenon_Hc2 zenon_H1d5 zenon_H36 zenon_Hca zenon_H38 zenon_H196 zenon_H201 zenon_He4 zenon_H1d8 zenon_H234 zenon_H55 zenon_H1a8 zenon_H1cd zenon_H231 zenon_H192 zenon_Hbc zenon_H191 zenon_H140 zenon_H1cf zenon_Ha0 zenon_H1a2 zenon_H190 zenon_H141 zenon_H5d zenon_H139 zenon_H13a zenon_H82 zenon_H133 zenon_H16a zenon_H5c zenon_H195 zenon_Hb6 zenon_H13f zenon_H1c2 zenon_H121 zenon_H33 zenon_H9f zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_H1c3 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1cb zenon_H54 zenon_H1c7. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.22 apply (zenon_L55_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.22 apply (zenon_L1332_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.22 apply (zenon_L1432_); trivial. % 22.12/22.22 exact (zenon_H1c7 zenon_Hac). % 22.12/22.22 (* end of lemma zenon_L1540_ *) % 22.12/22.22 assert (zenon_L1541_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (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 (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.12/22.22 do 0 intro. intros zenon_H13a zenon_H11a zenon_H3d zenon_H2c zenon_H111 zenon_H1f1 zenon_H23c zenon_He4 zenon_H26a zenon_H1d8 zenon_H82 zenon_H1b7 zenon_H1cd zenon_H7d zenon_H24e zenon_H104 zenon_H162 zenon_H19a zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H1c6 zenon_H25b zenon_Hf5 zenon_H27e zenon_H189 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H18a zenon_H191 zenon_Hf0 zenon_H38 zenon_H196 zenon_H201 zenon_H1a2 zenon_H54 zenon_H141 zenon_H186 zenon_H16a zenon_H5c zenon_H195 zenon_H117 zenon_Hb6 zenon_Ha0 zenon_Ha5 zenon_H13f zenon_H1c2 zenon_H121 zenon_H33 zenon_H9f zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_H1c3 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1cb zenon_H109 zenon_H1c7. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.22 apply (zenon_L55_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.22 apply (zenon_L1306_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.22 apply (zenon_L1435_); trivial. % 22.12/22.22 exact (zenon_H1c7 zenon_Hac). % 22.12/22.22 (* end of lemma zenon_L1541_ *) % 22.12/22.22 assert (zenon_L1542_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (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 (e1) (e2)) = (op (e1) (e3)))) -> (((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)) = (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) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.12/22.22 do 0 intro. intros zenon_H24 zenon_Hca zenon_H36 zenon_H1d5 zenon_Hc2 zenon_H12e zenon_Hfa zenon_Hcb zenon_H11a zenon_H2c zenon_H111 zenon_H1f1 zenon_H23c zenon_H26a zenon_H1b7 zenon_H7d zenon_H24e zenon_H104 zenon_H162 zenon_H19a zenon_H283 zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H1c6 zenon_H25b zenon_Hf5 zenon_H27e zenon_H189 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H18a zenon_Hf0 zenon_H201 zenon_H186 zenon_H16a zenon_H195 zenon_H117 zenon_H13f zenon_H1c2 zenon_H121 zenon_H33 zenon_H9f zenon_H18d zenon_H109 zenon_H1c7 zenon_H34 zenon_He4 zenon_H1d8 zenon_H234 zenon_H55 zenon_H1a8 zenon_H1cd zenon_H231 zenon_H192 zenon_H183 zenon_Hbc zenon_H191 zenon_H140 zenon_H196 zenon_H1cf zenon_H1a3 zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H1a2 zenon_H190 zenon_H1c3 zenon_H68 zenon_Hc4 zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H141 zenon_H77 zenon_H5d zenon_H139 zenon_H13a zenon_H82 zenon_H38 zenon_H48. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.22 apply (zenon_L253_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.22 apply (zenon_L1149_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.22 apply (zenon_L17_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.22 apply (zenon_L900_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.22 apply (zenon_L1306_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.22 apply (zenon_L1540_); trivial. % 22.12/22.22 apply (zenon_L1541_); trivial. % 22.12/22.22 apply (zenon_L456_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.22 apply (zenon_L1431_); trivial. % 22.12/22.22 apply (zenon_L246_); trivial. % 22.12/22.22 (* end of lemma zenon_L1542_ *) % 22.12/22.22 assert (zenon_L1543_ : ((op (e0) (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)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (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) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((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)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.22 do 0 intro. intros zenon_H9f zenon_H24 zenon_H13a zenon_H33 zenon_H121 zenon_H3d zenon_H140 zenon_H26d zenon_H36 zenon_H131 zenon_H191 zenon_H162 zenon_H19a zenon_H120 zenon_H24e zenon_H7d zenon_H1cd zenon_H1b7 zenon_H82 zenon_H1d8 zenon_Hc2 zenon_Hcb zenon_H104 zenon_H231 zenon_H1ef zenon_H6f zenon_H1f1 zenon_H13f zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H26a zenon_H190 zenon_Hf5 zenon_H25b zenon_H5d zenon_H2c zenon_H139 zenon_Hbc zenon_H283 zenon_H163 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H266 zenon_H13c zenon_H1c6 zenon_H189 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1fb zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_Hfa zenon_H1d5 zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H183 zenon_H18a zenon_H1c2 zenon_H68 zenon_H1c3 zenon_Hef zenon_H11a zenon_H27e zenon_H5c zenon_H195 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_Ha0 zenon_H16a zenon_H186 zenon_H1a2 zenon_H1a3 zenon_H201 zenon_H196 zenon_H38. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.22 apply (zenon_L900_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.22 apply (zenon_L1330_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.22 apply (zenon_L1244_); trivial. % 22.12/22.22 apply (zenon_L1421_); trivial. % 22.12/22.22 (* end of lemma zenon_L1543_ *) % 22.12/22.22 assert (zenon_L1544_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((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 (e1) (e3)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.22 do 0 intro. intros zenon_H141 zenon_H54 zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H1c3 zenon_H1a3 zenon_H183 zenon_H68 zenon_H34 zenon_Ha9 zenon_H9f zenon_H33 zenon_H121 zenon_H1c2 zenon_H13f zenon_Ha5 zenon_Ha0 zenon_Hb6 zenon_H117 zenon_H195 zenon_H5c zenon_H10d zenon_H16a zenon_H72 zenon_H1a2 zenon_H186 zenon_H201 zenon_H196 zenon_H38. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.22 apply (zenon_L217_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.22 apply (zenon_L152_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.22 apply (zenon_L1417_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.22 apply (zenon_L59_); trivial. % 22.12/22.22 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.22 apply (zenon_L255_); trivial. % 22.12/22.22 apply (zenon_L1434_); trivial. % 22.12/22.22 apply (zenon_L1162_); trivial. % 22.12/22.22 (* end of lemma zenon_L1544_ *) % 22.12/22.22 assert (zenon_L1545_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((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) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.12/22.23 do 0 intro. intros zenon_H1a8 zenon_H3d zenon_H156 zenon_H72 zenon_H38 zenon_H196 zenon_H13f zenon_Ha5 zenon_Ha0 zenon_Hb6 zenon_H117 zenon_H77 zenon_H48 zenon_H195 zenon_H5c zenon_H68 zenon_H141 zenon_Ha9 zenon_Hac. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.23 apply (zenon_L214_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.23 apply (zenon_L100_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.23 apply (zenon_L1397_); trivial. % 22.12/22.23 apply (zenon_L371_); trivial. % 22.12/22.23 (* end of lemma zenon_L1545_ *) % 22.12/22.23 assert (zenon_L1546_ : ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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 (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((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)) = (op (e2) (e1)))) -> (((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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (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)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e0)) = (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> ((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)) = (op (e2) (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 (e1) (e2)) = (op (e1) (e3)))) -> (((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) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (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) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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 (e3) (e0)) = (op (e3) (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)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (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) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.12/22.23 do 0 intro. intros zenon_H67 zenon_H234 zenon_H192 zenon_H27e zenon_Hf0 zenon_He7 zenon_H1d5 zenon_Hfa zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H1fb zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H189 zenon_H266 zenon_H55 zenon_H13e zenon_H158 zenon_H173 zenon_H1ec zenon_H73 zenon_H163 zenon_H283 zenon_Ha9 zenon_H141 zenon_H68 zenon_H195 zenon_H48 zenon_H117 zenon_Hb6 zenon_Ha0 zenon_H13f zenon_H196 zenon_H38 zenon_H156 zenon_H3d zenon_H1a8 zenon_H54 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H1c3 zenon_H1a3 zenon_H183 zenon_H34 zenon_H9f zenon_H33 zenon_H121 zenon_H1c2 zenon_H16a zenon_H1a2 zenon_H186 zenon_H201 zenon_H140 zenon_H26d zenon_H36 zenon_H131 zenon_H191 zenon_H162 zenon_H19a zenon_H120 zenon_H24e zenon_H7d zenon_H1cd zenon_H1b7 zenon_H11a zenon_H82 zenon_H1d8 zenon_Hc2 zenon_Hcb zenon_H104 zenon_H231 zenon_H18a zenon_H1ef zenon_H13a zenon_H6f zenon_H109 zenon_H1f1 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H26a zenon_H190 zenon_Hf5 zenon_H25b zenon_H5d zenon_H2c zenon_H139 zenon_Hbc zenon_H1c6 zenon_H24 zenon_H13c zenon_H5c zenon_H77. % 22.12/22.23 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.23 apply (zenon_L214_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.23 apply (zenon_L1543_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.23 apply (zenon_L1312_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.23 apply (zenon_L900_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.23 apply (zenon_L1330_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.23 apply (zenon_L55_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.23 apply (zenon_L1330_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.23 apply (zenon_L1432_); trivial. % 22.12/22.23 apply (zenon_L371_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.23 apply (zenon_L55_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.23 apply (zenon_L1329_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.23 apply (zenon_L1435_); trivial. % 22.12/22.23 apply (zenon_L371_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.23 apply (zenon_L1543_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.23 apply (zenon_L900_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.23 apply (zenon_L1328_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.23 apply (zenon_L436_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.23 apply (zenon_L55_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.23 apply (zenon_L1328_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.23 apply (zenon_L1544_); trivial. % 22.12/22.23 apply (zenon_L1545_); trivial. % 22.12/22.23 apply (zenon_L206_); trivial. % 22.12/22.23 (* end of lemma zenon_L1546_ *) % 22.12/22.23 assert (zenon_L1547_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (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) (e3)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.12/22.23 do 0 intro. intros zenon_Hca zenon_Hc2 zenon_Hbc zenon_H34 zenon_H104 zenon_H105 zenon_H1bb zenon_H1cb zenon_H162 zenon_H231 zenon_Hcb zenon_Hac. % 22.12/22.23 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.12/22.23 exact (zenon_H1c7 zenon_Hac). % 22.12/22.23 apply (zenon_L1321_); trivial. % 22.12/22.23 (* end of lemma zenon_L1547_ *) % 22.12/22.23 assert (zenon_L1548_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (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)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e2)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((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)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (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 (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.12/22.23 do 0 intro. intros zenon_H13a zenon_H1a3 zenon_H11a zenon_H33 zenon_H121 zenon_H3d zenon_H140 zenon_H26d zenon_H36 zenon_H131 zenon_H1c3 zenon_H19a zenon_H120 zenon_H24e zenon_H7d zenon_H1b7 zenon_H82 zenon_H1d8 zenon_H183 zenon_H18a zenon_H1ef zenon_H6f zenon_H109 zenon_H1f1 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H26a zenon_H190 zenon_Hf5 zenon_H25b zenon_H5d zenon_H2c zenon_H139 zenon_H1c2 zenon_H283 zenon_H163 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H266 zenon_H13c zenon_H1c6 zenon_H27e zenon_H189 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1fb zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_Hf0 zenon_Hfa zenon_H1d5 zenon_H201 zenon_H1cd zenon_H191 zenon_H186 zenon_H1a2 zenon_Hf3 zenon_Hcb zenon_H231 zenon_H162 zenon_H104 zenon_H34 zenon_Hbc zenon_Hc2 zenon_Hca zenon_H16a zenon_H196 zenon_H13f zenon_H5c zenon_H68 zenon_H141 zenon_H195 zenon_Ha5 zenon_Ha9 zenon_Hdd zenon_Ha0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.23 apply (zenon_L55_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.23 apply (zenon_L1330_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.23 apply (zenon_L152_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.23 apply (zenon_L1439_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.23 apply (zenon_L117_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.23 apply (zenon_L1547_); trivial. % 22.12/22.23 apply (zenon_L1441_); trivial. % 22.12/22.23 (* end of lemma zenon_L1548_ *) % 22.12/22.23 assert (zenon_L1549_ : ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (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) (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) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((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 (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((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 (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e1)) = (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 (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((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)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.23 do 0 intro. intros zenon_H9f zenon_H24 zenon_H67 zenon_H141 zenon_H13f zenon_Hca zenon_Hc2 zenon_Hbc zenon_H34 zenon_H104 zenon_H162 zenon_H231 zenon_Hcb zenon_Hf3 zenon_H191 zenon_H1cd zenon_H1d5 zenon_Hfa zenon_Hf0 zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H1fb zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H189 zenon_H1c6 zenon_H13c zenon_H266 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H163 zenon_H283 zenon_H139 zenon_H2c zenon_H5d zenon_H25b zenon_Hf5 zenon_H190 zenon_H26a zenon_H1cf zenon_He4 zenon_H23c zenon_H4e zenon_H1f1 zenon_H109 zenon_H6f zenon_H1ef zenon_H1d8 zenon_H82 zenon_H1b7 zenon_H7d zenon_H24e zenon_H120 zenon_H19a zenon_H131 zenon_H36 zenon_H26d zenon_H140 zenon_H3d zenon_H121 zenon_H33 zenon_H13a zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H183 zenon_H18a zenon_H1c2 zenon_H68 zenon_H1c3 zenon_Hef zenon_H11a zenon_H27e zenon_H5c zenon_H195 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_Ha0 zenon_H16a zenon_H186 zenon_H1a2 zenon_H1a3 zenon_H201 zenon_H196 zenon_H38. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.23 apply (zenon_L900_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.23 apply (zenon_L1317_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.23 apply (zenon_L162_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.23 apply (zenon_L217_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.23 apply (zenon_L1548_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.23 apply (zenon_L1420_); trivial. % 22.12/22.23 apply (zenon_L1162_); trivial. % 22.12/22.23 (* end of lemma zenon_L1549_ *) % 22.12/22.23 assert (zenon_L1550_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.12/22.23 do 0 intro. intros zenon_H16a zenon_H5c zenon_H195 zenon_H14c zenon_Hb6 zenon_H13f zenon_Ha9 zenon_H10d zenon_H66 zenon_H111 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H106 zenon_H1cb. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.23 apply (zenon_L256_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.23 apply (zenon_L289_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.23 apply (zenon_L258_); trivial. % 22.12/22.23 apply (zenon_L1159_); trivial. % 22.12/22.23 (* end of lemma zenon_L1550_ *) % 22.12/22.23 assert (zenon_L1551_ : ((op (e0) (e0)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (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 (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)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e2)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((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)) = (op (e0) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (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) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 22.12/22.23 do 0 intro. intros zenon_H9f zenon_He7 zenon_H177 zenon_H234 zenon_H12e zenon_H192 zenon_H125 zenon_Hb2 zenon_H1fe zenon_H1a8 zenon_H212 zenon_H164 zenon_H13b zenon_H288 zenon_H179 zenon_H68 zenon_H13a zenon_H11a zenon_H33 zenon_H121 zenon_H3d zenon_H140 zenon_H26d zenon_H36 zenon_H131 zenon_H117 zenon_H191 zenon_H1c3 zenon_H19a zenon_H24e zenon_H7d zenon_H1cd zenon_H1b7 zenon_H82 zenon_H1d8 zenon_Hcb zenon_H183 zenon_H18a zenon_H1ef zenon_H6f zenon_H109 zenon_H1f1 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H26a zenon_H190 zenon_H1a2 zenon_Hf5 zenon_H25b zenon_H5d zenon_H2c zenon_H139 zenon_H1c2 zenon_H283 zenon_H163 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H266 zenon_H13c zenon_H1c6 zenon_H27e zenon_H189 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1fb zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_Hf0 zenon_Hfa zenon_H1d5 zenon_H38 zenon_H196 zenon_H201 zenon_H186 zenon_H231 zenon_H1a3 zenon_H162 zenon_H120 zenon_H104 zenon_H34 zenon_Hbc zenon_Hc2 zenon_H16a zenon_H5c zenon_H195 zenon_Hb6 zenon_H13f zenon_H66 zenon_H111 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1cb zenon_Ha0 zenon_H54 zenon_H141 zenon_Ha9. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.23 apply (zenon_L214_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.23 apply (zenon_L1392_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.23 apply (zenon_L55_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.23 apply (zenon_L1391_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.23 apply (zenon_L289_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.23 apply (zenon_L359_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.23 apply (zenon_L929_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.23 apply (zenon_L1423_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.23 apply (zenon_L379_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.23 apply (zenon_L255_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.12/22.23 apply (zenon_L151_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.12/22.23 apply (zenon_L1550_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.12/22.23 exact (zenon_H191 zenon_H110). % 22.12/22.23 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.12/22.23 apply (zenon_L1255_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.12/22.23 apply (zenon_L493_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.12/22.23 apply (zenon_L367_); trivial. % 22.12/22.23 apply (zenon_L1157_); trivial. % 22.12/22.23 apply (zenon_L1162_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.23 apply (zenon_L55_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.23 apply (zenon_L1330_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.23 apply (zenon_L217_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.23 apply (zenon_L152_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.23 apply (zenon_L94_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.23 apply (zenon_L138_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.23 apply (zenon_L477_); trivial. % 22.12/22.23 apply (zenon_L1550_); trivial. % 22.12/22.23 apply (zenon_L1162_); trivial. % 22.12/22.23 apply (zenon_L371_); trivial. % 22.12/22.23 (* end of lemma zenon_L1551_ *) % 22.12/22.23 assert (zenon_L1552_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.12/22.23 do 0 intro. intros zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hf3 zenon_H14c zenon_Ha0 zenon_Hac zenon_H1cd. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.12/22.23 apply (zenon_L193_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.12/22.23 apply (zenon_L162_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.12/22.23 apply (zenon_L278_); trivial. % 22.12/22.23 apply (zenon_L360_); trivial. % 22.12/22.23 (* end of lemma zenon_L1552_ *) % 22.12/22.23 assert (zenon_L1553_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.23 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_H6d zenon_H68 zenon_H1cd zenon_Hac zenon_Ha0 zenon_Hf3 zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H196 zenon_H38. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.23 apply (zenon_L359_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.23 apply (zenon_L54_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.23 apply (zenon_L1552_); trivial. % 22.12/22.23 apply (zenon_L1162_); trivial. % 22.12/22.23 (* end of lemma zenon_L1553_ *) % 22.12/22.23 assert (zenon_L1554_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (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)) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.12/22.23 do 0 intro. intros zenon_H1a8 zenon_H3d zenon_H1bb zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H16a zenon_H1cb zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_Hf0 zenon_H54 zenon_H38 zenon_H196 zenon_H1a2 zenon_H66 zenon_Hf3 zenon_Ha0 zenon_H1cd zenon_H68 zenon_H109 zenon_H34 zenon_H141 zenon_Ha9 zenon_Hac. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.23 apply (zenon_L214_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.23 apply (zenon_L1392_); trivial. % 22.12/22.23 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.23 apply (zenon_L1553_); trivial. % 22.12/22.23 apply (zenon_L371_); trivial. % 22.12/22.23 (* end of lemma zenon_L1554_ *) % 22.12/22.24 assert (zenon_L1555_ : ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (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)) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 22.12/22.24 do 0 intro. intros zenon_H9f zenon_H24 zenon_Hc4 zenon_H11a zenon_H33 zenon_H121 zenon_H140 zenon_H36 zenon_H191 zenon_H162 zenon_H120 zenon_H24e zenon_H7d zenon_H82 zenon_H1d8 zenon_Hc2 zenon_Hcb zenon_H183 zenon_H104 zenon_H231 zenon_H18a zenon_H1f1 zenon_H13f zenon_H201 zenon_H23c zenon_He4 zenon_H26a zenon_H2c zenon_Hbc zenon_H1c2 zenon_Hfa zenon_H1d5 zenon_H1a3 zenon_H1a8 zenon_H3d zenon_H1bb zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H16a zenon_H1cb zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_Hf0 zenon_H54 zenon_H38 zenon_H196 zenon_H1a2 zenon_H66 zenon_Hf3 zenon_Ha0 zenon_H1cd zenon_H68 zenon_H109 zenon_H34 zenon_H141 zenon_Ha9. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.24 apply (zenon_L900_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.24 apply (zenon_L1330_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.24 apply (zenon_L162_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.24 apply (zenon_L55_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.24 apply (zenon_L1330_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.24 apply (zenon_L1173_); trivial. % 22.12/22.24 apply (zenon_L1554_); trivial. % 22.12/22.24 (* end of lemma zenon_L1555_ *) % 22.12/22.24 assert (zenon_L1556_ : (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (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 (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e1) (e1)) = (op (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 (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((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)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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 (e0) (e3)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (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) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 22.12/22.24 do 0 intro. intros zenon_H177 zenon_H125 zenon_Hb2 zenon_H1fe zenon_H212 zenon_H164 zenon_H288 zenon_H179 zenon_H13b zenon_H139 zenon_H68 zenon_Ha9 zenon_Ha0 zenon_H38 zenon_H13a zenon_H77 zenon_H5d zenon_H5c zenon_Hca zenon_H36 zenon_H1d5 zenon_Hc2 zenon_H234 zenon_H12e zenon_H192 zenon_H231 zenon_Hbc zenon_H140 zenon_Hfa zenon_Hcb zenon_H1a8 zenon_H48 zenon_H201 zenon_H18a zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H162 zenon_H19a zenon_H1c2 zenon_H104 zenon_H24e zenon_H1cd zenon_H34 zenon_H7d zenon_H183 zenon_H191 zenon_Hf0 zenon_H186 zenon_H82 zenon_H23c zenon_H13f zenon_H109 zenon_H1f1 zenon_He4 zenon_H26a zenon_H111 zenon_H1d8 zenon_H2c zenon_H141 zenon_H33 zenon_H11a zenon_Hc4 zenon_H121 zenon_H24 zenon_H9f zenon_Hb6. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.12/22.24 apply (zenon_L1542_); trivial. % 22.12/22.24 apply (zenon_L414_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.24 apply (zenon_L253_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.24 apply (zenon_L253_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.24 apply (zenon_L17_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.12/22.24 apply (zenon_L297_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.12/22.24 apply (zenon_L1546_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.24 apply (zenon_L214_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.24 apply (zenon_L1549_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.24 apply (zenon_L1312_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.24 apply (zenon_L900_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.24 apply (zenon_L1330_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.24 apply (zenon_L162_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.24 apply (zenon_L55_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.24 apply (zenon_L1330_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.24 apply (zenon_L1438_); trivial. % 22.12/22.24 apply (zenon_L371_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.24 apply (zenon_L1549_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.24 apply (zenon_L62_); trivial. % 22.12/22.24 apply (zenon_L206_); trivial. % 22.12/22.24 apply (zenon_L663_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.24 apply (zenon_L214_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.12/22.24 apply (zenon_L297_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.12/22.24 apply (zenon_L1551_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.12/22.24 apply (zenon_L1555_); trivial. % 22.12/22.24 apply (zenon_L157_); trivial. % 22.12/22.24 apply (zenon_L165_); trivial. % 22.12/22.24 apply (zenon_L456_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.24 apply (zenon_L1431_); trivial. % 22.12/22.24 apply (zenon_L192_); trivial. % 22.12/22.24 apply (zenon_L434_); trivial. % 22.12/22.24 (* end of lemma zenon_L1556_ *) % 22.12/22.24 assert (zenon_L1557_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((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). % 22.12/22.24 do 0 intro. intros zenon_H15d zenon_H9f zenon_H192 zenon_H7f zenon_H7d zenon_H2d zenon_H48 zenon_H61 zenon_H5d zenon_H139 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H77 zenon_H38 zenon_H68 zenon_H82 zenon_H5c zenon_Hf5. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.24 apply (zenon_L253_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.24 apply (zenon_L146_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.24 apply (zenon_L1341_); trivial. % 22.12/22.24 apply (zenon_L192_); trivial. % 22.12/22.24 (* end of lemma zenon_L1557_ *) % 22.12/22.24 assert (zenon_L1558_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.12/22.24 do 0 intro. intros zenon_H121 zenon_Ha0 zenon_H38 zenon_H153 zenon_Hb6 zenon_H6e zenon_Ha9 zenon_H33 zenon_H13a zenon_H11a zenon_H10c zenon_H1a3 zenon_Hc4. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 22.12/22.24 apply (zenon_L1408_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 22.12/22.24 apply (zenon_L79_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 22.12/22.24 exact (zenon_H1a3 zenon_Hbb). % 22.12/22.24 exact (zenon_Hc4 zenon_Hc3). % 22.12/22.24 (* end of lemma zenon_L1558_ *) % 22.12/22.24 assert (zenon_L1559_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.24 do 0 intro. intros zenon_H141 zenon_H7f zenon_H7d zenon_H48 zenon_H61 zenon_H5d zenon_H139 zenon_H13a zenon_H77 zenon_H82 zenon_H6d zenon_H68 zenon_H1a3 zenon_Ha0 zenon_H72 zenon_Ha9 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H196 zenon_H38. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.24 apply (zenon_L1341_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.24 apply (zenon_L54_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.24 apply (zenon_L1170_); trivial. % 22.12/22.24 apply (zenon_L1162_); trivial. % 22.12/22.24 (* end of lemma zenon_L1559_ *) % 22.12/22.24 assert (zenon_L1560_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (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 (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.12/22.24 do 0 intro. intros zenon_H1a8 zenon_Hc4 zenon_H10c zenon_H11a zenon_H33 zenon_H121 zenon_H156 zenon_H38 zenon_H196 zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Ha9 zenon_H72 zenon_Ha0 zenon_H1a3 zenon_H68 zenon_H82 zenon_H13a zenon_H139 zenon_H5d zenon_H61 zenon_H48 zenon_H7d zenon_H141 zenon_H7f zenon_H77. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.24 apply (zenon_L1558_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.24 apply (zenon_L100_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.24 apply (zenon_L1559_); trivial. % 22.12/22.24 apply (zenon_L169_); trivial. % 22.12/22.24 (* end of lemma zenon_L1560_ *) % 22.12/22.24 assert (zenon_L1561_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (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 (e2) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (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))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.12/22.24 do 0 intro. intros zenon_H1c6 zenon_Ha9 zenon_H6e zenon_H173 zenon_H121 zenon_H33 zenon_H11a zenon_Hc4 zenon_H13a zenon_H38 zenon_H196 zenon_Ha0 zenon_H1a3 zenon_H54 zenon_H48 zenon_H141 zenon_H1a2 zenon_Hb6 zenon_H153 zenon_H186 zenon_Ha5 zenon_H191 zenon_H1cd. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.24 apply (zenon_L110_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.24 apply (zenon_L1252_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.24 apply (zenon_L1433_); trivial. % 22.12/22.24 apply (zenon_L1439_); trivial. % 22.12/22.24 (* end of lemma zenon_L1561_ *) % 22.12/22.24 assert (zenon_L1562_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (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 (e2) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (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))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.12/22.24 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H77 zenon_H7f zenon_H7d zenon_H61 zenon_H5d zenon_H139 zenon_H82 zenon_H68 zenon_H156 zenon_H1a8 zenon_H72 zenon_H1c6 zenon_Ha9 zenon_H6e zenon_H173 zenon_H121 zenon_H33 zenon_H11a zenon_Hc4 zenon_H13a zenon_H38 zenon_H196 zenon_Ha0 zenon_H1a3 zenon_H54 zenon_H48 zenon_H141 zenon_H1a2 zenon_Hb6 zenon_H153 zenon_H186 zenon_H191 zenon_H1cd. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.24 apply (zenon_L900_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.24 apply (zenon_L1560_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.24 apply (zenon_L436_); trivial. % 22.12/22.24 apply (zenon_L1561_); trivial. % 22.12/22.24 (* end of lemma zenon_L1562_ *) % 22.12/22.24 assert (zenon_L1563_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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 (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (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)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.12/22.24 do 0 intro. intros zenon_H1cd zenon_H191 zenon_H186 zenon_H54 zenon_Hc4 zenon_H11a zenon_H33 zenon_H121 zenon_H173 zenon_H1c6 zenon_H1a8 zenon_H24 zenon_H9f zenon_H13c zenon_H156 zenon_H38 zenon_H196 zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Ha9 zenon_H72 zenon_Ha0 zenon_H1a3 zenon_H68 zenon_H82 zenon_H13a zenon_H139 zenon_H5d zenon_H61 zenon_H48 zenon_H7d zenon_H141 zenon_H7f zenon_H77. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.24 apply (zenon_L1562_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.24 apply (zenon_L100_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.24 apply (zenon_L1559_); trivial. % 22.12/22.24 apply (zenon_L169_); trivial. % 22.12/22.24 (* end of lemma zenon_L1563_ *) % 22.12/22.24 assert (zenon_L1564_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((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)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.12/22.24 do 0 intro. intros zenon_H183 zenon_H1c2 zenon_H5c zenon_H77 zenon_H38 zenon_H68 zenon_H1c3 zenon_Hef zenon_H11a zenon_H8a zenon_H104 zenon_H121 zenon_H33 zenon_H9f zenon_H7d zenon_H18a zenon_H7f zenon_H231 zenon_Hbc zenon_H1cd zenon_H1cb zenon_H212 zenon_H1a3 zenon_Hc4. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.12/22.24 apply (zenon_L1259_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.12/22.24 apply (zenon_L119_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.12/22.24 apply (zenon_L231_); trivial. % 22.12/22.24 apply (zenon_L1167_); trivial. % 22.12/22.24 (* end of lemma zenon_L1564_ *) % 22.12/22.24 assert (zenon_L1565_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.12/22.24 do 0 intro. intros zenon_H15d zenon_H9f zenon_H192 zenon_H7f zenon_H7d zenon_H1a8 zenon_H1c7 zenon_H13a zenon_H33 zenon_H121 zenon_H34 zenon_Hbc zenon_H191 zenon_H140 zenon_H38 zenon_H196 zenon_H1cf zenon_H1a3 zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H1a2 zenon_H190 zenon_H1c3 zenon_H68 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H48 zenon_H141 zenon_H77 zenon_H5d zenon_H139 zenon_H82 zenon_H5c zenon_Hf5. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.24 apply (zenon_L253_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.24 apply (zenon_L146_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.24 apply (zenon_L1284_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.24 apply (zenon_L17_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.24 apply (zenon_L1409_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.24 apply (zenon_L1316_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.24 apply (zenon_L1428_); trivial. % 22.12/22.24 apply (zenon_L169_); trivial. % 22.12/22.24 apply (zenon_L31_); trivial. % 22.12/22.24 apply (zenon_L192_); trivial. % 22.12/22.24 (* end of lemma zenon_L1565_ *) % 22.12/22.24 assert (zenon_L1566_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((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))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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 (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((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) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.12/22.24 do 0 intro. intros zenon_Hfa zenon_H25 zenon_H1cd zenon_H191 zenon_H186 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H141 zenon_H48 zenon_H54 zenon_H1a3 zenon_Ha0 zenon_H196 zenon_H38 zenon_H13a zenon_Hc4 zenon_H11a zenon_H33 zenon_H121 zenon_H173 zenon_H6e zenon_Ha9 zenon_H1c6 zenon_H1a8 zenon_H156 zenon_H68 zenon_H82 zenon_H139 zenon_H5d zenon_H61 zenon_H7d zenon_H7f zenon_H24 zenon_H9f zenon_H13c zenon_H5c zenon_H77. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.24 apply (zenon_L171_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.24 apply (zenon_L226_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.24 apply (zenon_L1562_); trivial. % 22.12/22.24 apply (zenon_L206_); trivial. % 22.12/22.24 (* end of lemma zenon_L1566_ *) % 22.12/22.24 assert (zenon_L1567_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((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) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (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 (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((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)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (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) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> False). % 22.12/22.24 do 0 intro. intros zenon_Hca zenon_H2c zenon_H18d zenon_H1fe zenon_H140 zenon_H190 zenon_H1cf zenon_Hb6 zenon_H192 zenon_H7f zenon_H1fb zenon_Hfa zenon_H13c zenon_H173 zenon_H186 zenon_H1cd zenon_H1c6 zenon_H121 zenon_Hc4 zenon_H11a zenon_H33 zenon_H156 zenon_H1a8 zenon_H24 zenon_H15d zenon_H5c zenon_Hf5 zenon_H61 zenon_H5d zenon_H7d zenon_H82 zenon_Hf0 zenon_H1a2 zenon_H191 zenon_H196 zenon_H141 zenon_H13f zenon_H195 zenon_H111 zenon_H183 zenon_H212 zenon_Hbc zenon_H1cb zenon_H231 zenon_H104 zenon_H1c2 zenon_H18a zenon_H1c3 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H16a zenon_He2 zenon_H48 zenon_H77 zenon_H13a zenon_H38 zenon_Ha9 zenon_H68 zenon_H139 zenon_H9f zenon_Ha0 zenon_Hcb. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.12/22.24 apply (zenon_L41_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.24 apply (zenon_L253_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.24 apply (zenon_L146_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.24 apply (zenon_L1284_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.24 apply (zenon_L25_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.12/22.24 apply (zenon_L316_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.24 apply (zenon_L171_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.24 apply (zenon_L1557_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.24 apply (zenon_L929_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.24 apply (zenon_L1150_); trivial. % 22.12/22.24 apply (zenon_L1162_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.24 apply (zenon_L1563_); trivial. % 22.12/22.24 apply (zenon_L206_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.24 apply (zenon_L171_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.24 apply (zenon_L150_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.24 apply (zenon_L61_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.24 apply (zenon_L1564_); trivial. % 22.12/22.24 apply (zenon_L413_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.24 apply (zenon_L1563_); trivial. % 22.12/22.24 apply (zenon_L206_); trivial. % 22.12/22.24 apply (zenon_L57_); trivial. % 22.12/22.24 apply (zenon_L31_); trivial. % 22.12/22.24 apply (zenon_L246_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.12/22.24 apply (zenon_L1557_); trivial. % 22.12/22.24 apply (zenon_L1565_); trivial. % 22.12/22.24 apply (zenon_L414_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.12/22.24 apply (zenon_L41_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.24 apply (zenon_L253_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.24 apply (zenon_L146_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.24 apply (zenon_L1284_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.24 apply (zenon_L17_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.24 apply (zenon_L171_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.24 apply (zenon_L180_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.24 apply (zenon_L1428_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.24 apply (zenon_L1564_); trivial. % 22.12/22.24 apply (zenon_L555_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.24 apply (zenon_L1563_); trivial. % 22.12/22.24 apply (zenon_L206_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.24 apply (zenon_L1566_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.24 apply (zenon_L94_); trivial. % 22.12/22.24 apply (zenon_L165_); trivial. % 22.12/22.24 apply (zenon_L31_); trivial. % 22.12/22.24 apply (zenon_L192_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.12/22.24 apply (zenon_L1557_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.24 apply (zenon_L253_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.24 apply (zenon_L146_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.24 apply (zenon_L1284_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.24 apply (zenon_L18_); trivial. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.24 apply (zenon_L1429_); trivial. % 22.12/22.24 apply (zenon_L456_); trivial. % 22.12/22.24 apply (zenon_L246_); trivial. % 22.12/22.24 apply (zenon_L414_); trivial. % 22.12/22.24 (* end of lemma zenon_L1567_ *) % 22.12/22.24 assert (zenon_L1568_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.24 do 0 intro. intros zenon_H23b zenon_H9f zenon_H38. % 22.12/22.24 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.12/22.24 exact (zenon_H238 zenon_H38). % 22.12/22.24 exact (zenon_Ha4 zenon_H9f). % 22.12/22.24 (* end of lemma zenon_L1568_ *) % 22.12/22.24 assert (zenon_L1569_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.24 do 0 intro. intros zenon_H63 zenon_H9f zenon_H38. % 22.12/22.24 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.12/22.24 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.12/22.24 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.12/22.25 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.12/22.25 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.12/22.25 apply (zenon_L1568_); trivial. % 22.12/22.25 (* end of lemma zenon_L1569_ *) % 22.12/22.25 assert (zenon_L1570_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (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 (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H16a zenon_H2d zenon_H13f zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H117 zenon_H141 zenon_H195 zenon_Ha5 zenon_H5c zenon_H196 zenon_H27e zenon_H11a zenon_Hef zenon_H1c3 zenon_H68 zenon_H1c2 zenon_H18a zenon_H183 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H106 zenon_H1cb. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.25 apply (zenon_L27_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.25 apply (zenon_L1397_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.25 apply (zenon_L1418_); trivial. % 22.12/22.25 apply (zenon_L1159_); trivial. % 22.12/22.25 (* end of lemma zenon_L1570_ *) % 22.12/22.25 assert (zenon_L1571_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (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 (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (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 (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H201 zenon_H1d4 zenon_H1cd zenon_Hac zenon_H191 zenon_H186 zenon_H67 zenon_H1a2 zenon_H16a zenon_H2d zenon_H13f zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H117 zenon_H141 zenon_H195 zenon_Ha5 zenon_H5c zenon_H196 zenon_H27e zenon_H11a zenon_Hef zenon_H1c3 zenon_H68 zenon_H1c2 zenon_H18a zenon_H183 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.25 apply (zenon_L1439_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.25 exact (zenon_H1d4 zenon_H4d). % 22.12/22.25 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.25 apply (zenon_L1440_); trivial. % 22.12/22.25 apply (zenon_L1570_); trivial. % 22.12/22.25 (* end of lemma zenon_L1571_ *) % 22.12/22.25 assert (zenon_L1572_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (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 (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (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 (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H201 zenon_H1d4 zenon_H1cd zenon_Hac zenon_H191 zenon_H186 zenon_H67 zenon_H1a2 zenon_H16a zenon_H196 zenon_H13f zenon_H5c zenon_H68 zenon_H141 zenon_H195 zenon_Ha5 zenon_Ha9 zenon_Hdd zenon_Ha0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.25 apply (zenon_L1439_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.25 exact (zenon_H1d4 zenon_H4d). % 22.12/22.25 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.25 apply (zenon_L1440_); trivial. % 22.12/22.25 apply (zenon_L1441_); trivial. % 22.12/22.25 (* end of lemma zenon_L1572_ *) % 22.12/22.25 assert (zenon_L1573_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (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 (e1) (e3)) = (e3)) -> ((op (e1) (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 (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H201 zenon_H1d8 zenon_H3d zenon_H1d4 zenon_H16a zenon_Ha0 zenon_H14c zenon_Ha9 zenon_H54 zenon_Hb6 zenon_H117 zenon_H195 zenon_Ha5 zenon_H5c zenon_H196 zenon_H27e zenon_H11a zenon_Hef zenon_H1c3 zenon_H68 zenon_H1c2 zenon_H18a zenon_H183 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.25 apply (zenon_L738_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.25 exact (zenon_H1d4 zenon_H4d). % 22.12/22.25 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.25 apply (zenon_L255_); trivial. % 22.12/22.25 apply (zenon_L1419_); trivial. % 22.12/22.25 (* end of lemma zenon_L1573_ *) % 22.12/22.25 assert (zenon_L1574_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (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) (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)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.12/22.25 do 0 intro. intros zenon_H1a8 zenon_H3d zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H183 zenon_H18a zenon_H1c2 zenon_H1c3 zenon_H11a zenon_H27e zenon_H16a zenon_H1a2 zenon_H67 zenon_H186 zenon_H191 zenon_H1cd zenon_H1d4 zenon_H201 zenon_H5c zenon_H195 zenon_H117 zenon_Ha0 zenon_H2d zenon_Hb6 zenon_Ha5 zenon_H77 zenon_H141 zenon_H48 zenon_H68 zenon_H196 zenon_H38 zenon_H13f zenon_Ha9 zenon_Hac. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.25 apply (zenon_L214_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.25 apply (zenon_L1571_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.25 apply (zenon_L1395_); trivial. % 22.12/22.25 apply (zenon_L371_); trivial. % 22.12/22.25 (* end of lemma zenon_L1574_ *) % 22.12/22.25 assert (zenon_L1575_ : (((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 (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H183 zenon_H77 zenon_H7e zenon_Hac zenon_Ha9 zenon_H66 zenon_H177 zenon_H93 zenon_H129. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.12/22.25 apply (zenon_L71_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.12/22.25 apply (zenon_L371_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.12/22.25 apply (zenon_L122_); trivial. % 22.12/22.25 apply (zenon_L126_); trivial. % 22.12/22.25 (* end of lemma zenon_L1575_ *) % 22.12/22.25 assert (zenon_L1576_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H16a zenon_H68 zenon_H195 zenon_Ha5 zenon_H105 zenon_Hb6 zenon_H2d zenon_Ha0 zenon_H117 zenon_H111 zenon_H183 zenon_H77 zenon_H7e zenon_Hac zenon_Ha9 zenon_H66 zenon_H177 zenon_H129. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.25 apply (zenon_L27_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.25 apply (zenon_L1394_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.25 apply (zenon_L258_); trivial. % 22.12/22.25 apply (zenon_L1575_); trivial. % 22.12/22.25 (* end of lemma zenon_L1576_ *) % 22.12/22.25 assert (zenon_L1577_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (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 (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H201 zenon_H1d4 zenon_H177 zenon_H66 zenon_Hac zenon_H7e zenon_H111 zenon_H16a zenon_H2d zenon_H13f zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H117 zenon_H141 zenon_H195 zenon_Ha5 zenon_H5c zenon_H196 zenon_H27e zenon_H11a zenon_Hef zenon_H1c3 zenon_H68 zenon_H1c2 zenon_H18a zenon_H183 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.25 apply (zenon_L94_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.25 exact (zenon_H1d4 zenon_H4d). % 22.12/22.25 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.25 apply (zenon_L1576_); trivial. % 22.12/22.25 apply (zenon_L1570_); trivial. % 22.12/22.25 (* end of lemma zenon_L1577_ *) % 22.12/22.25 assert (zenon_L1578_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (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) (e0)) = (e0)) -> (((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)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((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 (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H15d zenon_H9f zenon_H68 zenon_H38 zenon_H1a8 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H183 zenon_H18a zenon_H1c2 zenon_H1c3 zenon_H11a zenon_H27e zenon_H2d zenon_H16a zenon_H111 zenon_H177 zenon_H1d4 zenon_H201 zenon_H196 zenon_H13f zenon_Ha0 zenon_H117 zenon_H77 zenon_H48 zenon_H195 zenon_H141 zenon_Ha9 zenon_H139 zenon_H7a zenon_H13a zenon_H82 zenon_H1cd zenon_Hac zenon_H191 zenon_Ha5 zenon_H186 zenon_Hb6 zenon_H1a2 zenon_H5c zenon_Hf5. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.25 apply (zenon_L253_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.25 apply (zenon_L1149_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.25 exact (zenon_H7a zenon_H3c). % 22.12/22.25 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.25 apply (zenon_L217_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.25 apply (zenon_L1574_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.25 apply (zenon_L214_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.25 apply (zenon_L214_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.25 apply (zenon_L1577_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.25 apply (zenon_L1397_); trivial. % 22.12/22.25 apply (zenon_L371_); trivial. % 22.12/22.25 apply (zenon_L165_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.25 apply (zenon_L1439_); trivial. % 22.12/22.25 apply (zenon_L192_); trivial. % 22.12/22.25 (* end of lemma zenon_L1578_ *) % 22.12/22.25 assert (zenon_L1579_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 22.12/22.25 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H153 zenon_H40 zenon_Hdd zenon_H48 zenon_H7d zenon_H7e. % 22.12/22.25 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.12/22.25 apply (zenon_L738_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.12/22.25 exact (zenon_H40 zenon_H3f). % 22.12/22.25 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.12/22.25 apply (zenon_L111_); trivial. % 22.12/22.25 apply (zenon_L31_); trivial. % 22.12/22.25 (* end of lemma zenon_L1579_ *) % 22.12/22.25 assert (zenon_L1580_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (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 (e1) (e2)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (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 (e1) (e3)) = (e1)) -> False). % 22.12/22.25 do 0 intro. intros zenon_H1cb zenon_H77 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H117 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H141 zenon_H68 zenon_H13f zenon_H196 zenon_H16a zenon_H1d4 zenon_He4 zenon_H1d8 zenon_H40 zenon_H7d zenon_H7e zenon_H201 zenon_Hdd zenon_H48 zenon_H1cd zenon_Hac zenon_H191 zenon_Ha5 zenon_H186 zenon_H67 zenon_H1a2 zenon_H195 zenon_H5c. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.25 apply (zenon_L1579_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.25 exact (zenon_H1d4 zenon_H4d). % 22.12/22.25 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.25 apply (zenon_L1440_); trivial. % 22.12/22.25 apply (zenon_L1441_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.12/22.25 apply (zenon_L111_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.12/22.25 apply (zenon_L1440_); trivial. % 22.12/22.25 apply (zenon_L149_); trivial. % 22.12/22.25 (* end of lemma zenon_L1580_ *) % 22.12/22.25 assert (zenon_L1581_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H65 zenon_Hb6 zenon_H53 zenon_H14c zenon_Ha0 zenon_Ha5 zenon_H195. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.12/22.25 apply (zenon_L43_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.12/22.25 apply (zenon_L113_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.12/22.25 apply (zenon_L278_); trivial. % 22.12/22.25 apply (zenon_L172_); trivial. % 22.12/22.25 (* end of lemma zenon_L1581_ *) % 22.12/22.25 assert (zenon_L1582_ : (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((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)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (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) (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H68 zenon_H38 zenon_H125 zenon_H1d5 zenon_Ha9 zenon_H1a8 zenon_H156 zenon_H196 zenon_H13f zenon_Ha0 zenon_H117 zenon_H48 zenon_H195 zenon_H5c zenon_H141 zenon_H111 zenon_H177 zenon_H201 zenon_H1d8 zenon_H16a zenon_H27e zenon_H11a zenon_H1c3 zenon_H1c2 zenon_H18a zenon_H183 zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H25 zenon_Hfa zenon_H77 zenon_He4 zenon_H7d zenon_H15d zenon_H9f zenon_H139 zenon_H13a zenon_H82 zenon_Hf0 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H236 zenon_H189 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1cd zenon_Hac zenon_H191 zenon_Ha5 zenon_H186 zenon_Hb6 zenon_H1a2 zenon_Heb zenon_H7a zenon_H40 zenon_H1d4 zenon_Hf5. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.25 apply (zenon_L253_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.25 apply (zenon_L1149_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.25 exact (zenon_H7a zenon_H3c). % 22.12/22.25 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.25 apply (zenon_L171_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.25 apply (zenon_L1571_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.25 apply (zenon_L1572_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.25 apply (zenon_L1573_); trivial. % 22.12/22.25 apply (zenon_L1162_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.25 apply (zenon_L1545_); trivial. % 22.12/22.25 apply (zenon_L299_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.25 apply (zenon_L214_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.25 apply (zenon_L1398_); trivial. % 22.12/22.25 apply (zenon_L165_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.25 apply (zenon_L171_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.25 apply (zenon_L1578_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.25 apply (zenon_L1580_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.12/22.25 apply (zenon_L1573_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.25 apply (zenon_L738_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.25 exact (zenon_H1d4 zenon_H4d). % 22.12/22.25 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.25 apply (zenon_L1440_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.25 apply (zenon_L1581_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.25 apply (zenon_L56_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.25 apply (zenon_L1418_); trivial. % 22.12/22.25 apply (zenon_L1159_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.12/22.25 apply (zenon_L255_); trivial. % 22.12/22.25 apply (zenon_L149_); trivial. % 22.12/22.25 apply (zenon_L1162_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.25 apply (zenon_L1545_); trivial. % 22.12/22.25 apply (zenon_L299_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.25 apply (zenon_L214_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.12/22.25 apply (zenon_L252_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.12/22.25 apply (zenon_L171_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.25 apply (zenon_L171_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.25 apply (zenon_L1577_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.25 apply (zenon_L1459_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.12/22.25 apply (zenon_L1573_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.12/22.25 apply (zenon_L1581_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.12/22.25 apply (zenon_L255_); trivial. % 22.12/22.25 apply (zenon_L149_); trivial. % 22.12/22.25 apply (zenon_L1162_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.25 apply (zenon_L1545_); trivial. % 22.12/22.25 apply (zenon_L299_); trivial. % 22.12/22.25 apply (zenon_L71_); trivial. % 22.12/22.25 apply (zenon_L165_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.25 apply (zenon_L1439_); trivial. % 22.12/22.25 apply (zenon_L461_); trivial. % 22.12/22.25 (* end of lemma zenon_L1582_ *) % 22.12/22.25 assert (zenon_L1583_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((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)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.25 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H183 zenon_H18a zenon_H1c2 zenon_H68 zenon_H1c3 zenon_Hef zenon_H11a zenon_H27e zenon_H5c zenon_Ha5 zenon_H195 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_Ha0 zenon_H16a zenon_H1d4 zenon_H3d zenon_H1d8 zenon_H201 zenon_H196 zenon_H38. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.25 apply (zenon_L359_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.25 apply (zenon_L929_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.25 apply (zenon_L1573_); trivial. % 22.12/22.25 apply (zenon_L1162_); trivial. % 22.12/22.25 (* end of lemma zenon_L1583_ *) % 22.12/22.25 assert (zenon_L1584_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (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)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.12/22.25 do 0 intro. intros zenon_H1a8 zenon_H201 zenon_H1d8 zenon_H3d zenon_H1d4 zenon_H16a zenon_H5c zenon_H27e zenon_H11a zenon_H1c3 zenon_H1c2 zenon_H18a zenon_H183 zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1cb zenon_Hf0 zenon_He7 zenon_H109 zenon_H34 zenon_H38 zenon_H196 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha0 zenon_Ha5 zenon_H195 zenon_H68 zenon_H48 zenon_H141 zenon_Ha9 zenon_Hac. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.25 apply (zenon_L214_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.25 apply (zenon_L1583_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.25 apply (zenon_L1393_); trivial. % 22.12/22.25 apply (zenon_L371_); trivial. % 22.12/22.25 (* end of lemma zenon_L1584_ *) % 22.12/22.25 assert (zenon_L1585_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H16a zenon_H5c zenon_H111 zenon_H153 zenon_H13f zenon_H68 zenon_H195 zenon_Ha5 zenon_Ha9 zenon_Hdd zenon_Ha0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H7f zenon_H1b7. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.25 apply (zenon_L150_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.25 apply (zenon_L54_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.25 apply (zenon_L173_); trivial. % 22.12/22.25 apply (zenon_L1276_); trivial. % 22.12/22.25 (* end of lemma zenon_L1585_ *) % 22.12/22.25 assert (zenon_L1586_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.25 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H40 zenon_H55 zenon_H141 zenon_H1b7 zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H117 zenon_H54 zenon_Ha9 zenon_Ha5 zenon_H195 zenon_H68 zenon_H13f zenon_H111 zenon_H5c zenon_H16a zenon_H1cd zenon_Hb1 zenon_Ha0 zenon_Hf3 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H196 zenon_H38. % 22.12/22.25 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.12/22.25 apply (zenon_L738_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.12/22.25 exact (zenon_H40 zenon_H3f). % 22.12/22.25 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.12/22.25 apply (zenon_L15_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.25 apply (zenon_L217_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.25 apply (zenon_L1585_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.25 apply (zenon_L362_); trivial. % 22.12/22.25 apply (zenon_L1162_); trivial. % 22.12/22.25 (* end of lemma zenon_L1586_ *) % 22.12/22.25 assert (zenon_L1587_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> False). % 22.12/22.25 do 0 intro. intros zenon_H117 zenon_H54 zenon_Ha9 zenon_H6d zenon_Hb6 zenon_H105 zenon_Ha0 zenon_H115. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.12/22.25 apply (zenon_L151_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.12/22.25 apply (zenon_L289_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.12/22.25 apply (zenon_L400_); trivial. % 22.12/22.25 apply (zenon_L77_); trivial. % 22.12/22.25 (* end of lemma zenon_L1587_ *) % 22.12/22.25 assert (zenon_L1588_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e3))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_H68 zenon_H195 zenon_Ha5 zenon_H117 zenon_H54 zenon_Ha9 zenon_H6d zenon_Hb6 zenon_H105 zenon_Ha0. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.25 apply (zenon_L359_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.25 apply (zenon_L54_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.25 apply (zenon_L1090_); trivial. % 22.12/22.25 apply (zenon_L1587_); trivial. % 22.12/22.25 (* end of lemma zenon_L1588_ *) % 22.12/22.25 assert (zenon_L1589_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.12/22.25 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_H1d4 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_H93 zenon_Hc4. % 22.12/22.25 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.12/22.25 exact (zenon_H7a zenon_H3c). % 22.12/22.25 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.12/22.25 exact (zenon_H40 zenon_H3f). % 22.12/22.25 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.12/22.25 exact (zenon_H1d4 zenon_H4d). % 22.12/22.25 apply (zenon_L413_); trivial. % 22.12/22.25 (* end of lemma zenon_L1589_ *) % 22.12/22.25 assert (zenon_L1590_ : (((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 (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (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 (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.12/22.25 do 0 intro. intros zenon_H201 zenon_H1a2 zenon_Hf3 zenon_Hb1 zenon_H1cd zenon_H111 zenon_H1b7 zenon_H55 zenon_H1d8 zenon_He4 zenon_H1d4 zenon_H40 zenon_H7a zenon_Heb zenon_H34 zenon_H109 zenon_H67 zenon_H2c zenon_H16a zenon_H196 zenon_H13f zenon_H5c zenon_H68 zenon_H141 zenon_H195 zenon_Ha5 zenon_Ha9 zenon_Hdd zenon_Ha0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.25 apply (zenon_L1586_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.25 exact (zenon_H1d4 zenon_H4d). % 22.12/22.25 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.25 apply (zenon_L180_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.25 apply (zenon_L1588_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.25 apply (zenon_L173_); trivial. % 22.12/22.25 apply (zenon_L1589_); trivial. % 22.12/22.25 apply (zenon_L1441_); trivial. % 22.12/22.25 (* end of lemma zenon_L1590_ *) % 22.12/22.25 assert (zenon_L1591_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((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 (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((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)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.25 do 0 intro. intros zenon_H141 zenon_H13f zenon_H2c zenon_H67 zenon_H109 zenon_H34 zenon_Heb zenon_H7a zenon_H40 zenon_He4 zenon_H1d8 zenon_H55 zenon_H1b7 zenon_H111 zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H183 zenon_H18a zenon_H1c2 zenon_H68 zenon_H1c3 zenon_Hef zenon_H11a zenon_H27e zenon_H5c zenon_Ha5 zenon_H195 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_Ha0 zenon_H16a zenon_H1d4 zenon_H1a2 zenon_Hf3 zenon_Hb1 zenon_H1cd zenon_H201 zenon_H196 zenon_H38. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.25 apply (zenon_L217_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.25 apply (zenon_L1590_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.25 apply (zenon_L362_); trivial. % 22.12/22.25 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.25 exact (zenon_H1d4 zenon_H4d). % 22.12/22.25 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.25 apply (zenon_L255_); trivial. % 22.12/22.25 apply (zenon_L1419_); trivial. % 22.12/22.25 apply (zenon_L1162_); trivial. % 22.12/22.25 (* end of lemma zenon_L1591_ *) % 22.12/22.26 assert (zenon_L1592_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (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 (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((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) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((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)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (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 (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (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)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H169 zenon_Ha0 zenon_H9f zenon_H139 zenon_H68 zenon_Ha9 zenon_H38 zenon_H13a zenon_H77 zenon_H7a zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H1b7 zenon_H1c6 zenon_H25b zenon_Hf5 zenon_H189 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_Hf0 zenon_H1d8 zenon_H1a2 zenon_Hac zenon_H1cd zenon_H191 zenon_Ha5 zenon_H186 zenon_H16a zenon_H1bb zenon_Hc4 zenon_H20f zenon_H1b4 zenon_H1cb zenon_H18d zenon_H1c3 zenon_H18a zenon_H1c2 zenon_H11a zenon_H27e zenon_H129 zenon_H183 zenon_H13f zenon_H5c zenon_H48 zenon_H117 zenon_H195 zenon_H196 zenon_H141 zenon_H201 zenon_H1a8 zenon_H156 zenon_Hfa zenon_H1d5 zenon_H125 zenon_H40 zenon_H7d zenon_He4 zenon_H82 zenon_H177 zenon_Hb6 zenon_H179 zenon_H109 zenon_H2c zenon_Hb1 zenon_H13b zenon_H1fe. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.12/22.26 apply (zenon_L41_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.12/22.26 apply (zenon_L1582_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.12/22.26 apply (zenon_L1578_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.26 apply (zenon_L253_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.26 apply (zenon_L1149_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.26 exact (zenon_H7a zenon_H3c). % 22.12/22.26 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.12/22.26 apply (zenon_L297_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.12/22.26 apply (zenon_L1584_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.26 apply (zenon_L214_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.26 apply (zenon_L1591_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.26 apply (zenon_L1393_); trivial. % 22.12/22.26 apply (zenon_L371_); trivial. % 22.12/22.26 apply (zenon_L157_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.26 apply (zenon_L214_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.26 apply (zenon_L1398_); trivial. % 22.12/22.26 apply (zenon_L165_); trivial. % 22.12/22.26 apply (zenon_L456_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.26 apply (zenon_L1439_); trivial. % 22.12/22.26 apply (zenon_L461_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.26 apply (zenon_L253_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.26 apply (zenon_L214_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.26 exact (zenon_H1b3 zenon_Hef). % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.26 apply (zenon_L1397_); trivial. % 22.12/22.26 apply (zenon_L371_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.26 apply (zenon_L1439_); trivial. % 22.12/22.26 apply (zenon_L192_); trivial. % 22.12/22.26 (* end of lemma zenon_L1592_ *) % 22.12/22.26 assert (zenon_L1593_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (((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 (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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) (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 (e0) (e3)) = (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))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (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 (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 (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (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))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (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) (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H3e zenon_H1fe zenon_H13b zenon_Hb1 zenon_H2c zenon_H109 zenon_H179 zenon_Hb6 zenon_H177 zenon_H82 zenon_He4 zenon_H7d zenon_H125 zenon_H1d5 zenon_Hfa zenon_H156 zenon_H1a8 zenon_H201 zenon_H141 zenon_H196 zenon_H195 zenon_H117 zenon_H48 zenon_H5c zenon_H13f zenon_H183 zenon_H129 zenon_H27e zenon_H11a zenon_H1c2 zenon_H18a zenon_H1c3 zenon_H18d zenon_H1cb zenon_H1b4 zenon_H20f zenon_Hc4 zenon_H1bb zenon_H16a zenon_H186 zenon_Ha5 zenon_H191 zenon_H1cd zenon_Hac zenon_H1a2 zenon_H1d8 zenon_Hf0 zenon_H111 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H189 zenon_Hf5 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H7a zenon_H77 zenon_H13a zenon_H38 zenon_Ha9 zenon_H68 zenon_H139 zenon_H9f zenon_Ha0 zenon_H169. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.12/22.26 apply (zenon_L1592_); trivial. % 22.12/22.26 apply (zenon_L1592_); trivial. % 22.12/22.26 (* end of lemma zenon_L1593_ *) % 22.12/22.26 assert (zenon_L1594_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.12/22.26 do 0 intro. intros zenon_He2 zenon_H1fb zenon_H38 zenon_He3 zenon_H2d zenon_H55 zenon_Ha0 zenon_Hac. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.12/22.26 apply (zenon_L316_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.12/22.26 exact (zenon_He3 zenon_He7). % 22.12/22.26 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.12/22.26 apply (zenon_L702_); trivial. % 22.12/22.26 apply (zenon_L107_); trivial. % 22.12/22.26 (* end of lemma zenon_L1594_ *) % 22.12/22.26 assert (zenon_L1595_ : (((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)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H139 zenon_H2c zenon_H65 zenon_H159 zenon_H173 zenon_H40 zenon_He3 zenon_H158 zenon_H153 zenon_H77 zenon_H38 zenon_H68. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.26 apply (zenon_L180_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.26 apply (zenon_L306_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.26 apply (zenon_L94_); trivial. % 22.12/22.26 apply (zenon_L165_); trivial. % 22.12/22.26 (* end of lemma zenon_L1595_ *) % 22.12/22.26 assert (zenon_L1596_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H183 zenon_H68 zenon_H34 zenon_Hac zenon_Ha9 zenon_H66 zenon_H177 zenon_H93 zenon_H129. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.12/22.26 apply (zenon_L291_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.12/22.26 apply (zenon_L371_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.12/22.26 apply (zenon_L122_); trivial. % 22.12/22.26 apply (zenon_L126_); trivial. % 22.12/22.26 (* end of lemma zenon_L1596_ *) % 22.12/22.26 assert (zenon_L1597_ : (((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) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((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)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H139 zenon_H77 zenon_H47 zenon_H159 zenon_H173 zenon_H40 zenon_He3 zenon_H158 zenon_H129 zenon_H177 zenon_Ha9 zenon_Hac zenon_H34 zenon_H68 zenon_H183 zenon_H93 zenon_H196. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.26 apply (zenon_L251_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.26 apply (zenon_L306_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.26 apply (zenon_L1596_); trivial. % 22.12/22.26 apply (zenon_L167_); trivial. % 22.12/22.26 (* end of lemma zenon_L1597_ *) % 22.12/22.26 assert (zenon_L1598_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H183 zenon_H68 zenon_Hac zenon_Ha9 zenon_Hc4 zenon_H1cb zenon_H106 zenon_H34 zenon_H18a zenon_H1bb zenon_H93 zenon_H129. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.12/22.26 apply (zenon_L291_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.12/22.26 apply (zenon_L371_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.12/22.26 apply (zenon_L847_); trivial. % 22.12/22.26 apply (zenon_L126_); trivial. % 22.12/22.26 (* end of lemma zenon_L1598_ *) % 22.12/22.26 assert (zenon_L1599_ : (((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 (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H12e zenon_H48 zenon_H3d zenon_H192 zenon_H129 zenon_H93 zenon_H1bb zenon_H18a zenon_H34 zenon_H1cb zenon_Hc4 zenon_Ha9 zenon_Hac zenon_H68 zenon_H183 zenon_H5c zenon_H20f. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.12/22.26 apply (zenon_L456_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.12/22.26 apply (zenon_L146_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.12/22.26 apply (zenon_L1598_); trivial. % 22.12/22.26 apply (zenon_L412_); trivial. % 22.12/22.26 (* end of lemma zenon_L1599_ *) % 22.12/22.26 assert (zenon_L1600_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.12/22.26 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H153 zenon_H40 zenon_Hdd zenon_H48 zenon_H11f zenon_H1b7. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.12/22.26 apply (zenon_L738_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.12/22.26 exact (zenon_H40 zenon_H3f). % 22.12/22.26 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.12/22.26 apply (zenon_L111_); trivial. % 22.12/22.26 apply (zenon_L780_); trivial. % 22.12/22.26 (* end of lemma zenon_L1600_ *) % 22.12/22.26 assert (zenon_L1601_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.12/22.26 do 0 intro. intros zenon_He2 zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha5 zenon_Hf5 zenon_Ha9 zenon_H9f zenon_H1c3 zenon_He3 zenon_H1b7 zenon_H11f zenon_H48 zenon_H40 zenon_H153 zenon_H1d8 zenon_He4 zenon_Ha0 zenon_Hac. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.12/22.26 apply (zenon_L1517_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.12/22.26 exact (zenon_He3 zenon_He7). % 22.12/22.26 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.12/22.26 apply (zenon_L1600_); trivial. % 22.12/22.26 apply (zenon_L107_); trivial. % 22.12/22.26 (* end of lemma zenon_L1601_ *) % 22.12/22.26 assert (zenon_L1602_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.12/22.26 do 0 intro. intros zenon_He2 zenon_Hdb zenon_He3 zenon_H1b7 zenon_H11f zenon_H48 zenon_H40 zenon_H153 zenon_H1d8 zenon_He4 zenon_Ha0 zenon_Hac. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.12/22.26 apply (zenon_L53_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.12/22.26 exact (zenon_He3 zenon_He7). % 22.12/22.26 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.12/22.26 apply (zenon_L1600_); trivial. % 22.12/22.26 apply (zenon_L107_); trivial. % 22.12/22.26 (* end of lemma zenon_L1602_ *) % 22.12/22.26 assert (zenon_L1603_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((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). % 22.12/22.26 do 0 intro. intros zenon_H13a zenon_H1c3 zenon_Ha9 zenon_Hf5 zenon_Ha5 zenon_H196 zenon_H1b4 zenon_H1fb zenon_H25e zenon_H77 zenon_Hac zenon_He4 zenon_H1d8 zenon_H40 zenon_H48 zenon_H11f zenon_H1b7 zenon_He3 zenon_He2 zenon_Hb6 zenon_H153 zenon_H38 zenon_Ha0. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.12/22.26 apply (zenon_L1601_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.12/22.26 apply (zenon_L1602_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.12/22.26 apply (zenon_L95_); trivial. % 22.12/22.26 apply (zenon_L156_); trivial. % 22.12/22.26 (* end of lemma zenon_L1603_ *) % 22.12/22.26 assert (zenon_L1604_ : (((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)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H1bb zenon_H18a zenon_H34 zenon_Ha0 zenon_H38 zenon_H153 zenon_Hb6 zenon_He2 zenon_He3 zenon_H1b7 zenon_H48 zenon_H40 zenon_H1d8 zenon_He4 zenon_Hac zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha5 zenon_Hf5 zenon_Ha9 zenon_H1c3 zenon_H13a zenon_H1cb zenon_H160 zenon_Hc4. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 22.12/22.26 apply (zenon_L416_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 22.12/22.26 apply (zenon_L1603_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 22.12/22.26 apply (zenon_L236_); trivial. % 22.12/22.26 exact (zenon_Hc4 zenon_Hc3). % 22.12/22.26 (* end of lemma zenon_L1604_ *) % 22.12/22.26 assert (zenon_L1605_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((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))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H183 zenon_H68 zenon_Hc4 zenon_H1cb zenon_H13a zenon_H1c3 zenon_Ha9 zenon_Hf5 zenon_Ha5 zenon_H196 zenon_H1b4 zenon_H1fb zenon_H25e zenon_H77 zenon_Hac zenon_He4 zenon_H1d8 zenon_H40 zenon_H48 zenon_H1b7 zenon_He3 zenon_He2 zenon_Hb6 zenon_H153 zenon_H38 zenon_Ha0 zenon_H34 zenon_H18a zenon_H1bb zenon_H93 zenon_H129. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.12/22.26 apply (zenon_L291_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.12/22.26 apply (zenon_L371_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.12/22.26 apply (zenon_L1604_); trivial. % 22.12/22.26 apply (zenon_L126_); trivial. % 22.12/22.26 (* end of lemma zenon_L1605_ *) % 22.12/22.26 assert (zenon_L1606_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (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)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((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)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H15d zenon_H177 zenon_H158 zenon_H173 zenon_H159 zenon_H139 zenon_H20f zenon_H5c zenon_H192 zenon_H12e zenon_H129 zenon_H93 zenon_H1bb zenon_H18a zenon_H34 zenon_Ha0 zenon_Hb6 zenon_He2 zenon_He3 zenon_H1b7 zenon_H40 zenon_H1d8 zenon_He4 zenon_Hac zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha5 zenon_Hf5 zenon_Ha9 zenon_H1c3 zenon_H13a zenon_H1cb zenon_Hc4 zenon_H68 zenon_H183 zenon_H38 zenon_H48. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.26 apply (zenon_L1597_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.26 apply (zenon_L1599_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.26 apply (zenon_L1605_); trivial. % 22.12/22.26 apply (zenon_L246_); trivial. % 22.12/22.26 (* end of lemma zenon_L1606_ *) % 22.12/22.26 assert (zenon_L1607_ : (((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) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (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)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((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)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.12/22.26 do 0 intro. intros zenon_Heb zenon_H54 zenon_H100 zenon_H1d4 zenon_H15d zenon_H177 zenon_H158 zenon_H173 zenon_H159 zenon_H139 zenon_H20f zenon_H192 zenon_H12e zenon_H129 zenon_H93 zenon_H1bb zenon_H18a zenon_H34 zenon_Ha0 zenon_Hb6 zenon_He2 zenon_He3 zenon_H1b7 zenon_H40 zenon_H1d8 zenon_He4 zenon_Hac zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha5 zenon_Hf5 zenon_Ha9 zenon_H1c3 zenon_H13a zenon_H1cb zenon_Hc4 zenon_H68 zenon_H183 zenon_H38 zenon_H48. % 22.12/22.26 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.12/22.26 apply (zenon_L69_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.12/22.26 exact (zenon_H40 zenon_H3f). % 22.12/22.26 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.12/22.26 exact (zenon_H1d4 zenon_H4d). % 22.12/22.26 apply (zenon_L1606_); trivial. % 22.12/22.26 (* end of lemma zenon_L1607_ *) % 22.12/22.26 assert (zenon_L1608_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e0)) -> (((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 (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (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)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((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) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H16a zenon_H153 zenon_H2c zenon_H195 zenon_Hdd zenon_H117 zenon_Heb zenon_H54 zenon_H100 zenon_H1d4 zenon_H15d zenon_H177 zenon_H158 zenon_H173 zenon_H159 zenon_H139 zenon_H20f zenon_H192 zenon_H12e zenon_H129 zenon_H1bb zenon_H18a zenon_H34 zenon_Ha0 zenon_Hb6 zenon_He2 zenon_He3 zenon_H1b7 zenon_H40 zenon_H1d8 zenon_He4 zenon_Hac zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha5 zenon_Hf5 zenon_Ha9 zenon_H1c3 zenon_H13a zenon_H1cb zenon_Hc4 zenon_H68 zenon_H183 zenon_H38 zenon_H48. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.26 apply (zenon_L1595_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.26 apply (zenon_L54_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.26 apply (zenon_L173_); trivial. % 22.12/22.26 apply (zenon_L1607_); trivial. % 22.12/22.26 (* end of lemma zenon_L1608_ *) % 22.12/22.26 assert (zenon_L1609_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e3))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H141 zenon_H48 zenon_H68 zenon_H195 zenon_Ha5 zenon_H117 zenon_H54 zenon_Ha9 zenon_H6d zenon_Hb6 zenon_H105 zenon_Ha0. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.26 apply (zenon_L217_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.26 apply (zenon_L54_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.26 apply (zenon_L1090_); trivial. % 22.12/22.26 apply (zenon_L1587_); trivial. % 22.12/22.26 (* end of lemma zenon_L1609_ *) % 22.12/22.26 assert (zenon_L1610_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H158 zenon_He3 zenon_H40 zenon_Hf0 zenon_H6d zenon_H159. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_He7 | zenon_intro zenon_H15a ]. % 22.12/22.26 exact (zenon_He3 zenon_He7). % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H3f | zenon_intro zenon_H15b ]. % 22.12/22.26 exact (zenon_H40 zenon_H3f). % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hef | zenon_intro zenon_H10c ]. % 22.12/22.26 apply (zenon_L61_); trivial. % 22.12/22.26 exact (zenon_H159 zenon_H10c). % 22.12/22.26 (* end of lemma zenon_L1610_ *) % 22.12/22.26 assert (zenon_L1611_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (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)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H16a zenon_H159 zenon_Hf0 zenon_H40 zenon_He3 zenon_H158 zenon_H195 zenon_Ha5 zenon_Ha9 zenon_Hdd zenon_Ha0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H106 zenon_H1cb. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.26 apply (zenon_L30_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.26 apply (zenon_L1610_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.26 apply (zenon_L173_); trivial. % 22.12/22.26 apply (zenon_L1159_); trivial. % 22.12/22.26 (* end of lemma zenon_L1611_ *) % 22.12/22.26 assert (zenon_L1612_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (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)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H201 zenon_H2c zenon_H183 zenon_H68 zenon_H13a zenon_H1c3 zenon_Hf5 zenon_H196 zenon_H1fb zenon_H25e zenon_Hac zenon_He4 zenon_H1d8 zenon_H1b7 zenon_He2 zenon_H34 zenon_H18a zenon_H12e zenon_H192 zenon_H139 zenon_H173 zenon_H177 zenon_H15d zenon_H1d4 zenon_H100 zenon_Heb zenon_H141 zenon_H16a zenon_H159 zenon_Hf0 zenon_H40 zenon_He3 zenon_H158 zenon_H195 zenon_Ha5 zenon_Ha9 zenon_Hdd zenon_Ha0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.26 apply (zenon_L1608_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.26 exact (zenon_H1d4 zenon_H4d). % 22.12/22.26 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.26 apply (zenon_L30_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.26 apply (zenon_L1609_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.26 apply (zenon_L173_); trivial. % 22.12/22.26 apply (zenon_L1607_); trivial. % 22.12/22.26 apply (zenon_L1611_); trivial. % 22.12/22.26 (* end of lemma zenon_L1612_ *) % 22.12/22.26 assert (zenon_L1613_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (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)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((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))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.12/22.26 do 0 intro. intros zenon_H1cb zenon_H77 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_Ha5 zenon_H195 zenon_H158 zenon_He3 zenon_H40 zenon_Hf0 zenon_H159 zenon_H16a zenon_H141 zenon_Heb zenon_H100 zenon_H1d4 zenon_H15d zenon_H177 zenon_H173 zenon_H139 zenon_H192 zenon_H12e zenon_H18a zenon_H34 zenon_He2 zenon_H1b7 zenon_H1d8 zenon_He4 zenon_H25e zenon_H1fb zenon_H196 zenon_Hf5 zenon_H1c3 zenon_H13a zenon_H68 zenon_H183 zenon_H2c zenon_H201 zenon_Ha0 zenon_Hac. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.12/22.26 apply (zenon_L316_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.12/22.26 exact (zenon_He3 zenon_He7). % 22.12/22.26 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.12/22.26 apply (zenon_L1612_); trivial. % 22.12/22.26 apply (zenon_L107_); trivial. % 22.12/22.26 (* end of lemma zenon_L1613_ *) % 22.12/22.26 assert (zenon_L1614_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> False). % 22.12/22.26 do 0 intro. intros zenon_H15c zenon_He3 zenon_H40 zenon_H1b3 zenon_H158 zenon_H5c. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.12/22.26 exact (zenon_Hec zenon_H5c). % 22.12/22.26 apply (zenon_L1113_); trivial. % 22.12/22.26 (* end of lemma zenon_L1614_ *) % 22.12/22.26 assert (zenon_L1615_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((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 (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H169 zenon_H5c zenon_H1fe zenon_Hb6 zenon_H5d zenon_H16a zenon_H100 zenon_H15d zenon_H1d8 zenon_H1b7 zenon_He4 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H1c3 zenon_H13a zenon_H48 zenon_H192 zenon_H18a zenon_H1cb zenon_Hc4 zenon_H1bb zenon_H20f zenon_H12e zenon_H183 zenon_H129 zenon_H177 zenon_H196 zenon_Heb zenon_Ha9 zenon_H195 zenon_H117 zenon_H2c zenon_H173 zenon_H77 zenon_H68 zenon_H139 zenon_H141 zenon_H18d zenon_Hf0 zenon_H201 zenon_H82 zenon_H1fb zenon_H38 zenon_H55 zenon_Hac zenon_He2 zenon_H4e zenon_H158 zenon_H156 zenon_H40 zenon_He3 zenon_H186 zenon_Ha5 zenon_H1ec zenon_H9f zenon_Ha0 zenon_H15c. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.12/22.26 exact (zenon_Hec zenon_H5c). % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.12/22.26 apply (zenon_L41_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.12/22.26 apply (zenon_L309_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.12/22.26 apply (zenon_L1594_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.26 apply (zenon_L253_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.26 apply (zenon_L17_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.26 apply (zenon_L1613_); trivial. % 22.12/22.26 apply (zenon_L456_); trivial. % 22.12/22.26 apply (zenon_L1614_); trivial. % 22.12/22.26 (* end of lemma zenon_L1615_ *) % 22.12/22.26 assert (zenon_L1616_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (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 (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 22.12/22.26 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H153 zenon_H234 zenon_H1bb zenon_H129 zenon_H5c zenon_H20f zenon_H38 zenon_H1b4 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H8b zenon_H7b zenon_H7d zenon_H7e. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.12/22.26 apply (zenon_L738_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.12/22.26 apply (zenon_L484_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.12/22.26 apply (zenon_L1357_); trivial. % 22.12/22.26 apply (zenon_L31_); trivial. % 22.12/22.26 (* end of lemma zenon_L1616_ *) % 22.12/22.26 assert (zenon_L1617_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (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 (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H82 zenon_H1ba zenon_He4 zenon_H1d8 zenon_H153 zenon_H234 zenon_H1bb zenon_H129 zenon_H5c zenon_H20f zenon_H38 zenon_H1b4 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H8b zenon_H7b zenon_H7d. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.26 apply (zenon_L1284_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.26 apply (zenon_L17_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.26 apply (zenon_L1356_); trivial. % 22.12/22.26 apply (zenon_L1616_); trivial. % 22.12/22.26 (* end of lemma zenon_L1617_ *) % 22.12/22.26 assert (zenon_L1618_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (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). % 22.12/22.26 do 0 intro. intros zenon_H1fe zenon_H13f zenon_H140 zenon_Hc4 zenon_H9f zenon_Hbb zenon_H177 zenon_H7d zenon_H7b zenon_H8b zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H129 zenon_H1bb zenon_H234 zenon_H1d8 zenon_He4 zenon_H1ba zenon_H82 zenon_H5c zenon_Hf5. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.12/22.26 apply (zenon_L41_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.12/22.26 apply (zenon_L1359_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.12/22.26 apply (zenon_L1360_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.26 apply (zenon_L253_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.26 apply (zenon_L1364_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.26 apply (zenon_L1617_); trivial. % 22.12/22.26 apply (zenon_L192_); trivial. % 22.12/22.26 (* end of lemma zenon_L1618_ *) % 22.12/22.26 assert (zenon_L1619_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (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) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (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) (e1)))) -> (~((op (e3) (e0)) = (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))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((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)) = (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)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (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 (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e1) (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 (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H201 zenon_H5c zenon_H1a8 zenon_H156 zenon_H38 zenon_H1b4 zenon_Ha0 zenon_Hbb zenon_H183 zenon_H189 zenon_H68 zenon_H1c3 zenon_H163 zenon_H212 zenon_H7d zenon_H18a zenon_Hbc zenon_H13b zenon_H179 zenon_H173 zenon_H10c zenon_H6f zenon_H192 zenon_H288 zenon_H16a zenon_H7b zenon_Hf0 zenon_H8b zenon_H19a zenon_H1b7 zenon_H1bb zenon_H20f zenon_Hc4 zenon_H18d zenon_H1cf zenon_H1d5 zenon_H67 zenon_H4e zenon_H1cb zenon_Hfa zenon_H54 zenon_H55 zenon_H234 zenon_H1d8 zenon_He4 zenon_H48 zenon_H164 zenon_H77 zenon_H72 zenon_H1bf zenon_H121 zenon_H33 zenon_H9f zenon_H171 zenon_Ha9 zenon_Hb6 zenon_Hb9 zenon_H129. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.26 apply (zenon_L1378_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.26 apply (zenon_L59_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.26 exact (zenon_H1bf zenon_H105). % 22.12/22.26 apply (zenon_L493_); trivial. % 22.12/22.26 (* end of lemma zenon_L1619_ *) % 22.12/22.26 assert (zenon_L1620_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (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) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (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) (e1)))) -> (~((op (e3) (e0)) = (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))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((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)) = (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)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (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 (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (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 (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((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)) = (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) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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) (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.12/22.26 do 0 intro. intros zenon_H195 zenon_Hb9 zenon_Hbb zenon_H163 zenon_H201 zenon_H1a8 zenon_H156 zenon_H38 zenon_H1b4 zenon_Ha0 zenon_H183 zenon_H189 zenon_H68 zenon_H1c3 zenon_H212 zenon_H7d zenon_H18a zenon_Hbc zenon_H13b zenon_H179 zenon_H173 zenon_H6f zenon_H192 zenon_H288 zenon_H16a zenon_H7b zenon_Hf0 zenon_H8b zenon_H19a zenon_H1b7 zenon_H1bb zenon_H20f zenon_Hc4 zenon_H18d zenon_H1cf zenon_H1d5 zenon_H67 zenon_H4e zenon_H1cb zenon_Hfa zenon_H54 zenon_H55 zenon_H234 zenon_H1d8 zenon_He4 zenon_H48 zenon_H164 zenon_H1bf zenon_H121 zenon_H33 zenon_H9f zenon_Ha9 zenon_Hb6 zenon_H129 zenon_H24 zenon_H13c zenon_H186 zenon_H283 zenon_H131 zenon_H73 zenon_H1ec zenon_H158 zenon_H13a zenon_H13e zenon_H190 zenon_H266 zenon_H1ef zenon_H139 zenon_H1a2 zenon_H1c6 zenon_H25b zenon_Hf5 zenon_H27e zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H13f zenon_H141 zenon_H117 zenon_H196 zenon_H5c zenon_H77. % 22.12/22.26 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.26 apply (zenon_L1367_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.26 apply (zenon_L1373_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.26 apply (zenon_L1381_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.26 apply (zenon_L100_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.26 apply (zenon_L900_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.26 apply (zenon_L1383_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.26 apply (zenon_L436_); trivial. % 22.12/22.26 apply (zenon_L1393_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.26 apply (zenon_L900_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.26 apply (zenon_L1619_); trivial. % 22.12/22.26 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.26 apply (zenon_L617_); trivial. % 22.12/22.26 apply (zenon_L172_); trivial. % 22.12/22.26 apply (zenon_L206_); trivial. % 22.12/22.26 (* end of lemma zenon_L1620_ *) % 22.12/22.26 assert (zenon_L1621_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (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 (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (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) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (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) (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) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.12/22.27 do 0 intro. intros zenon_H196 zenon_H117 zenon_H141 zenon_H13f zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H27e zenon_Hf5 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H139 zenon_H1ef zenon_H266 zenon_H190 zenon_H13e zenon_H13a zenon_H158 zenon_H1ec zenon_H73 zenon_H131 zenon_H283 zenon_H13c zenon_H24 zenon_H129 zenon_Ha9 zenon_H9f zenon_H33 zenon_H121 zenon_H164 zenon_H48 zenon_He4 zenon_H1d8 zenon_H234 zenon_H55 zenon_H54 zenon_Hfa zenon_H1cb zenon_H4e zenon_H1d5 zenon_H1cf zenon_H18d zenon_Hc4 zenon_H20f zenon_H1bb zenon_H1b7 zenon_H19a zenon_H8b zenon_Hf0 zenon_H7b zenon_H16a zenon_H288 zenon_H192 zenon_H6f zenon_H173 zenon_H179 zenon_H13b zenon_Hbc zenon_H18a zenon_H7d zenon_H212 zenon_H1c3 zenon_H189 zenon_H183 zenon_Ha0 zenon_H1b4 zenon_H156 zenon_H1a8 zenon_H163 zenon_Hb9 zenon_H195 zenon_H3d zenon_Hbb zenon_Hb6 zenon_H1bf zenon_H5c zenon_H186 zenon_H77 zenon_H201 zenon_H38 zenon_H68. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.27 apply (zenon_L1620_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.27 apply (zenon_L214_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.27 apply (zenon_L1382_); trivial. % 22.12/22.27 apply (zenon_L165_); trivial. % 22.12/22.27 (* end of lemma zenon_L1621_ *) % 22.12/22.27 assert (zenon_L1622_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 22.12/22.27 do 0 intro. intros zenon_He4 zenon_H6e zenon_H234 zenon_H1bb zenon_H129 zenon_H5c zenon_H20f zenon_H38 zenon_H1b4 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H8b zenon_H7b zenon_H7d zenon_H7e. % 22.12/22.27 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.12/22.27 apply (zenon_L214_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.12/22.27 apply (zenon_L484_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.12/22.27 apply (zenon_L1357_); trivial. % 22.12/22.27 apply (zenon_L31_); trivial. % 22.12/22.27 (* end of lemma zenon_L1622_ *) % 22.12/22.27 assert (zenon_L1623_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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 (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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((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 (e3) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((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). % 22.12/22.27 do 0 intro. intros zenon_H1fe zenon_H125 zenon_H191 zenon_H13f zenon_H33 zenon_H121 zenon_H201 zenon_H177 zenon_H7d zenon_H7b zenon_H8b zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H129 zenon_H1bb zenon_H234 zenon_H1d8 zenon_He4 zenon_H1a8 zenon_H141 zenon_H164 zenon_Hfa zenon_H1d5 zenon_Hf0 zenon_H288 zenon_H192 zenon_H179 zenon_H13b zenon_Hbc zenon_H212 zenon_H183 zenon_Hbb zenon_H24 zenon_H9f zenon_H22d zenon_H89 zenon_H1bf zenon_H92 zenon_Hb9 zenon_H18a zenon_Hc4 zenon_H82 zenon_H5c zenon_Hf5. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.12/22.27 apply (zenon_L41_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.27 apply (zenon_L253_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.27 apply (zenon_L253_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.27 apply (zenon_L25_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.27 apply (zenon_L1621_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.27 apply (zenon_L171_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.27 apply (zenon_L1373_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.27 apply (zenon_L116_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.27 apply (zenon_L1379_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.27 apply (zenon_L436_); trivial. % 22.12/22.27 apply (zenon_L172_); trivial. % 22.12/22.27 apply (zenon_L206_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.27 apply (zenon_L1622_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.27 apply (zenon_L651_); trivial. % 22.12/22.27 apply (zenon_L165_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.27 apply (zenon_L1284_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.27 apply (zenon_L17_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.27 apply (zenon_L1620_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.27 apply (zenon_L1381_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.27 apply (zenon_L94_); trivial. % 22.12/22.27 apply (zenon_L165_); trivial. % 22.12/22.27 apply (zenon_L1616_); trivial. % 22.12/22.27 apply (zenon_L246_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.12/22.27 apply (zenon_L644_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.27 apply (zenon_L253_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.27 apply (zenon_L1363_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.27 apply (zenon_L17_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.27 apply (zenon_L1621_); trivial. % 22.12/22.27 apply (zenon_L456_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.27 apply (zenon_L1284_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.27 apply (zenon_L17_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.27 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.12/22.27 apply (zenon_L738_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.12/22.27 apply (zenon_L484_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.12/22.27 apply (zenon_L998_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.27 apply (zenon_L1367_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.27 apply (zenon_L1373_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.27 apply (zenon_L1374_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.27 apply (zenon_L100_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.27 apply (zenon_L900_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.27 apply (zenon_L1377_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.27 apply (zenon_L436_); trivial. % 22.12/22.27 apply (zenon_L1393_); trivial. % 22.12/22.27 apply (zenon_L169_); trivial. % 22.12/22.27 apply (zenon_L206_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.27 apply (zenon_L1370_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.27 apply (zenon_L94_); trivial. % 22.12/22.27 apply (zenon_L165_); trivial. % 22.12/22.27 apply (zenon_L1616_); trivial. % 22.12/22.27 apply (zenon_L192_); trivial. % 22.12/22.27 (* end of lemma zenon_L1623_ *) % 22.12/22.27 assert (zenon_L1624_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((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). % 22.12/22.27 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H153 zenon_H234 zenon_H5c zenon_H191 zenon_H8b zenon_H190 zenon_H13d zenon_H13e zenon_H7d zenon_H7e. % 22.12/22.27 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.12/22.27 apply (zenon_L738_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.12/22.27 apply (zenon_L484_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.12/22.27 apply (zenon_L144_); trivial. % 22.12/22.27 apply (zenon_L31_); trivial. % 22.12/22.27 (* end of lemma zenon_L1624_ *) % 22.12/22.27 assert (zenon_L1625_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((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)))) -> False). % 22.12/22.27 do 0 intro. intros zenon_H82 zenon_H1bb zenon_H129 zenon_H20f zenon_H38 zenon_H1b4 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H55 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H1ba zenon_He4 zenon_H1d8 zenon_H153 zenon_H234 zenon_H5c zenon_H191 zenon_H8b zenon_H190 zenon_H13d zenon_H13e zenon_H7d. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.12/22.27 apply (zenon_L1284_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.12/22.27 apply (zenon_L17_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.12/22.27 apply (zenon_L1356_); trivial. % 22.12/22.27 apply (zenon_L1624_); trivial. % 22.12/22.27 (* end of lemma zenon_L1625_ *) % 22.12/22.27 assert (zenon_L1626_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (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)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.12/22.27 do 0 intro. intros zenon_H1fe zenon_H140 zenon_Hc4 zenon_H9f zenon_Hbb zenon_H177 zenon_H7d zenon_H13e zenon_H13d zenon_H190 zenon_H8b zenon_H191 zenon_H5c zenon_H234 zenon_H1d8 zenon_He4 zenon_H1ba zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H55 zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H82 zenon_H38 zenon_H48. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.12/22.27 apply (zenon_L41_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.12/22.27 apply (zenon_L1385_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.12/22.27 apply (zenon_L1360_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.12/22.27 apply (zenon_L253_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.12/22.27 apply (zenon_L1364_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.12/22.27 apply (zenon_L1625_); trivial. % 22.12/22.27 apply (zenon_L246_); trivial. % 22.12/22.27 (* end of lemma zenon_L1626_ *) % 22.12/22.27 assert (zenon_L1627_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 22.12/22.27 do 0 intro. intros zenon_Hb2 zenon_H24e zenon_H1f1 zenon_H23c zenon_H26a zenon_H104 zenon_H231 zenon_H2c zenon_H109 zenon_H11a zenon_H1c2 zenon_H1cd zenon_H111 zenon_He2 zenon_H12e zenon_H100 zenon_H22d zenon_H191 zenon_H125 zenon_H141 zenon_H201 zenon_H164 zenon_H212 zenon_Hbc zenon_H179 zenon_H288 zenon_H192 zenon_H183 zenon_H18a zenon_Hfa zenon_H13b zenon_H1a8 zenon_H24 zenon_H121 zenon_H33 zenon_Hf0 zenon_H1d5 zenon_H1fe zenon_H82 zenon_H177 zenon_H1d8 zenon_H234 zenon_H7d zenon_He4 zenon_Hc4 zenon_H26d zenon_H38 zenon_H4e zenon_H13f zenon_H77 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H5c zenon_H129 zenon_H1bb zenon_H140 zenon_H9f zenon_Ha0. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.12/22.27 apply (zenon_L2_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.12/22.27 apply (zenon_L1146_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.12/22.27 apply (zenon_L1147_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.12/22.27 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.12/22.27 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.12/22.27 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.12/22.27 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.12/22.27 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.12/22.27 apply (zenon_L1442_); trivial. % 22.12/22.27 apply (zenon_L1556_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.12/22.27 apply (zenon_L1206_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.12/22.27 apply (zenon_L11_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.12/22.27 apply (zenon_L1207_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.12/22.27 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.12/22.27 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.12/22.27 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.12/22.27 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.12/22.27 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.12/22.27 apply (zenon_L1567_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.12/22.27 apply (zenon_L1569_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.12/22.27 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.12/22.27 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.12/22.27 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.12/22.27 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.12/22.27 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.12/22.27 exact (zenon_Hec zenon_H5c). % 22.12/22.27 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.27 apply (zenon_L900_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.27 exact (zenon_H159 zenon_H10c). % 22.12/22.27 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.27 apply (zenon_L436_); trivial. % 22.12/22.27 apply (zenon_L1397_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.12/22.27 apply (zenon_L37_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.12/22.27 apply (zenon_L1352_); trivial. % 22.12/22.27 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.12/22.28 apply (zenon_L1353_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.12/22.28 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.12/22.28 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.12/22.28 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.12/22.28 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.12/22.28 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.12/22.28 apply (zenon_L1593_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.12/22.28 apply (zenon_L1615_); trivial. % 22.12/22.28 apply (zenon_L1615_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.12/22.28 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.12/22.28 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.12/22.28 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.12/22.28 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.12/22.28 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.12/22.28 apply (zenon_L1618_); trivial. % 22.12/22.28 apply (zenon_L1618_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.12/22.28 apply (zenon_L1623_); trivial. % 22.12/22.28 apply (zenon_L1623_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.12/22.28 apply (zenon_L1626_); trivial. % 22.12/22.28 apply (zenon_L1626_); trivial. % 22.12/22.28 apply (zenon_L1389_); trivial. % 22.12/22.28 apply (zenon_L51_); trivial. % 22.12/22.28 (* end of lemma zenon_L1627_ *) % 22.12/22.28 assert (zenon_L1628_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.12/22.28 do 0 intro. intros zenon_H1c6 zenon_H159 zenon_H38 zenon_H196 zenon_H201 zenon_H6f zenon_H183 zenon_H68 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H181 zenon_H1d8 zenon_H13a zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H1c3 zenon_Ha0 zenon_Hf5 zenon_H288 zenon_H11a zenon_H3f zenon_H191 zenon_H171 zenon_He7 zenon_H163 zenon_H192 zenon_H3d zenon_H34 zenon_H12e zenon_H48 zenon_H1a2 zenon_Ha9 zenon_H66 zenon_H186 zenon_Ha5 zenon_H190 zenon_Hb6 zenon_H54 zenon_H141 zenon_H1c7. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.28 apply (zenon_L55_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.28 exact (zenon_H159 zenon_H10c). % 22.12/22.28 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.28 apply (zenon_L217_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.28 apply (zenon_L152_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.28 apply (zenon_L1535_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.28 apply (zenon_L965_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.28 apply (zenon_L255_); trivial. % 22.12/22.28 apply (zenon_L512_); trivial. % 22.12/22.28 apply (zenon_L1162_); trivial. % 22.12/22.28 exact (zenon_H1c7 zenon_Hac). % 22.12/22.28 (* end of lemma zenon_L1628_ *) % 22.12/22.28 assert (zenon_L1629_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 22.12/22.28 do 0 intro. intros zenon_Hfa zenon_H77 zenon_H6e zenon_H173 zenon_H68 zenon_H13c zenon_Hb6 zenon_H3c zenon_H159 zenon_Ha0 zenon_Hf3 zenon_Ha9. % 22.12/22.28 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.28 apply (zenon_L24_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.28 apply (zenon_L226_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.28 apply (zenon_L62_); trivial. % 22.12/22.28 apply (zenon_L1447_); trivial. % 22.12/22.28 (* end of lemma zenon_L1629_ *) % 22.12/22.28 assert (zenon_L1630_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.12/22.28 do 0 intro. intros zenon_H1c6 zenon_H6e zenon_H159 zenon_H6f zenon_H183 zenon_H68 zenon_H192 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H181 zenon_H153 zenon_H1d8 zenon_H13a zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha9 zenon_H1c3 zenon_Ha0 zenon_Hb6 zenon_Ha5 zenon_Hf5 zenon_H288 zenon_H11a zenon_H3f zenon_H48 zenon_H12e zenon_H191 zenon_H186 zenon_H1a2 zenon_H1c7. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.28 apply (zenon_L110_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.28 exact (zenon_H159 zenon_H10c). % 22.12/22.28 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.28 apply (zenon_L1535_); trivial. % 22.12/22.28 exact (zenon_H1c7 zenon_Hac). % 22.12/22.28 (* end of lemma zenon_L1630_ *) % 22.12/22.28 assert (zenon_L1631_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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 (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (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) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.12/22.28 do 0 intro. intros zenon_Heb zenon_H173 zenon_Hfa zenon_H1c7 zenon_H1a2 zenon_H186 zenon_H191 zenon_H12e zenon_H11a zenon_H288 zenon_Hf5 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H196 zenon_H1fb zenon_H25e zenon_H13a zenon_H1d8 zenon_H153 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H192 zenon_H183 zenon_H6f zenon_H159 zenon_H6e zenon_H1c6 zenon_H24 zenon_H9f zenon_H13c zenon_Hf3 zenon_H48 zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H181. % 22.12/22.28 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.12/22.28 apply (zenon_L1629_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.28 apply (zenon_L900_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.28 exact (zenon_H159 zenon_H10c). % 22.12/22.28 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.28 apply (zenon_L162_); trivial. % 22.12/22.28 apply (zenon_L1630_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.12/22.28 apply (zenon_L117_); trivial. % 22.12/22.28 apply (zenon_L414_); trivial. % 22.12/22.28 (* end of lemma zenon_L1631_ *) % 22.12/22.28 assert (zenon_L1632_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((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) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (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 (e3) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.12/22.28 do 0 intro. intros zenon_H139 zenon_H2c zenon_Ha0 zenon_Ha9 zenon_H3d zenon_Hb6 zenon_H141 zenon_He7 zenon_Hf0 zenon_H1cb zenon_H3c zenon_H5d zenon_H48 zenon_H18d zenon_H121 zenon_H33 zenon_H1c7 zenon_H104 zenon_Hc4 zenon_H1a2 zenon_H181 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1d8 zenon_H34 zenon_H18a zenon_H65 zenon_H1ef zenon_H186 zenon_H13a zenon_H6f zenon_H109 zenon_H117 zenon_H1b7 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H1c3 zenon_H190 zenon_H196 zenon_H38 zenon_H68. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.28 apply (zenon_L180_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.28 apply (zenon_L214_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.28 apply (zenon_L1506_); trivial. % 22.12/22.28 apply (zenon_L165_); trivial. % 22.12/22.28 (* end of lemma zenon_L1632_ *) % 22.12/22.28 assert (zenon_L1633_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.12/22.28 do 0 intro. intros zenon_H183 zenon_H34 zenon_H1b7 zenon_H77 zenon_H128 zenon_Ha9 zenon_Ha5 zenon_H38 zenon_H68 zenon_H1c3 zenon_H72 zenon_H163 zenon_H181. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.12/22.28 apply (zenon_L291_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.12/22.28 apply (zenon_L1444_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.12/22.28 apply (zenon_L227_); trivial. % 22.12/22.28 exact (zenon_H181 zenon_H17c). % 22.12/22.28 (* end of lemma zenon_L1633_ *) % 22.12/22.28 assert (zenon_L1634_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.12/22.28 do 0 intro. intros zenon_H13f zenon_H65 zenon_Hb6 zenon_H10d zenon_H48 zenon_H14c zenon_H183 zenon_H34 zenon_H1b7 zenon_H77 zenon_Ha9 zenon_Ha5 zenon_H38 zenon_H68 zenon_H1c3 zenon_H72 zenon_H163 zenon_H181. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.12/22.28 apply (zenon_L30_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.12/22.28 apply (zenon_L113_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.12/22.28 apply (zenon_L255_); trivial. % 22.12/22.28 apply (zenon_L1633_); trivial. % 22.12/22.28 (* end of lemma zenon_L1634_ *) % 22.12/22.28 assert (zenon_L1635_ : (((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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.12/22.28 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H16a zenon_H54 zenon_H1cf zenon_H104 zenon_H38 zenon_H20f zenon_H129 zenon_H18d zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H1c6 zenon_H6e zenon_H159 zenon_H6f zenon_H183 zenon_H68 zenon_H192 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H181 zenon_H153 zenon_H1d8 zenon_H13a zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha9 zenon_H1c3 zenon_Ha0 zenon_Hb6 zenon_Hf5 zenon_H288 zenon_H11a zenon_H3f zenon_H48 zenon_H12e zenon_H191 zenon_H186 zenon_H1a2 zenon_H1c7. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.28 apply (zenon_L900_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.28 exact (zenon_H159 zenon_H10c). % 22.12/22.28 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.28 apply (zenon_L110_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.28 exact (zenon_H159 zenon_H10c). % 22.12/22.28 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.28 apply (zenon_L30_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.28 apply (zenon_L289_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.28 apply (zenon_L1509_); trivial. % 22.12/22.28 apply (zenon_L1511_); trivial. % 22.12/22.28 exact (zenon_H1c7 zenon_Hac). % 22.12/22.28 apply (zenon_L1630_); trivial. % 22.12/22.28 (* end of lemma zenon_L1635_ *) % 22.12/22.28 assert (zenon_L1636_ : ((op (e1) (e0)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 22.12/22.28 do 0 intro. intros zenon_H76 zenon_H1c7 zenon_H181 zenon_H34 zenon_H159 zenon_H6e zenon_H54 zenon_H153 zenon_Hb2 zenon_H24e zenon_H1f1 zenon_H23c zenon_H26a zenon_H104 zenon_H231 zenon_H2c zenon_H109 zenon_H11a zenon_H1c2 zenon_H1cd zenon_H111 zenon_He2 zenon_H12e zenon_H100 zenon_H22d zenon_H191 zenon_H125 zenon_H141 zenon_H201 zenon_H164 zenon_H212 zenon_Hbc zenon_H179 zenon_H288 zenon_H192 zenon_H183 zenon_H18a zenon_Hfa zenon_H13b zenon_H1a8 zenon_H24 zenon_H121 zenon_H33 zenon_Hf0 zenon_H1d5 zenon_H1fe zenon_H82 zenon_H177 zenon_H1d8 zenon_H234 zenon_H7d zenon_He4 zenon_Hc4 zenon_H26d zenon_H38 zenon_H4e zenon_H13f zenon_H77 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H140 zenon_H9f zenon_Ha0. % 22.12/22.28 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.12/22.28 apply (zenon_L24_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.12/22.28 apply (zenon_L1635_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.12/22.28 apply (zenon_L184_); trivial. % 22.12/22.28 apply (zenon_L1627_); trivial. % 22.12/22.28 (* end of lemma zenon_L1636_ *) % 22.12/22.28 assert (zenon_L1637_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.12/22.28 do 0 intro. intros zenon_H1c6 zenon_H38 zenon_H117 zenon_H54 zenon_H195 zenon_Hf0 zenon_He7 zenon_H109 zenon_H141 zenon_H159 zenon_H6f zenon_H183 zenon_H68 zenon_H192 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H181 zenon_H153 zenon_H1d8 zenon_H13a zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha9 zenon_H1c3 zenon_Ha0 zenon_Hb6 zenon_Ha5 zenon_Hf5 zenon_H288 zenon_H11a zenon_H3f zenon_H48 zenon_H12e zenon_H191 zenon_H186 zenon_H1a2 zenon_H1c7. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.28 apply (zenon_L1534_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.28 exact (zenon_H159 zenon_H10c). % 22.12/22.28 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.28 apply (zenon_L1535_); trivial. % 22.12/22.28 exact (zenon_H1c7 zenon_Hac). % 22.12/22.28 (* end of lemma zenon_L1637_ *) % 22.12/22.28 assert (zenon_L1638_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (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) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (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 (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 (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (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 (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)) = (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 (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.28 do 0 intro. intros zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H133 zenon_Hb6 zenon_H179 zenon_H1c2 zenon_H13b zenon_H34 zenon_H7d zenon_H100 zenon_H1a8 zenon_H1c7 zenon_H9f zenon_H24 zenon_H159 zenon_H1d5 zenon_H67 zenon_H54 zenon_H1cd zenon_Hfa zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H16a zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H2c zenon_H109 zenon_H23c zenon_He4 zenon_Hbc zenon_H18a zenon_H104 zenon_H231 zenon_H36 zenon_H12e zenon_H11a zenon_H288 zenon_H1d8 zenon_H24e zenon_H192 zenon_H183 zenon_H141 zenon_H111 zenon_H13f zenon_Hf0 zenon_H181 zenon_He2 zenon_Hf5 zenon_H201 zenon_H153 zenon_H177 zenon_He7 zenon_H171 zenon_H196 zenon_H38. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.28 apply (zenon_L359_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.28 apply (zenon_L929_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.28 apply (zenon_L180_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.28 apply (zenon_L1482_); trivial. % 22.12/22.28 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.28 apply (zenon_L1495_); trivial. % 22.12/22.28 apply (zenon_L1531_); trivial. % 22.12/22.28 apply (zenon_L1162_); trivial. % 22.12/22.28 (* end of lemma zenon_L1638_ *) % 22.12/22.28 assert (zenon_L1639_ : ((op (e3) (e1)) = (e2)) -> (~((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) (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 (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (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 (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H171 zenon_H177 zenon_H201 zenon_He2 zenon_H13f zenon_H111 zenon_H36 zenon_H231 zenon_H104 zenon_H18a zenon_Hbc zenon_He4 zenon_H23c zenon_H2c zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H16a zenon_H25b zenon_H27e zenon_H189 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H284 zenon_Hfa zenon_H67 zenon_H1d5 zenon_H24 zenon_H9f zenon_H1a8 zenon_H100 zenon_H13b zenon_H1c2 zenon_H179 zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1bb zenon_H1cb zenon_H1c6 zenon_H38 zenon_H117 zenon_H54 zenon_H195 zenon_Hf0 zenon_He7 zenon_H109 zenon_H141 zenon_H159 zenon_H6f zenon_H183 zenon_H68 zenon_H192 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H181 zenon_H153 zenon_H1d8 zenon_H13a zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha9 zenon_H1c3 zenon_Ha0 zenon_Hb6 zenon_Hf5 zenon_H288 zenon_H11a zenon_H3f zenon_H48 zenon_H12e zenon_H191 zenon_H186 zenon_H1a2 zenon_H1c7. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.29 apply (zenon_L900_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.29 exact (zenon_H159 zenon_H10c). % 22.12/22.29 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.29 apply (zenon_L1638_); trivial. % 22.12/22.29 apply (zenon_L1637_); trivial. % 22.12/22.29 (* end of lemma zenon_L1639_ *) % 22.12/22.29 assert (zenon_L1640_ : (((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)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((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) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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 (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.12/22.29 do 0 intro. intros zenon_Heb zenon_H100 zenon_H1c7 zenon_H1a2 zenon_H186 zenon_H191 zenon_H12e zenon_H48 zenon_H11a zenon_H288 zenon_Hf5 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H196 zenon_H1fb zenon_H25e zenon_H13a zenon_H1d8 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H192 zenon_H183 zenon_H6f zenon_H159 zenon_H6e zenon_H1c6 zenon_H18a zenon_H1cb zenon_H18d zenon_H104 zenon_H1cf zenon_H54 zenon_H16a zenon_H24 zenon_H9f zenon_H13c zenon_H73 zenon_H153 zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H181. % 22.12/22.29 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.12/22.29 apply (zenon_L69_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.12/22.29 apply (zenon_L1635_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.12/22.29 apply (zenon_L184_); trivial. % 22.12/22.29 apply (zenon_L414_); trivial. % 22.12/22.29 (* end of lemma zenon_L1640_ *) % 22.12/22.29 assert (zenon_L1641_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((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). % 22.12/22.29 do 0 intro. intros zenon_H141 zenon_H54 zenon_He7 zenon_Hf0 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H1bb zenon_H18a zenon_H1cb zenon_Hc4 zenon_H11a zenon_H3f zenon_H48 zenon_H12e zenon_H6d zenon_H190 zenon_H186 zenon_Hf7 zenon_H201 zenon_H159 zenon_H24 zenon_H9f zenon_H13c zenon_H121 zenon_H209 zenon_H20f zenon_H77 zenon_Ha9 zenon_H68 zenon_H183 zenon_Hb6 zenon_H1cf zenon_H196 zenon_H38. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.29 apply (zenon_L217_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.29 apply (zenon_L929_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.12/22.29 apply (zenon_L1457_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.12/22.29 apply (zenon_L438_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.12/22.29 apply (zenon_L366_); trivial. % 22.12/22.29 apply (zenon_L1480_); trivial. % 22.12/22.29 apply (zenon_L1162_); trivial. % 22.12/22.29 (* end of lemma zenon_L1641_ *) % 22.12/22.29 assert (zenon_L1642_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((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) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((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)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e2))) -> (((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))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 22.12/22.29 do 0 intro. intros zenon_Hfa zenon_H1c7 zenon_H1a2 zenon_H186 zenon_H191 zenon_H12e zenon_H48 zenon_H11a zenon_H288 zenon_Hf5 zenon_Hb6 zenon_H1c3 zenon_H196 zenon_H1b4 zenon_H1fb zenon_H25e zenon_H13a zenon_H1d8 zenon_H153 zenon_H181 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H192 zenon_H183 zenon_H6f zenon_H141 zenon_H4e zenon_H67 zenon_H1d5 zenon_H1cf zenon_H1c6 zenon_H1a8 zenon_H195 zenon_H54 zenon_H117 zenon_H38 zenon_H77 zenon_H3f zenon_H68 zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_Ha0 zenon_Hf3 zenon_Ha9. % 22.12/22.29 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.29 apply (zenon_L900_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.29 exact (zenon_H159 zenon_H10c). % 22.12/22.29 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.29 apply (zenon_L162_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.29 apply (zenon_L1467_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.29 exact (zenon_H159 zenon_H10c). % 22.12/22.29 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.29 apply (zenon_L1535_); trivial. % 22.12/22.29 exact (zenon_H1c7 zenon_Hac). % 22.12/22.29 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.29 apply (zenon_L186_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.29 apply (zenon_L62_); trivial. % 22.12/22.29 apply (zenon_L1468_); trivial. % 22.12/22.29 (* end of lemma zenon_L1642_ *) % 22.12/22.29 assert (zenon_L1643_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (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 (e0) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H12e zenon_H48 zenon_H212 zenon_H1cb zenon_H1cd zenon_Hbc zenon_H231 zenon_H18a zenon_H7d zenon_H104 zenon_H14c zenon_H1c2 zenon_H8a zenon_H121 zenon_H33 zenon_H9f zenon_H20f zenon_H77 zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_Hc4 zenon_H38 zenon_H1c3 zenon_H120. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.12/22.29 apply (zenon_L456_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.12/22.29 apply (zenon_L1168_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.12/22.29 apply (zenon_L1158_); trivial. % 22.12/22.29 exact (zenon_H120 zenon_H11f). % 22.12/22.29 (* end of lemma zenon_L1643_ *) % 22.12/22.29 assert (zenon_L1644_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (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 (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (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))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H16a zenon_H2c zenon_H67 zenon_H195 zenon_Ha5 zenon_Ha0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H1c3 zenon_H1a3 zenon_H183 zenon_H68 zenon_H34 zenon_Ha9 zenon_H9f zenon_H33 zenon_H121 zenon_H1c2 zenon_H14c zenon_H104 zenon_H7d zenon_H18a zenon_H231 zenon_Hbc zenon_H1cd zenon_H1cb zenon_H212 zenon_H12e zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H120. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.29 apply (zenon_L180_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.29 apply (zenon_L1090_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.29 apply (zenon_L1643_); trivial. % 22.12/22.29 apply (zenon_L555_); trivial. % 22.12/22.29 (* end of lemma zenon_L1644_ *) % 22.12/22.29 assert (zenon_L1645_ : (((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 (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H18d zenon_H48 zenon_H38 zenon_H234 zenon_H3f zenon_Hb9 zenon_Hb6 zenon_H120. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.12/22.29 apply (zenon_L246_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.12/22.29 apply (zenon_L484_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.12/22.29 apply (zenon_L182_); trivial. % 22.12/22.29 exact (zenon_H120 zenon_H11f). % 22.12/22.29 (* end of lemma zenon_L1645_ *) % 22.12/22.29 assert (zenon_L1646_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (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 (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H117 zenon_H54 zenon_Ha9 zenon_H6d zenon_H14c zenon_Ha0 zenon_H18d zenon_H48 zenon_H38 zenon_H234 zenon_H3f zenon_Hb6 zenon_H120. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.12/22.29 apply (zenon_L151_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.12/22.29 apply (zenon_L289_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.12/22.29 apply (zenon_L278_); trivial. % 22.12/22.29 apply (zenon_L1645_); trivial. % 22.12/22.29 (* end of lemma zenon_L1646_ *) % 22.12/22.29 assert (zenon_L1647_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.29 do 0 intro. intros zenon_H141 zenon_H68 zenon_H120 zenon_Hb6 zenon_H3f zenon_H234 zenon_H48 zenon_H18d zenon_Ha0 zenon_H6d zenon_Ha9 zenon_H54 zenon_H117 zenon_H196 zenon_H38. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.29 apply (zenon_L217_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.29 apply (zenon_L54_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.29 apply (zenon_L1646_); trivial. % 22.12/22.29 apply (zenon_L1162_); trivial. % 22.12/22.29 (* end of lemma zenon_L1647_ *) % 22.12/22.29 assert (zenon_L1648_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H12e zenon_H48 zenon_H34 zenon_H3f zenon_H11a zenon_H153 zenon_H177 zenon_H120. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.12/22.29 apply (zenon_L456_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.12/22.29 apply (zenon_L552_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.12/22.29 apply (zenon_L566_); trivial. % 22.12/22.29 exact (zenon_H120 zenon_H11f). % 22.12/22.29 (* end of lemma zenon_L1648_ *) % 22.12/22.29 assert (zenon_L1649_ : ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H54 zenon_H120 zenon_H34 zenon_H153 zenon_Hb2 zenon_H24e zenon_H1f1 zenon_H23c zenon_H26a zenon_H104 zenon_H231 zenon_H2c zenon_H109 zenon_H11a zenon_H1c2 zenon_H1cd zenon_H111 zenon_He2 zenon_H12e zenon_H100 zenon_H22d zenon_H191 zenon_H125 zenon_H141 zenon_H201 zenon_H164 zenon_H212 zenon_Hbc zenon_H179 zenon_H288 zenon_H192 zenon_H183 zenon_H18a zenon_Hfa zenon_H13b zenon_H1a8 zenon_H24 zenon_H121 zenon_H33 zenon_Hf0 zenon_H1d5 zenon_H1fe zenon_H82 zenon_H177 zenon_H1d8 zenon_H234 zenon_H7d zenon_He4 zenon_Hc4 zenon_H26d zenon_H38 zenon_H4e zenon_H13f zenon_H77 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H140 zenon_H9f zenon_Ha0. % 22.12/22.29 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.12/22.29 apply (zenon_L69_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.12/22.29 apply (zenon_L1648_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.12/22.29 apply (zenon_L184_); trivial. % 22.12/22.29 apply (zenon_L1627_); trivial. % 22.12/22.29 (* end of lemma zenon_L1649_ *) % 22.12/22.29 assert (zenon_L1650_ : (((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 (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H105 zenon_H104 zenon_H120. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.12/22.29 apply (zenon_L456_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.12/22.29 apply (zenon_L146_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.12/22.29 apply (zenon_L72_); trivial. % 22.12/22.29 exact (zenon_H120 zenon_H11f). % 22.12/22.29 (* end of lemma zenon_L1650_ *) % 22.12/22.29 assert (zenon_L1651_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H1c3 zenon_H38 zenon_Hc4 zenon_H1a3 zenon_H183 zenon_H68 zenon_H34 zenon_Ha9 zenon_H106 zenon_H20f zenon_H9f zenon_H33 zenon_H121 zenon_H128 zenon_H77 zenon_H171 zenon_H1b7. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 22.12/22.29 apply (zenon_L165_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 22.12/22.29 apply (zenon_L1154_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 22.12/22.29 apply (zenon_L218_); trivial. % 22.12/22.29 apply (zenon_L188_); trivial. % 22.12/22.29 (* end of lemma zenon_L1651_ *) % 22.12/22.29 assert (zenon_L1652_ : (((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 (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H18d zenon_H48 zenon_H234 zenon_H3f zenon_H1b7 zenon_H171 zenon_H77 zenon_H121 zenon_H33 zenon_H9f zenon_H20f zenon_H106 zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_Hc4 zenon_H38 zenon_H1c3 zenon_H120. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.12/22.29 apply (zenon_L246_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.12/22.29 apply (zenon_L484_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.12/22.29 apply (zenon_L1651_); trivial. % 22.12/22.29 exact (zenon_H120 zenon_H11f). % 22.12/22.29 (* end of lemma zenon_L1652_ *) % 22.12/22.29 assert (zenon_L1653_ : (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((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)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (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) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (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)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.12/22.29 do 0 intro. intros zenon_Ha0 zenon_H140 zenon_H1bb zenon_H129 zenon_H1b4 zenon_H283 zenon_H1cf zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H13f zenon_H4e zenon_H26d zenon_He4 zenon_H7d zenon_H1d8 zenon_H177 zenon_H82 zenon_H1fe zenon_H1d5 zenon_Hf0 zenon_H24 zenon_H1a8 zenon_H13b zenon_Hfa zenon_H18a zenon_H288 zenon_H179 zenon_Hbc zenon_H212 zenon_H164 zenon_H201 zenon_H141 zenon_H125 zenon_H191 zenon_H22d zenon_H100 zenon_He2 zenon_H111 zenon_H1cd zenon_H1c2 zenon_H11a zenon_H109 zenon_H2c zenon_H231 zenon_H26a zenon_H23c zenon_H1f1 zenon_H24e zenon_Hb2 zenon_H54 zenon_He7 zenon_H163 zenon_H104 zenon_H192 zenon_H3d zenon_H12e zenon_H18d zenon_H48 zenon_H234 zenon_H3f zenon_H1b7 zenon_H77 zenon_H121 zenon_H33 zenon_H9f zenon_H20f zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_Hc4 zenon_H38 zenon_H1c3 zenon_H120. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.29 apply (zenon_L214_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.29 apply (zenon_L186_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.29 apply (zenon_L1647_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.12/22.29 apply (zenon_L1649_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.12/22.29 apply (zenon_L965_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.12/22.29 apply (zenon_L1650_); trivial. % 22.12/22.29 apply (zenon_L1652_); trivial. % 22.12/22.29 (* end of lemma zenon_L1653_ *) % 22.12/22.29 assert (zenon_L1654_ : (((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)) = (e1)) -> (((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) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((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))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.29 do 0 intro. intros zenon_H13c zenon_H24 zenon_H159 zenon_H4d zenon_H141 zenon_He7 zenon_Hf0 zenon_H120 zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H12e zenon_H212 zenon_H1cb zenon_H1cd zenon_Hbc zenon_H231 zenon_H18a zenon_H7d zenon_H104 zenon_H1c2 zenon_H121 zenon_H33 zenon_H9f zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_H1c3 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha0 zenon_H195 zenon_H67 zenon_H2c zenon_H16a zenon_H196 zenon_H38. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.29 apply (zenon_L900_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.29 exact (zenon_H159 zenon_H10c). % 22.12/22.29 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.29 apply (zenon_L124_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.29 apply (zenon_L217_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.29 apply (zenon_L929_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.29 apply (zenon_L1644_); trivial. % 22.12/22.29 apply (zenon_L1162_); trivial. % 22.12/22.29 (* end of lemma zenon_L1654_ *) % 22.12/22.29 assert (zenon_L1655_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e2) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H26a zenon_Ha0 zenon_H38 zenon_H5d zenon_Ha6 zenon_H128 zenon_Hb6 zenon_Hc4. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H9e | zenon_intro zenon_H26b ]. % 22.12/22.29 apply (zenon_L156_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H26c ]. % 22.12/22.29 apply (zenon_L42_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc3 ]. % 22.12/22.29 apply (zenon_L182_); trivial. % 22.12/22.29 exact (zenon_Hc4 zenon_Hc3). % 22.12/22.29 (* end of lemma zenon_L1655_ *) % 22.12/22.29 assert (zenon_L1656_ : (((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 (e1) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H18d zenon_H48 zenon_H234 zenon_H3f zenon_Hc4 zenon_Hb6 zenon_Ha6 zenon_H5d zenon_H38 zenon_Ha0 zenon_H26a zenon_H120. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.12/22.29 apply (zenon_L246_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.12/22.29 apply (zenon_L484_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.12/22.29 apply (zenon_L1655_); trivial. % 22.12/22.29 exact (zenon_H120 zenon_H11f). % 22.12/22.29 (* end of lemma zenon_L1656_ *) % 22.12/22.29 assert (zenon_L1657_ : (((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 (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H18d zenon_H48 zenon_H234 zenon_H3f zenon_H1b7 zenon_H171 zenon_H77 zenon_Ha9 zenon_Ha5 zenon_H38 zenon_H68 zenon_H1c3 zenon_H120. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.12/22.29 apply (zenon_L246_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.12/22.29 apply (zenon_L484_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.12/22.29 apply (zenon_L1444_); trivial. % 22.12/22.29 exact (zenon_H120 zenon_H11f). % 22.12/22.29 (* end of lemma zenon_L1657_ *) % 22.12/22.29 assert (zenon_L1658_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (((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 (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.12/22.29 do 0 intro. intros zenon_H13c zenon_H26a zenon_H5d zenon_Hc4 zenon_Hb6 zenon_Ha0 zenon_Hf3 zenon_H18d zenon_H48 zenon_H234 zenon_H3f zenon_H1b7 zenon_H171 zenon_H77 zenon_Ha9 zenon_H38 zenon_H68 zenon_H1c3 zenon_H120. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.29 apply (zenon_L1656_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.29 apply (zenon_L216_); trivial. % 22.12/22.29 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.29 apply (zenon_L162_); trivial. % 22.12/22.29 apply (zenon_L1657_); trivial. % 22.12/22.29 (* end of lemma zenon_L1658_ *) % 22.12/22.29 assert (zenon_L1659_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (((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 (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.12/22.30 do 0 intro. intros zenon_H1a8 zenon_H3d zenon_H196 zenon_H117 zenon_H54 zenon_H141 zenon_H13c zenon_H26a zenon_H5d zenon_Hc4 zenon_Hb6 zenon_Ha0 zenon_Hf3 zenon_H18d zenon_H48 zenon_H234 zenon_H3f zenon_H1b7 zenon_H77 zenon_Ha9 zenon_H38 zenon_H68 zenon_H1c3 zenon_H120. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.30 apply (zenon_L214_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.30 apply (zenon_L186_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.30 apply (zenon_L1647_); trivial. % 22.12/22.30 apply (zenon_L1658_); trivial. % 22.12/22.30 (* end of lemma zenon_L1659_ *) % 22.12/22.30 assert (zenon_L1660_ : (~((op (e3) (e3)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 22.12/22.30 do 0 intro. intros zenon_H120 zenon_H54 zenon_H3d zenon_Hf3 zenon_Hb2 zenon_H24e zenon_H1f1 zenon_H23c zenon_H26a zenon_H104 zenon_H231 zenon_H2c zenon_H109 zenon_H11a zenon_H1c2 zenon_H1cd zenon_H111 zenon_He2 zenon_H12e zenon_H100 zenon_H22d zenon_H191 zenon_H125 zenon_H141 zenon_H201 zenon_H164 zenon_H212 zenon_Hbc zenon_H179 zenon_H288 zenon_H192 zenon_H183 zenon_H18a zenon_Hfa zenon_H13b zenon_H1a8 zenon_H24 zenon_H121 zenon_H33 zenon_Hf0 zenon_H1d5 zenon_H1fe zenon_H82 zenon_H177 zenon_H1d8 zenon_H234 zenon_H7d zenon_He4 zenon_Hc4 zenon_H26d zenon_H38 zenon_H4e zenon_H13f zenon_H77 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H140 zenon_H9f zenon_Ha0. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.12/22.30 apply (zenon_L69_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.12/22.30 apply (zenon_L1659_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.12/22.30 apply (zenon_L117_); trivial. % 22.12/22.30 apply (zenon_L1627_); trivial. % 22.12/22.30 (* end of lemma zenon_L1660_ *) % 22.12/22.30 assert (zenon_L1661_ : (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.30 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_H4d zenon_H141 zenon_H48 zenon_H68 zenon_H195 zenon_Ha0 zenon_H6d zenon_Ha9 zenon_H54 zenon_Hb6 zenon_H117 zenon_H196 zenon_H38. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.30 apply (zenon_L900_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.30 exact (zenon_H159 zenon_H10c). % 22.12/22.30 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.30 apply (zenon_L124_); trivial. % 22.12/22.30 apply (zenon_L1393_); trivial. % 22.12/22.30 (* end of lemma zenon_L1661_ *) % 22.12/22.30 assert (zenon_L1662_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (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)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((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)) = (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 (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 (e1) (e1)) = (e0)) -> False). % 22.12/22.30 do 0 intro. intros zenon_H1a8 zenon_H77 zenon_H1cd zenon_H191 zenon_H66 zenon_H1a2 zenon_H186 zenon_H190 zenon_H1a3 zenon_H1c6 zenon_Hf0 zenon_H38 zenon_H196 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_Ha0 zenon_H195 zenon_H68 zenon_H141 zenon_H159 zenon_H24 zenon_H9f zenon_H13c zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H4d zenon_H163 zenon_He7. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.12/22.30 apply (zenon_L214_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.12/22.30 apply (zenon_L900_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.12/22.30 exact (zenon_H159 zenon_H10c). % 22.12/22.30 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.12/22.30 apply (zenon_L1244_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.12/22.30 apply (zenon_L55_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.12/22.30 exact (zenon_H159 zenon_H10c). % 22.12/22.30 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.12/22.30 apply (zenon_L1173_); trivial. % 22.12/22.30 apply (zenon_L379_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.12/22.30 apply (zenon_L1661_); trivial. % 22.12/22.30 apply (zenon_L965_); trivial. % 22.12/22.30 (* end of lemma zenon_L1662_ *) % 22.12/22.30 assert (zenon_L1663_ : ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (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)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (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) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.12/22.30 do 0 intro. intros zenon_H34 zenon_H77 zenon_H54 zenon_H1a3 zenon_H209 zenon_H159 zenon_Ha0 zenon_H9f zenon_H140 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H13f zenon_H4e zenon_H26d zenon_Hc4 zenon_He4 zenon_H7d zenon_H234 zenon_H1d8 zenon_H177 zenon_H82 zenon_H1fe zenon_H1d5 zenon_Hf0 zenon_H33 zenon_H121 zenon_H24 zenon_H1a8 zenon_H13b zenon_Hfa zenon_H18a zenon_H183 zenon_H192 zenon_H288 zenon_H179 zenon_Hbc zenon_H212 zenon_H164 zenon_H201 zenon_H141 zenon_H125 zenon_H191 zenon_H22d zenon_H100 zenon_H12e zenon_He2 zenon_H111 zenon_H1cd zenon_H1c2 zenon_H11a zenon_H109 zenon_H2c zenon_H231 zenon_H104 zenon_H26a zenon_H23c zenon_H1f1 zenon_H24e zenon_Hb2 zenon_H3d zenon_H120 zenon_Hf5 zenon_H38 zenon_H68. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.12/22.30 apply (zenon_L297_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.12/22.30 apply (zenon_L69_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.12/22.30 apply (zenon_L1653_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.12/22.30 apply (zenon_L1654_); trivial. % 22.12/22.30 apply (zenon_L1436_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.12/22.30 apply (zenon_L1660_); trivial. % 22.12/22.30 apply (zenon_L663_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.12/22.30 apply (zenon_L214_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.12/22.30 apply (zenon_L252_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.12/22.30 apply (zenon_L171_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.12/22.30 apply (zenon_L69_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.12/22.30 apply (zenon_L1653_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.12/22.30 apply (zenon_L1662_); trivial. % 22.12/22.30 apply (zenon_L1436_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.12/22.30 apply (zenon_L1660_); trivial. % 22.12/22.30 apply (zenon_L663_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.12/22.30 apply (zenon_L30_); trivial. % 22.12/22.30 apply (zenon_L291_); trivial. % 22.12/22.30 apply (zenon_L165_); trivial. % 22.12/22.30 (* end of lemma zenon_L1663_ *) % 22.12/22.30 assert (zenon_L1664_ : (((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)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((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)) = (e1))) -> False). % 22.12/22.30 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H65 zenon_H53 zenon_H191 zenon_H12e zenon_H34 zenon_H1b7 zenon_H3c zenon_H5d zenon_H1cb zenon_Hb6 zenon_Hf7 zenon_H77 zenon_H38 zenon_H48 zenon_H18d zenon_H120. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.12/22.30 apply (zenon_L43_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.12/22.30 apply (zenon_L113_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.12/22.30 exact (zenon_H191 zenon_H110). % 22.12/22.30 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.12/22.30 apply (zenon_L456_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.12/22.30 apply (zenon_L1290_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.12/22.30 apply (zenon_L1278_); trivial. % 22.12/22.30 exact (zenon_H120 zenon_H11f). % 22.12/22.30 (* end of lemma zenon_L1664_ *) % 22.12/22.30 assert (zenon_L1665_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((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)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (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 (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (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)))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.12/22.30 do 0 intro. intros zenon_H16a zenon_H18d zenon_Hf7 zenon_H5d zenon_H1b7 zenon_H191 zenon_H120 zenon_H1c3 zenon_Hc4 zenon_H1a3 zenon_H183 zenon_H68 zenon_H20f zenon_H33 zenon_H121 zenon_H1c2 zenon_H14c zenon_H104 zenon_H7d zenon_H18a zenon_H231 zenon_Hbc zenon_H1cd zenon_H1cb zenon_H212 zenon_H12e zenon_Hfa zenon_H77 zenon_H24 zenon_H38 zenon_H196 zenon_H117 zenon_H9f zenon_H2c zenon_Hb6 zenon_H53 zenon_Ha0 zenon_H48 zenon_H109 zenon_H34 zenon_H141 zenon_Ha9 zenon_H159 zenon_H3c zenon_H13c zenon_H195. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.30 apply (zenon_L1664_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.30 apply (zenon_L56_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.30 apply (zenon_L1643_); trivial. % 22.12/22.30 apply (zenon_L1496_); trivial. % 22.12/22.30 (* end of lemma zenon_L1665_ *) % 22.12/22.30 assert (zenon_L1666_ : (((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 (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) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (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 (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.12/22.30 do 0 intro. intros zenon_H16a zenon_H2c zenon_H190 zenon_H13c zenon_H24 zenon_H159 zenon_H141 zenon_Ha0 zenon_H54 zenon_Hb6 zenon_H117 zenon_H196 zenon_H67 zenon_H1d5 zenon_H1cf zenon_H171 zenon_He7 zenon_H1c3 zenon_H38 zenon_Hc4 zenon_H1a3 zenon_H183 zenon_H68 zenon_H34 zenon_Ha9 zenon_H77 zenon_H20f zenon_H9f zenon_H33 zenon_H121 zenon_H1c2 zenon_H14c zenon_H104 zenon_H7d zenon_H18a zenon_H231 zenon_Hbc zenon_H1cd zenon_H1cb zenon_H212 zenon_H48 zenon_H12e zenon_Hf7 zenon_H195. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.12/22.30 apply (zenon_L180_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.12/22.30 apply (zenon_L1482_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.12/22.30 apply (zenon_L1411_); trivial. % 22.12/22.30 apply (zenon_L228_); trivial. % 22.12/22.30 (* end of lemma zenon_L1666_ *) % 22.12/22.30 assert (zenon_L1667_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((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)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (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) (e0)) = (op (e1) (e0)))) -> (~((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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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 (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.12/22.30 do 0 intro. intros zenon_H140 zenon_H1a2 zenon_H153 zenon_H186 zenon_Hf0 zenon_He7 zenon_H195 zenon_H13c zenon_H3c zenon_H159 zenon_Ha9 zenon_H141 zenon_H34 zenon_H109 zenon_H48 zenon_Ha0 zenon_H53 zenon_Hb6 zenon_H2c zenon_H9f zenon_H117 zenon_H24 zenon_H77 zenon_Hfa zenon_H12e zenon_H212 zenon_H1cb zenon_H1cd zenon_Hbc zenon_H231 zenon_H18a zenon_H7d zenon_H104 zenon_H1c2 zenon_H121 zenon_H33 zenon_H20f zenon_H68 zenon_H183 zenon_H1a3 zenon_Hc4 zenon_H1c3 zenon_H120 zenon_H191 zenon_H1b7 zenon_H5d zenon_H18d zenon_H16a zenon_H196 zenon_H38. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.30 apply (zenon_L24_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.30 apply (zenon_L1316_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.30 apply (zenon_L1478_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.12/22.30 apply (zenon_L359_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.12/22.30 apply (zenon_L111_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.12/22.30 apply (zenon_L1665_); trivial. % 22.12/22.30 apply (zenon_L1162_); trivial. % 22.12/22.30 (* end of lemma zenon_L1667_ *) % 22.12/22.30 assert (zenon_L1668_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((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))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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 (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 22.12/22.30 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H177 zenon_H11a zenon_H16a zenon_H120 zenon_H1c3 zenon_H183 zenon_H68 zenon_H20f zenon_H33 zenon_H1c2 zenon_H104 zenon_H7d zenon_H18a zenon_H231 zenon_H1cb zenon_H212 zenon_H12e zenon_H117 zenon_H2c zenon_H195 zenon_Hfa zenon_H77 zenon_Hbc zenon_H140 zenon_H196 zenon_H1a3 zenon_Hf0 zenon_He7 zenon_H109 zenon_H34 zenon_H141 zenon_H24 zenon_H9f zenon_H13c zenon_H159 zenon_Hc4 zenon_H163 zenon_H26a zenon_Ha0 zenon_H1cd zenon_H191 zenon_H186 zenon_H153 zenon_H1a2 zenon_H1b7 zenon_Hb6 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_H209 zenon_H121 zenon_Ha9. % 22.12/22.30 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.12/22.30 apply (zenon_L738_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.12/22.30 apply (zenon_L1648_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.12/22.30 apply (zenon_L1667_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.12/22.30 apply (zenon_L24_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.12/22.30 apply (zenon_L1316_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.12/22.30 apply (zenon_L1478_); trivial. % 22.12/22.30 apply (zenon_L1492_); trivial. % 22.12/22.30 (* end of lemma zenon_L1668_ *) % 22.12/22.30 assert (zenon_L1669_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.12/22.30 do 0 intro. intros zenon_H1a2 zenon_H67 zenon_Ha0 zenon_Hf3 zenon_Hb6 zenon_H105 zenon_Hac zenon_H1cd. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.12/22.30 apply (zenon_L446_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.12/22.30 apply (zenon_L162_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.12/22.30 apply (zenon_L400_); trivial. % 22.12/22.30 apply (zenon_L360_); trivial. % 22.12/22.30 (* end of lemma zenon_L1669_ *) % 22.12/22.30 assert (zenon_L1670_ : (((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 (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e1)) -> False). % 22.12/22.30 do 0 intro. intros zenon_H117 zenon_H9f zenon_H2c zenon_Ha0 zenon_Hdd zenon_H191 zenon_Hb6 zenon_H128. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.12/22.30 apply (zenon_L1065_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.12/22.30 apply (zenon_L152_); trivial. % 22.12/22.30 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.12/22.30 exact (zenon_H191 zenon_H110). % 22.12/22.30 apply (zenon_L182_); trivial. % 22.12/22.30 (* end of lemma zenon_L1670_ *) % 22.12/22.30 assert (zenon_L1671_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (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)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (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) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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)))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> False). % 22.22/22.30 do 0 intro. intros zenon_H140 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H16a zenon_H1cb zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H77 zenon_H13f zenon_H4e zenon_H26d zenon_Hc4 zenon_He4 zenon_H7d zenon_H234 zenon_H1d8 zenon_H177 zenon_H82 zenon_H1fe zenon_H1d5 zenon_Hf0 zenon_H33 zenon_H121 zenon_H24 zenon_H1a8 zenon_H13b zenon_Hfa zenon_H18a zenon_H183 zenon_H192 zenon_H288 zenon_H179 zenon_Hbc zenon_H212 zenon_H164 zenon_H201 zenon_H125 zenon_H22d zenon_H100 zenon_H12e zenon_He2 zenon_H111 zenon_H1c2 zenon_H11a zenon_H231 zenon_H104 zenon_H26a zenon_H23c zenon_H1f1 zenon_H24e zenon_Hb2 zenon_H3d zenon_H120 zenon_H38 zenon_H196 zenon_Ha5 zenon_H195 zenon_H48 zenon_H109 zenon_H34 zenon_H141 zenon_H1cd zenon_Hac zenon_Hf3 zenon_H67 zenon_H1a2 zenon_H117 zenon_H9f zenon_H2c zenon_Ha0 zenon_Hdd zenon_H191 zenon_Hb6. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.30 apply (zenon_L1660_); trivial. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.30 apply (zenon_L1404_); trivial. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.30 apply (zenon_L1669_); trivial. % 22.22/22.30 apply (zenon_L1670_); trivial. % 22.22/22.30 (* end of lemma zenon_L1671_ *) % 22.22/22.30 assert (zenon_L1672_ : (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (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)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (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) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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)))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> False). % 22.22/22.30 do 0 intro. intros zenon_H159 zenon_H140 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H16a zenon_H1cb zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H77 zenon_H13f zenon_H4e zenon_H26d zenon_Hc4 zenon_He4 zenon_H7d zenon_H234 zenon_H1d8 zenon_H177 zenon_H82 zenon_H1fe zenon_H1d5 zenon_Hf0 zenon_H33 zenon_H121 zenon_H24 zenon_H1a8 zenon_H13b zenon_Hfa zenon_H18a zenon_H183 zenon_H192 zenon_H288 zenon_H179 zenon_Hbc zenon_H212 zenon_H164 zenon_H201 zenon_H125 zenon_H22d zenon_H100 zenon_H12e zenon_He2 zenon_H111 zenon_H1c2 zenon_H11a zenon_H231 zenon_H104 zenon_H26a zenon_H23c zenon_H1f1 zenon_H24e zenon_Hb2 zenon_H3d zenon_H120 zenon_H38 zenon_H196 zenon_Ha5 zenon_H195 zenon_H48 zenon_H109 zenon_H34 zenon_H141 zenon_H1cd zenon_Hf3 zenon_H67 zenon_H1a2 zenon_H117 zenon_H9f zenon_H2c zenon_Ha0 zenon_Hdd zenon_H191 zenon_Hb6. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.30 apply (zenon_L55_); trivial. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.30 exact (zenon_H159 zenon_H10c). % 22.22/22.30 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.30 apply (zenon_L152_); trivial. % 22.22/22.30 apply (zenon_L1671_); trivial. % 22.22/22.30 (* end of lemma zenon_L1672_ *) % 22.22/22.30 assert (zenon_L1673_ : (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (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)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (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) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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)))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> False). % 22.22/22.30 do 0 intro. intros zenon_H159 zenon_H140 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H16a zenon_H1cb zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H77 zenon_H13f zenon_H4e zenon_H26d zenon_Hc4 zenon_He4 zenon_H7d zenon_H234 zenon_H1d8 zenon_H177 zenon_H82 zenon_H1fe zenon_H1d5 zenon_Hf0 zenon_H33 zenon_H121 zenon_H24 zenon_H1a8 zenon_H13b zenon_Hfa zenon_H18a zenon_H183 zenon_H192 zenon_H288 zenon_H179 zenon_Hbc zenon_H212 zenon_H164 zenon_H201 zenon_H125 zenon_H22d zenon_H100 zenon_H12e zenon_He2 zenon_H111 zenon_H1c2 zenon_H11a zenon_H231 zenon_H104 zenon_H26a zenon_H23c zenon_H1f1 zenon_H24e zenon_Hb2 zenon_H3d zenon_H120 zenon_H38 zenon_H196 zenon_H195 zenon_H48 zenon_H109 zenon_H34 zenon_H141 zenon_H1cd zenon_Hf3 zenon_H67 zenon_H1a2 zenon_H117 zenon_H9f zenon_H2c zenon_Ha0 zenon_Hdd zenon_H191 zenon_Hb6. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.30 apply (zenon_L900_); trivial. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.30 exact (zenon_H159 zenon_H10c). % 22.22/22.30 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.30 apply (zenon_L162_); trivial. % 22.22/22.30 apply (zenon_L1672_); trivial. % 22.22/22.30 (* end of lemma zenon_L1673_ *) % 22.22/22.30 assert (zenon_L1674_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.22/22.30 do 0 intro. intros zenon_H183 zenon_H68 zenon_H34 zenon_Hac zenon_Ha9 zenon_H8a zenon_H104 zenon_H181. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.22/22.30 apply (zenon_L291_); trivial. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.22/22.30 apply (zenon_L371_); trivial. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.22/22.30 apply (zenon_L231_); trivial. % 22.22/22.30 exact (zenon_H181 zenon_H17c). % 22.22/22.30 (* end of lemma zenon_L1674_ *) % 22.22/22.30 assert (zenon_L1675_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.22/22.30 do 0 intro. intros zenon_H1c6 zenon_H6e zenon_H159 zenon_H16a zenon_Hf7 zenon_Hb6 zenon_H1cb zenon_H5d zenon_H3c zenon_H1b7 zenon_H12e zenon_H191 zenon_H117 zenon_H53 zenon_H181 zenon_H104 zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H120. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.30 apply (zenon_L110_); trivial. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.30 exact (zenon_H159 zenon_H10c). % 22.22/22.30 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.30 apply (zenon_L113_); trivial. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.22/22.30 apply (zenon_L1664_); trivial. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.22/22.30 apply (zenon_L56_); trivial. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.22/22.30 apply (zenon_L1674_); trivial. % 22.22/22.30 apply (zenon_L555_); trivial. % 22.22/22.30 (* end of lemma zenon_L1675_ *) % 22.22/22.30 assert (zenon_L1676_ : (((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)))) -> (~((e0) = (e3))) -> (~((e1) = (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) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.22/22.30 do 0 intro. intros zenon_H13f zenon_H3c zenon_H100 zenon_H195 zenon_Ha0 zenon_Hb6 zenon_H2c zenon_H9f zenon_H117 zenon_H48 zenon_H14c zenon_H183 zenon_H34 zenon_H1b7 zenon_H77 zenon_Ha9 zenon_Ha5 zenon_H38 zenon_H68 zenon_H1c3 zenon_H72 zenon_H163 zenon_H181. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.30 apply (zenon_L69_); trivial. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.30 apply (zenon_L1403_); trivial. % 22.22/22.30 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.30 apply (zenon_L255_); trivial. % 22.22/22.30 apply (zenon_L1633_); trivial. % 22.22/22.30 (* end of lemma zenon_L1676_ *) % 22.22/22.30 assert (zenon_L1677_ : (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (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)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (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) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.22/22.31 do 0 intro. intros zenon_H181 zenon_H159 zenon_H209 zenon_H36 zenon_Ha0 zenon_H9f zenon_H140 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H77 zenon_H13f zenon_H4e zenon_H38 zenon_H26d zenon_Hc4 zenon_He4 zenon_H7d zenon_H234 zenon_H1d8 zenon_H177 zenon_H82 zenon_H1fe zenon_H1d5 zenon_Hf0 zenon_H33 zenon_H121 zenon_H24 zenon_H1a8 zenon_H13b zenon_Hfa zenon_H18a zenon_H183 zenon_H192 zenon_H288 zenon_H179 zenon_Hbc zenon_H212 zenon_H164 zenon_H201 zenon_H141 zenon_H125 zenon_H191 zenon_H22d zenon_H100 zenon_H12e zenon_He2 zenon_H111 zenon_H1cd zenon_H1c2 zenon_H11a zenon_H109 zenon_H2c zenon_H231 zenon_H104 zenon_H26a zenon_H23c zenon_H1f1 zenon_H24e zenon_Hb2 zenon_H153 zenon_H120 zenon_H34 zenon_H48. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.31 apply (zenon_L1284_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.31 apply (zenon_L25_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.22/22.31 apply (zenon_L738_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.22/22.31 apply (zenon_L1648_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.31 apply (zenon_L24_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.31 apply (zenon_L1405_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.31 apply (zenon_L1473_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.31 apply (zenon_L1675_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.31 apply (zenon_L1455_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.31 apply (zenon_L56_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.31 apply (zenon_L46_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.31 exact (zenon_H159 zenon_H10c). % 22.22/22.31 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.22/22.31 apply (zenon_L1664_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.22/22.31 apply (zenon_L56_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.22/22.31 apply (zenon_L1495_); trivial. % 22.22/22.31 apply (zenon_L1527_); trivial. % 22.22/22.31 apply (zenon_L299_); trivial. % 22.22/22.31 apply (zenon_L1493_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.22/22.31 apply (zenon_L317_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.22/22.31 apply (zenon_L1499_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.22/22.31 apply (zenon_L1673_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.22/22.31 apply (zenon_L1648_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.22/22.31 apply (zenon_L111_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.31 apply (zenon_L900_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.31 exact (zenon_H159 zenon_H10c). % 22.22/22.31 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.31 apply (zenon_L1491_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.31 apply (zenon_L1649_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.31 apply (zenon_L1404_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.31 apply (zenon_L148_); trivial. % 22.22/22.31 apply (zenon_L1670_); trivial. % 22.22/22.31 apply (zenon_L802_); trivial. % 22.22/22.31 apply (zenon_L422_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.22/22.31 apply (zenon_L738_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.22/22.31 apply (zenon_L492_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.31 apply (zenon_L24_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.31 apply (zenon_L1405_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.31 apply (zenon_L1473_); trivial. % 22.22/22.31 apply (zenon_L1675_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.31 apply (zenon_L24_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.31 apply (zenon_L226_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.31 apply (zenon_L46_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.31 exact (zenon_H159 zenon_H10c). % 22.22/22.31 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.31 apply (zenon_L1491_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.31 apply (zenon_L110_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.31 exact (zenon_H159 zenon_H10c). % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.31 apply (zenon_L359_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.31 apply (zenon_L152_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.31 apply (zenon_L1676_); trivial. % 22.22/22.31 apply (zenon_L415_); trivial. % 22.22/22.31 apply (zenon_L1439_); trivial. % 22.22/22.31 apply (zenon_L1492_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.31 apply (zenon_L94_); trivial. % 22.22/22.31 apply (zenon_L165_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.31 apply (zenon_L1649_); trivial. % 22.22/22.31 apply (zenon_L456_); trivial. % 22.22/22.31 (* end of lemma zenon_L1677_ *) % 22.22/22.31 assert (zenon_L1678_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (((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)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> False). % 22.22/22.31 do 0 intro. intros zenon_Hcb zenon_H48 zenon_H34 zenon_H183 zenon_H8a zenon_H104 zenon_H77 zenon_H68 zenon_Hb6 zenon_H120 zenon_H12e zenon_Hbb. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.22/22.31 exact (zenon_H1a3 zenon_Hbb). % 22.22/22.31 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.22/22.31 apply (zenon_L456_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.22/22.31 apply (zenon_L420_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.22/22.31 apply (zenon_L363_); trivial. % 22.22/22.31 exact (zenon_H120 zenon_H11f). % 22.22/22.31 (* end of lemma zenon_L1678_ *) % 22.22/22.31 assert (zenon_L1679_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.22/22.31 do 0 intro. intros zenon_H121 zenon_H209 zenon_H181 zenon_Ha9 zenon_H12e zenon_H120 zenon_Hb6 zenon_H68 zenon_H77 zenon_H104 zenon_H8a zenon_H183 zenon_H34 zenon_H48 zenon_Hcb zenon_Hc4. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 22.22/22.31 exact (zenon_H209 zenon_H9d). % 22.22/22.31 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 22.22/22.31 apply (zenon_L1674_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 22.22/22.31 apply (zenon_L1678_); trivial. % 22.22/22.31 exact (zenon_Hc4 zenon_Hc3). % 22.22/22.31 (* end of lemma zenon_L1679_ *) % 22.22/22.31 assert (zenon_L1680_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (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) (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 (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.22/22.31 do 0 intro. intros zenon_Hb2 zenon_H24e zenon_H1f1 zenon_H23c zenon_H26a zenon_H231 zenon_H109 zenon_H11a zenon_H1c2 zenon_H1cd zenon_H111 zenon_He2 zenon_H100 zenon_H22d zenon_H125 zenon_H141 zenon_H201 zenon_H164 zenon_H212 zenon_Hbc zenon_H179 zenon_H288 zenon_H192 zenon_H18a zenon_Hfa zenon_H13b zenon_H1a8 zenon_H24 zenon_H33 zenon_Hf0 zenon_H1d5 zenon_H1fe zenon_H82 zenon_H177 zenon_H1d8 zenon_H234 zenon_H7d zenon_He4 zenon_H26d zenon_H13f zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H1fb zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H1cf zenon_H283 zenon_H140 zenon_Ha0 zenon_H36 zenon_H159 zenon_H4e zenon_H14c zenon_H16a zenon_H67 zenon_H3c zenon_H5d zenon_H191 zenon_H2c zenon_H9f zenon_H117 zenon_Hcb zenon_H34 zenon_H183 zenon_H104 zenon_H68 zenon_Hb6 zenon_H120 zenon_H12e zenon_Ha9 zenon_H181 zenon_H209 zenon_H121 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H1cb. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.22/22.31 apply (zenon_L1677_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.22/22.31 apply (zenon_L14_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.22/22.31 apply (zenon_L255_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.22/22.31 apply (zenon_L180_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.22/22.31 apply (zenon_L1152_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.22/22.31 apply (zenon_L1679_); trivial. % 22.22/22.31 apply (zenon_L1159_); trivial. % 22.22/22.31 (* end of lemma zenon_L1680_ *) % 22.22/22.31 assert (zenon_L1681_ : ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (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 (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (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 (e3) (e1)) = (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) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (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) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.22/22.31 do 0 intro. intros zenon_H10d zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H121 zenon_H209 zenon_H181 zenon_Ha9 zenon_H12e zenon_H120 zenon_Hb6 zenon_H68 zenon_H104 zenon_H183 zenon_H34 zenon_Hcb zenon_H117 zenon_H9f zenon_H2c zenon_H191 zenon_H5d zenon_H3c zenon_H67 zenon_H16a zenon_H4e zenon_H159 zenon_H36 zenon_Ha0 zenon_H140 zenon_H283 zenon_H1cf zenon_H163 zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H1fb zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H13f zenon_H26d zenon_He4 zenon_H7d zenon_H234 zenon_H1d8 zenon_H177 zenon_H82 zenon_H1fe zenon_H1d5 zenon_Hf0 zenon_H33 zenon_H24 zenon_H1a8 zenon_H13b zenon_Hfa zenon_H18a zenon_H192 zenon_H288 zenon_H179 zenon_Hbc zenon_H212 zenon_H164 zenon_H201 zenon_H141 zenon_H125 zenon_H22d zenon_H100 zenon_He2 zenon_H111 zenon_H1cd zenon_H1c2 zenon_H11a zenon_H109 zenon_H231 zenon_H26a zenon_H23c zenon_H1f1 zenon_H24e zenon_Hb2 zenon_H196 zenon_H38. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.31 apply (zenon_L359_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.31 apply (zenon_L152_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.31 apply (zenon_L1680_); trivial. % 22.22/22.31 apply (zenon_L1162_); trivial. % 22.22/22.31 (* end of lemma zenon_L1681_ *) % 22.22/22.31 assert (zenon_L1682_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.22/22.31 do 0 intro. intros zenon_H16a zenon_H2c zenon_H67 zenon_H3f zenon_H234 zenon_Ha0 zenon_H14c zenon_H54 zenon_H117 zenon_Hcb zenon_H34 zenon_H183 zenon_H104 zenon_H68 zenon_Hb6 zenon_H120 zenon_H12e zenon_Ha9 zenon_H181 zenon_H209 zenon_H121 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H106 zenon_H1cb. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.22/22.31 apply (zenon_L180_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.22/22.31 apply (zenon_L1646_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.22/22.31 apply (zenon_L1679_); trivial. % 22.22/22.31 apply (zenon_L1159_); trivial. % 22.22/22.31 (* end of lemma zenon_L1682_ *) % 22.22/22.31 assert (zenon_L1683_ : ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (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) (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 (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (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 (e0) (e0)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 22.22/22.31 do 0 intro. intros zenon_H3d zenon_Hc4 zenon_H181 zenon_H120 zenon_H129 zenon_H1bb zenon_Hb2 zenon_H24e zenon_H1f1 zenon_H23c zenon_H26a zenon_H231 zenon_H109 zenon_H11a zenon_H1c2 zenon_H1cd zenon_H111 zenon_He2 zenon_H100 zenon_H22d zenon_H191 zenon_H125 zenon_H141 zenon_H201 zenon_H164 zenon_H212 zenon_Hbc zenon_H179 zenon_H288 zenon_H192 zenon_H18a zenon_Hfa zenon_H13b zenon_H1a8 zenon_H24 zenon_H33 zenon_Hf0 zenon_H1d5 zenon_H1fe zenon_H82 zenon_H177 zenon_H1d8 zenon_H7d zenon_He4 zenon_H26d zenon_H4e zenon_H13f zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H1cf zenon_H283 zenon_H140 zenon_H9f zenon_H36 zenon_H159 zenon_H133 zenon_H16a zenon_H2c zenon_H67 zenon_H3f zenon_H234 zenon_Ha0 zenon_H54 zenon_H117 zenon_Hcb zenon_H34 zenon_H183 zenon_H104 zenon_H68 zenon_Hb6 zenon_H12e zenon_H209 zenon_H121 zenon_H18d zenon_H48 zenon_H20f zenon_H1b4 zenon_H38 zenon_H77 zenon_H1cb zenon_Ha9 zenon_H171. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.31 apply (zenon_L55_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.31 exact (zenon_H159 zenon_H10c). % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.31 apply (zenon_L359_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.31 apply (zenon_L152_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.22/22.31 apply (zenon_L1677_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.22/22.31 apply (zenon_L124_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.22/22.31 apply (zenon_L255_); trivial. % 22.22/22.31 apply (zenon_L1682_); trivial. % 22.22/22.31 apply (zenon_L415_); trivial. % 22.22/22.31 apply (zenon_L371_); trivial. % 22.22/22.31 (* end of lemma zenon_L1683_ *) % 22.22/22.31 assert (zenon_L1684_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.22/22.31 do 0 intro. intros zenon_H12e zenon_H48 zenon_H181 zenon_H104 zenon_H8a zenon_H77 zenon_H34 zenon_H68 zenon_H183 zenon_H4d zenon_H163 zenon_H120. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.22/22.31 apply (zenon_L456_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.22/22.31 apply (zenon_L420_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.22/22.31 apply (zenon_L285_); trivial. % 22.22/22.31 exact (zenon_H120 zenon_H11f). % 22.22/22.31 (* end of lemma zenon_L1684_ *) % 22.22/22.31 assert (zenon_L1685_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 22.22/22.31 do 0 intro. intros zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_H93 zenon_H77 zenon_Hef zenon_He0. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.22/22.31 apply (zenon_L246_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.22/22.31 apply (zenon_L17_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.22/22.31 apply (zenon_L218_); trivial. % 22.22/22.31 apply (zenon_L662_); trivial. % 22.22/22.31 (* end of lemma zenon_L1685_ *) % 22.22/22.31 assert (zenon_L1686_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.31 do 0 intro. intros zenon_H24e zenon_Hef zenon_H77 zenon_H93 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_H1b7 zenon_H11f zenon_H1cd zenon_H160 zenon_H1c7. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_He0 | zenon_intro zenon_H24f ]. % 22.22/22.31 apply (zenon_L1685_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H7f | zenon_intro zenon_H250 ]. % 22.22/22.31 apply (zenon_L780_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H171 | zenon_intro zenon_Hac ]. % 22.22/22.31 apply (zenon_L240_); trivial. % 22.22/22.31 exact (zenon_H1c7 zenon_Hac). % 22.22/22.31 (* end of lemma zenon_L1686_ *) % 22.22/22.31 assert (zenon_L1687_ : (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.31 do 0 intro. intros zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H53 zenon_H189 zenon_H24e zenon_Hef zenon_H77 zenon_H93 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_H1b7 zenon_H1cd zenon_H160 zenon_H1c7. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.22/22.31 apply (zenon_L246_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.22/22.31 apply (zenon_L413_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.22/22.31 apply (zenon_L139_); trivial. % 22.22/22.31 apply (zenon_L1686_); trivial. % 22.22/22.31 (* end of lemma zenon_L1687_ *) % 22.22/22.31 assert (zenon_L1688_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (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 (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.31 do 0 intro. intros zenon_H1cf zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Ha9 zenon_H1a2 zenon_H201 zenon_Hf3 zenon_H68 zenon_H1c2 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H53 zenon_H189 zenon_H24e zenon_Hef zenon_H77 zenon_H93 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_H1b7 zenon_H1cd zenon_H1c7. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.22/22.31 apply (zenon_L365_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.22/22.31 apply (zenon_L62_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.22/22.31 apply (zenon_L207_); trivial. % 22.22/22.31 apply (zenon_L1687_); trivial. % 22.22/22.31 (* end of lemma zenon_L1688_ *) % 22.22/22.31 assert (zenon_L1689_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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 (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.22/22.31 do 0 intro. intros zenon_Hfa zenon_He0 zenon_H77 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_Hf3 zenon_H68 zenon_H93 zenon_H195. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.31 apply (zenon_L24_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.31 apply (zenon_L1685_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.31 apply (zenon_L62_); trivial. % 22.22/22.31 apply (zenon_L228_); trivial. % 22.22/22.31 (* end of lemma zenon_L1689_ *) % 22.22/22.31 assert (zenon_L1690_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((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 (e0) (e3)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e1)) = (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) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((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 (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 22.22/22.31 do 0 intro. intros zenon_H1a8 zenon_Hc4 zenon_H1c7 zenon_H13a zenon_H33 zenon_H38 zenon_H121 zenon_H77 zenon_H3f zenon_H189 zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H1cd zenon_H1c2 zenon_H1a2 zenon_Hb6 zenon_H153 zenon_Ha9 zenon_Ha0 zenon_H1a3 zenon_H67 zenon_H1d5 zenon_H1cf zenon_H68 zenon_H93. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.31 apply (zenon_L1409_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.31 apply (zenon_L186_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.31 apply (zenon_L439_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.31 apply (zenon_L359_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.31 apply (zenon_L929_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.31 apply (zenon_L1171_); trivial. % 22.22/22.31 apply (zenon_L158_); trivial. % 22.22/22.31 (* end of lemma zenon_L1690_ *) % 22.22/22.31 assert (zenon_L1691_ : (((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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (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) (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) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (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 (e3) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (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 (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((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)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.22/22.31 do 0 intro. intros zenon_H288 zenon_H164 zenon_H212 zenon_H1fe zenon_Hb2 zenon_H125 zenon_H140 zenon_Hbc zenon_H231 zenon_H104 zenon_H18a zenon_H192 zenon_H12e zenon_H7d zenon_H24e zenon_H1f1 zenon_H183 zenon_H234 zenon_H26a zenon_H11a zenon_H177 zenon_H111 zenon_H13f zenon_H34 zenon_Hf5 zenon_He2 zenon_H36 zenon_H141 zenon_Hf0 zenon_H1c2 zenon_H201 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_Hfa zenon_H1cd zenon_H1d5 zenon_H159 zenon_H24 zenon_H1a8 zenon_H100 zenon_H9f zenon_H109 zenon_H179 zenon_H13b zenon_Hc4 zenon_H1a3 zenon_H1c7 zenon_H13a zenon_H33 zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H121 zenon_H77 zenon_H93 zenon_H196 zenon_He4 zenon_H1d8 zenon_H23c zenon_H2c zenon_H82 zenon_H38 zenon_H48. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.31 apply (zenon_L253_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.31 apply (zenon_L253_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.31 apply (zenon_L297_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.31 apply (zenon_L24_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.31 apply (zenon_L1406_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.31 apply (zenon_L214_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.31 apply (zenon_L100_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.31 apply (zenon_L439_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.31 apply (zenon_L55_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.31 exact (zenon_H159 zenon_H10c). % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.31 apply (zenon_L359_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.31 apply (zenon_L152_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.31 apply (zenon_L1172_); trivial. % 22.22/22.31 apply (zenon_L1162_); trivial. % 22.22/22.31 exact (zenon_H1c7 zenon_Hac). % 22.22/22.31 apply (zenon_L228_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.22/22.31 apply (zenon_L65_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.31 apply (zenon_L24_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.31 apply (zenon_L55_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.31 exact (zenon_H159 zenon_H10c). % 22.22/22.31 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.31 apply (zenon_L359_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.31 apply (zenon_L152_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.31 apply (zenon_L1237_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.31 apply (zenon_L1688_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.31 apply (zenon_L255_); trivial. % 22.22/22.31 apply (zenon_L218_); trivial. % 22.22/22.31 apply (zenon_L158_); trivial. % 22.22/22.31 exact (zenon_H1c7 zenon_Hac). % 22.22/22.31 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.31 apply (zenon_L62_); trivial. % 22.22/22.31 apply (zenon_L228_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.22/22.31 apply (zenon_L1242_); trivial. % 22.22/22.31 apply (zenon_L1689_); trivial. % 22.22/22.31 apply (zenon_L663_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.31 apply (zenon_L214_); trivial. % 22.22/22.31 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.32 apply (zenon_L1247_); trivial. % 22.22/22.32 apply (zenon_L165_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.32 apply (zenon_L1402_); trivial. % 22.22/22.32 apply (zenon_L456_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.32 apply (zenon_L1284_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.32 apply (zenon_L1523_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.32 apply (zenon_L297_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.32 apply (zenon_L69_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.32 apply (zenon_L1690_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.32 apply (zenon_L184_); trivial. % 22.22/22.32 apply (zenon_L1236_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.22/22.32 apply (zenon_L316_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.32 apply (zenon_L69_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.32 apply (zenon_L1409_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.32 apply (zenon_L186_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.32 apply (zenon_L439_); trivial. % 22.22/22.32 apply (zenon_L1239_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.32 apply (zenon_L117_); trivial. % 22.22/22.32 apply (zenon_L1241_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.22/22.32 apply (zenon_L1529_); trivial. % 22.22/22.32 apply (zenon_L1401_); trivial. % 22.22/22.32 apply (zenon_L663_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.32 apply (zenon_L1409_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.32 apply (zenon_L94_); trivial. % 22.22/22.32 apply (zenon_L167_); trivial. % 22.22/22.32 apply (zenon_L456_); trivial. % 22.22/22.32 apply (zenon_L246_); trivial. % 22.22/22.32 (* end of lemma zenon_L1691_ *) % 22.22/22.32 assert (zenon_L1692_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (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)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.32 do 0 intro. intros zenon_H1c6 zenon_H159 zenon_H38 zenon_H196 zenon_H201 zenon_H6f zenon_H183 zenon_H68 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H181 zenon_H1d8 zenon_H13a zenon_H25e zenon_H1fb zenon_Ha9 zenon_H1c3 zenon_Ha0 zenon_Hb6 zenon_Ha5 zenon_Hf5 zenon_H288 zenon_H11a zenon_H3f zenon_H36 zenon_H231 zenon_H104 zenon_H18a zenon_Hbc zenon_H186 zenon_H1a2 zenon_H171 zenon_He7 zenon_H163 zenon_H192 zenon_H3d zenon_H34 zenon_H12e zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H1cb zenon_H54 zenon_H141 zenon_H1c7. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.32 apply (zenon_L55_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.32 exact (zenon_H159 zenon_H10c). % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.32 apply (zenon_L217_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.32 apply (zenon_L152_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.22/22.32 apply (zenon_L1520_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.22/22.32 apply (zenon_L965_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.22/22.32 apply (zenon_L255_); trivial. % 22.22/22.32 apply (zenon_L1159_); trivial. % 22.22/22.32 apply (zenon_L1162_); trivial. % 22.22/22.32 exact (zenon_H1c7 zenon_Hac). % 22.22/22.32 (* end of lemma zenon_L1692_ *) % 22.22/22.32 assert (zenon_L1693_ : ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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 (e3) (e3)) = (e2))) -> False). % 22.22/22.32 do 0 intro. intros zenon_Hbb zenon_Hb6 zenon_H183 zenon_H68 zenon_He7 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H163 zenon_H4d zenon_H192 zenon_H3d zenon_H48 zenon_H12e zenon_H181. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.22/22.32 apply (zenon_L456_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.22/22.32 apply (zenon_L146_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.22/22.32 apply (zenon_L363_); trivial. % 22.22/22.32 apply (zenon_L1538_); trivial. % 22.22/22.32 (* end of lemma zenon_L1693_ *) % 22.22/22.32 assert (zenon_L1694_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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 (e3) (e3)) = (e2))) -> False). % 22.22/22.32 do 0 intro. intros zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hef zenon_H14c zenon_Hc4 zenon_H104 zenon_H209 zenon_H121 zenon_Hb6 zenon_H183 zenon_H68 zenon_He7 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H163 zenon_H4d zenon_H192 zenon_H3d zenon_H48 zenon_H12e zenon_H181. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.22/22.32 apply (zenon_L193_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.22/22.32 apply (zenon_L265_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.22/22.32 apply (zenon_L815_); trivial. % 22.22/22.32 apply (zenon_L1693_); trivial. % 22.22/22.32 (* end of lemma zenon_L1694_ *) % 22.22/22.32 assert (zenon_L1695_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.32 do 0 intro. intros zenon_H1c6 zenon_H159 zenon_H93 zenon_H68 zenon_H1cf zenon_H181 zenon_H3d zenon_H192 zenon_H163 zenon_He7 zenon_H183 zenon_Hb6 zenon_H121 zenon_H209 zenon_H104 zenon_Hef zenon_Ha9 zenon_H1a2 zenon_H4d zenon_H1c2 zenon_H12e zenon_H77 zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_Ha0 zenon_H13f zenon_H131 zenon_H141 zenon_H1c7. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.32 apply (zenon_L55_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.32 exact (zenon_H159 zenon_H10c). % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.32 apply (zenon_L825_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.32 apply (zenon_L152_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.22/22.32 apply (zenon_L1694_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.22/22.32 apply (zenon_L59_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.22/22.32 apply (zenon_L207_); trivial. % 22.22/22.32 apply (zenon_L1510_); trivial. % 22.22/22.32 apply (zenon_L158_); trivial. % 22.22/22.32 exact (zenon_H1c7 zenon_Hac). % 22.22/22.32 (* end of lemma zenon_L1695_ *) % 22.22/22.32 assert (zenon_L1696_ : ((op (e2) (e0)) = (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) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (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 (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (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 (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (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) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 22.22/22.32 do 0 intro. intros zenon_H54 zenon_Hbc zenon_H231 zenon_H36 zenon_H11a zenon_H288 zenon_H1d8 zenon_H201 zenon_He2 zenon_Hf0 zenon_H111 zenon_He4 zenon_H23c zenon_H109 zenon_H2c zenon_Hfa zenon_H67 zenon_H1d5 zenon_H24 zenon_H9f zenon_H100 zenon_H13b zenon_H179 zenon_He7 zenon_H192 zenon_H3d zenon_H34 zenon_H12e zenon_H159 zenon_H181 zenon_H183 zenon_H121 zenon_H209 zenon_H104 zenon_H1c2 zenon_Hc4 zenon_H18a zenon_H24e zenon_H7d zenon_H1cd zenon_H13f zenon_H141 zenon_H1c7 zenon_H1a8 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H129 zenon_H93 zenon_H1bb. % 22.22/22.32 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.32 apply (zenon_L69_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.32 apply (zenon_L214_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.32 apply (zenon_L186_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.32 apply (zenon_L439_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.32 apply (zenon_L900_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.32 exact (zenon_H159 zenon_H10c). % 22.22/22.32 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.32 apply (zenon_L55_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.32 exact (zenon_H159 zenon_H10c). % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.32 apply (zenon_L217_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.32 apply (zenon_L152_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.32 apply (zenon_L1531_); trivial. % 22.22/22.32 apply (zenon_L1162_); trivial. % 22.22/22.32 exact (zenon_H1c7 zenon_Hac). % 22.22/22.32 apply (zenon_L1692_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.32 apply (zenon_L214_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.32 apply (zenon_L1695_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.32 apply (zenon_L439_); trivial. % 22.22/22.32 apply (zenon_L965_); trivial. % 22.22/22.32 apply (zenon_L1236_); trivial. % 22.22/22.32 (* end of lemma zenon_L1696_ *) % 22.22/22.32 assert (zenon_L1697_ : ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (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) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((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) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (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 (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (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)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (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)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.32 do 0 intro. intros zenon_H93 zenon_H68 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H139 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H1a8 zenon_H13f zenon_H1cd zenon_H7d zenon_H24e zenon_H18a zenon_Hc4 zenon_H1c2 zenon_H104 zenon_H209 zenon_H121 zenon_H183 zenon_H181 zenon_H12e zenon_H3d zenon_H192 zenon_He7 zenon_H179 zenon_H13b zenon_H100 zenon_H1d5 zenon_H67 zenon_Hfa zenon_H23c zenon_He4 zenon_H111 zenon_Hf0 zenon_He2 zenon_H201 zenon_H1d8 zenon_H288 zenon_H11a zenon_H36 zenon_H231 zenon_Hbc zenon_H38 zenon_H196 zenon_H117 zenon_H9f zenon_H2c zenon_Hb6 zenon_Ha0 zenon_H195 zenon_H109 zenon_H34 zenon_H141 zenon_Hef zenon_H159 zenon_H24 zenon_H13c zenon_H48 zenon_H77 zenon_H1c7. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.32 apply (zenon_L55_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.32 exact (zenon_H159 zenon_H10c). % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.32 apply (zenon_L359_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.32 apply (zenon_L152_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.32 apply (zenon_L1696_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.32 apply (zenon_L1405_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.32 apply (zenon_L255_); trivial. % 22.22/22.32 apply (zenon_L218_); trivial. % 22.22/22.32 apply (zenon_L158_); trivial. % 22.22/22.32 exact (zenon_H1c7 zenon_Hac). % 22.22/22.32 (* end of lemma zenon_L1697_ *) % 22.22/22.32 assert (zenon_L1698_ : (~((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) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (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 (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e3) (e0)) = (e3))) -> (~((op (e2) (e2)) = (op (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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((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 (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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 (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (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) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.22/22.32 do 0 intro. intros zenon_Hbc zenon_H231 zenon_H11a zenon_H288 zenon_H1d8 zenon_H111 zenon_He4 zenon_H23c zenon_H109 zenon_H2c zenon_Hfa zenon_H24 zenon_H9f zenon_H179 zenon_H18a zenon_H34 zenon_H93 zenon_H94 zenon_H13b zenon_H181 zenon_Hc4 zenon_H13f zenon_H24e zenon_H183 zenon_H121 zenon_H209 zenon_H104 zenon_H12e zenon_H192 zenon_H7d zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_Ha0 zenon_H1c7 zenon_H100 zenon_H201 zenon_H1c2 zenon_H1cd zenon_Hf0 zenon_H54 zenon_H141 zenon_H1a8 zenon_H36 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_H186 zenon_H25b zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_He2 zenon_Hf5 zenon_H1d5 zenon_H125 zenon_H38 zenon_H68. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.32 apply (zenon_L297_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.32 apply (zenon_L1696_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.32 apply (zenon_L1243_); trivial. % 22.22/22.32 apply (zenon_L663_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.32 apply (zenon_L214_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.22/22.32 apply (zenon_L252_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.32 apply (zenon_L171_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.32 apply (zenon_L24_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.32 apply (zenon_L214_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.32 apply (zenon_L186_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.32 apply (zenon_L439_); trivial. % 22.22/22.32 apply (zenon_L1246_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.32 apply (zenon_L214_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.32 apply (zenon_L55_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.32 exact (zenon_H159 zenon_H10c). % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.32 apply (zenon_L825_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.32 apply (zenon_L1242_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.32 apply (zenon_L1694_); trivial. % 22.22/22.32 apply (zenon_L1162_); trivial. % 22.22/22.32 exact (zenon_H1c7 zenon_Hac). % 22.22/22.32 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.32 apply (zenon_L439_); trivial. % 22.22/22.32 apply (zenon_L965_); trivial. % 22.22/22.32 apply (zenon_L414_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.32 apply (zenon_L1243_); trivial. % 22.22/22.32 apply (zenon_L663_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.22/22.32 apply (zenon_L38_); trivial. % 22.22/22.32 apply (zenon_L291_); trivial. % 22.22/22.32 apply (zenon_L165_); trivial. % 22.22/22.32 (* end of lemma zenon_L1698_ *) % 22.22/22.32 assert (zenon_L1699_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((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 (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.22/22.32 do 0 intro. intros zenon_H26a zenon_Ha0 zenon_H186 zenon_H133 zenon_H195 zenon_H93 zenon_H11f zenon_H20f zenon_Hf5 zenon_H38 zenon_H25b zenon_Hc4. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H9e | zenon_intro zenon_H26b ]. % 22.22/22.32 apply (zenon_L156_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H26c ]. % 22.22/22.32 apply (zenon_L308_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc3 ]. % 22.22/22.32 apply (zenon_L671_); trivial. % 22.22/22.32 exact (zenon_Hc4 zenon_Hc3). % 22.22/22.32 (* end of lemma zenon_L1699_ *) % 22.22/22.32 assert (zenon_L1700_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (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 (e1) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.22/22.32 do 0 intro. intros zenon_H12e zenon_H181 zenon_H18a zenon_H162 zenon_H1b7 zenon_H1cb zenon_H77 zenon_H1bb zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_H26a zenon_Ha0 zenon_H186 zenon_H133 zenon_H195 zenon_H93 zenon_H20f zenon_Hf5 zenon_H38 zenon_H25b zenon_Hc4. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.22/22.32 apply (zenon_L211_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.22/22.32 apply (zenon_L1276_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.22/22.32 apply (zenon_L1159_); trivial. % 22.22/22.32 apply (zenon_L1699_); trivial. % 22.22/22.32 (* end of lemma zenon_L1700_ *) % 22.22/22.32 assert (zenon_L1701_ : (((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 (e3) (e3)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.22/22.32 do 0 intro. intros zenon_H183 zenon_H68 zenon_H6e zenon_H192 zenon_Hc4 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H162 zenon_H1bb zenon_H181. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.22/22.32 apply (zenon_L291_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.22/22.32 apply (zenon_L1128_); trivial. % 22.22/22.32 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.22/22.32 apply (zenon_L870_); trivial. % 22.22/22.32 exact (zenon_H181 zenon_H17c). % 22.22/22.32 (* end of lemma zenon_L1701_ *) % 22.22/22.32 assert (zenon_L1702_ : (((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (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)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.33 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H25b zenon_H195 zenon_H26a zenon_H162 zenon_H1c6 zenon_H159 zenon_H38 zenon_H196 zenon_H201 zenon_H6f zenon_H183 zenon_H68 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H181 zenon_H1d8 zenon_H13a zenon_H25e zenon_H1fb zenon_Ha9 zenon_H1c3 zenon_Ha0 zenon_Hb6 zenon_Hf5 zenon_H288 zenon_H11a zenon_H3f zenon_H36 zenon_H231 zenon_H104 zenon_H18a zenon_Hbc zenon_H186 zenon_H1a2 zenon_H171 zenon_He7 zenon_H163 zenon_H192 zenon_H3d zenon_H34 zenon_H12e zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H1cb zenon_H54 zenon_H141 zenon_H1c7. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.33 apply (zenon_L900_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.33 exact (zenon_H159 zenon_H10c). % 22.22/22.33 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.33 apply (zenon_L1700_); trivial. % 22.22/22.33 apply (zenon_L1692_); trivial. % 22.22/22.33 (* end of lemma zenon_L1702_ *) % 22.22/22.33 assert (zenon_L1703_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.22/22.33 do 0 intro. intros zenon_H141 zenon_H48 zenon_H54 zenon_Ha0 zenon_H10d zenon_Hef zenon_H133 zenon_H196 zenon_H38. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.33 apply (zenon_L217_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.33 apply (zenon_L152_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.33 apply (zenon_L265_); trivial. % 22.22/22.33 apply (zenon_L1162_); trivial. % 22.22/22.33 (* end of lemma zenon_L1703_ *) % 22.22/22.33 assert (zenon_L1704_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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 (e3) (e3)) = (e2))) -> False). % 22.22/22.33 do 0 intro. intros zenon_H1a2 zenon_Ha9 zenon_H66 zenon_H196 zenon_Hef zenon_H10d zenon_H54 zenon_H141 zenon_Ha0 zenon_H111 zenon_H121 zenon_H33 zenon_H104 zenon_H13a zenon_H18a zenon_H162 zenon_H77 zenon_H93 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_Hb6 zenon_H183 zenon_H68 zenon_He7 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H163 zenon_H4d zenon_H192 zenon_H3d zenon_H48 zenon_H12e zenon_H181. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.22/22.33 apply (zenon_L193_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.22/22.33 apply (zenon_L1703_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.22/22.33 apply (zenon_L1300_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.22/22.33 apply (zenon_L211_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.22/22.33 apply (zenon_L1276_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.22/22.33 apply (zenon_L363_); trivial. % 22.22/22.33 apply (zenon_L1538_); trivial. % 22.22/22.33 (* end of lemma zenon_L1704_ *) % 22.22/22.33 assert (zenon_L1705_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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 (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.33 do 0 intro. intros zenon_H1c6 zenon_H159 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H163 zenon_H4d zenon_H192 zenon_H3d zenon_H48 zenon_H12e zenon_H1c2 zenon_H93 zenon_Hef zenon_H156 zenon_H1a2 zenon_Ha9 zenon_H196 zenon_H54 zenon_H141 zenon_Ha0 zenon_H111 zenon_H121 zenon_H33 zenon_H104 zenon_H13a zenon_H18a zenon_H162 zenon_H77 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_Hb6 zenon_H183 zenon_H68 zenon_He7 zenon_H181 zenon_H1cf zenon_H1c7. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.33 apply (zenon_L55_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.33 exact (zenon_H159 zenon_H10c). % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.22/22.33 apply (zenon_L1704_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.22/22.33 apply (zenon_L100_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.22/22.33 apply (zenon_L207_); trivial. % 22.22/22.33 apply (zenon_L853_); trivial. % 22.22/22.33 exact (zenon_H1c7 zenon_Hac). % 22.22/22.33 (* end of lemma zenon_L1705_ *) % 22.22/22.33 assert (zenon_L1706_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((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)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (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 (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))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((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 (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.22/22.33 do 0 intro. intros zenon_Heb zenon_H100 zenon_H1cb zenon_H186 zenon_Hbc zenon_H231 zenon_H36 zenon_H11a zenon_H288 zenon_Hf5 zenon_H1fb zenon_H25e zenon_H1d8 zenon_H6f zenon_H201 zenon_H26a zenon_H195 zenon_H25b zenon_H24 zenon_H9f zenon_H13c zenon_He7 zenon_H163 zenon_H192 zenon_H3d zenon_H34 zenon_H48 zenon_H12e zenon_H93 zenon_H189 zenon_H1c6 zenon_H159 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H1c2 zenon_H156 zenon_H1a2 zenon_Ha9 zenon_H196 zenon_H54 zenon_H141 zenon_Ha0 zenon_H111 zenon_H121 zenon_H33 zenon_H104 zenon_H13a zenon_H18a zenon_H162 zenon_H18d zenon_Hb6 zenon_H183 zenon_H1cf zenon_H1c7 zenon_H1a8 zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H181. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.33 apply (zenon_L69_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.33 apply (zenon_L1701_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.33 apply (zenon_L186_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.33 apply (zenon_L439_); trivial. % 22.22/22.33 apply (zenon_L1702_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.33 apply (zenon_L214_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.33 apply (zenon_L1705_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.33 apply (zenon_L439_); trivial. % 22.22/22.33 apply (zenon_L965_); trivial. % 22.22/22.33 apply (zenon_L414_); trivial. % 22.22/22.33 (* end of lemma zenon_L1706_ *) % 22.22/22.33 assert (zenon_L1707_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (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) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e0)) -> (((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))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.22/22.33 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_H93 zenon_Hef zenon_H24e zenon_H189 zenon_H53 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1c2 zenon_Hf3 zenon_H201 zenon_H1a2 zenon_Ha0 zenon_Hb6 zenon_H1cf zenon_H1bb zenon_H162 zenon_H77 zenon_H68 zenon_Ha9 zenon_Ha5 zenon_H9f zenon_H1c3 zenon_H181 zenon_Hc4. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.33 apply (zenon_L359_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.33 apply (zenon_L111_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.33 apply (zenon_L1688_); trivial. % 22.22/22.33 apply (zenon_L886_); trivial. % 22.22/22.33 (* end of lemma zenon_L1707_ *) % 22.22/22.33 assert (zenon_L1708_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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))))) -> ((op (e1) (e1)) = (e1)) -> (~((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)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((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). % 22.22/22.33 do 0 intro. intros zenon_H1a8 zenon_H181 zenon_H1bb zenon_H162 zenon_H1c7 zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_Hc4 zenon_H192 zenon_H183 zenon_H3f zenon_H189 zenon_H141 zenon_H54 zenon_He7 zenon_Hf0 zenon_H1cd zenon_H1c2 zenon_H93 zenon_H68 zenon_Hf3 zenon_H201 zenon_H77 zenon_H48 zenon_H1a2 zenon_Ha9 zenon_Ha0 zenon_Hb6 zenon_H1cf zenon_H196 zenon_H38. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.33 apply (zenon_L1701_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.33 apply (zenon_L186_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.33 apply (zenon_L439_); trivial. % 22.22/22.33 apply (zenon_L1239_); trivial. % 22.22/22.33 (* end of lemma zenon_L1708_ *) % 22.22/22.33 assert (zenon_L1709_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (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 (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (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) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((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)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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 (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (e0)) -> False). % 22.22/22.33 do 0 intro. intros zenon_H13b zenon_H179 zenon_H18a zenon_H104 zenon_H33 zenon_H121 zenon_H111 zenon_H12e zenon_H9f zenon_H24 zenon_H26a zenon_H1d8 zenon_H288 zenon_H11a zenon_H36 zenon_H231 zenon_Hbc zenon_H34 zenon_H7d zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_Ha0 zenon_H1c7 zenon_H100 zenon_H201 zenon_H1c2 zenon_H1cd zenon_Hf0 zenon_H54 zenon_H141 zenon_H183 zenon_H192 zenon_Hc4 zenon_H24e zenon_H162 zenon_H181 zenon_H1a8 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_H186 zenon_H25b zenon_H68 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H93 zenon_H1bb zenon_He2 zenon_Hf5 zenon_H38. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.33 apply (zenon_L297_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.33 apply (zenon_L1706_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.33 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.22/22.33 apply (zenon_L316_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.33 apply (zenon_L69_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.33 apply (zenon_L1708_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.33 apply (zenon_L117_); trivial. % 22.22/22.33 apply (zenon_L1236_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.22/22.33 apply (zenon_L1242_); trivial. % 22.22/22.33 apply (zenon_L802_); trivial. % 22.22/22.33 apply (zenon_L663_); trivial. % 22.22/22.33 (* end of lemma zenon_L1709_ *) % 22.22/22.33 assert (zenon_L1710_ : (((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 (e3) (e3)) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (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))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (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 (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.22/22.33 do 0 intro. intros zenon_H13c zenon_H24 zenon_H159 zenon_Hc4 zenon_H25b zenon_Hf5 zenon_H20f zenon_H93 zenon_H186 zenon_H26a zenon_H18d zenon_H129 zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1cb zenon_H1b7 zenon_H162 zenon_H18a zenon_H181 zenon_H12e zenon_H141 zenon_H34 zenon_H109 zenon_H48 zenon_H195 zenon_Ha0 zenon_H53 zenon_Hb6 zenon_H2c zenon_H9f zenon_H117 zenon_H196 zenon_H38. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.33 apply (zenon_L900_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.33 exact (zenon_H159 zenon_H10c). % 22.22/22.33 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.33 apply (zenon_L1700_); trivial. % 22.22/22.33 apply (zenon_L1404_); trivial. % 22.22/22.33 (* end of lemma zenon_L1710_ *) % 22.22/22.33 assert (zenon_L1711_ : (((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)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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 (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (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 (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (((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 (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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) (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.22/22.33 do 0 intro. intros zenon_Heb zenon_H100 zenon_H1c7 zenon_H1a2 zenon_H186 zenon_Hbc zenon_H18a zenon_H104 zenon_H231 zenon_H1cb zenon_H93 zenon_H18d zenon_H36 zenon_H12e zenon_H48 zenon_H11a zenon_H288 zenon_Hf5 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H196 zenon_H1fb zenon_H25e zenon_H13a zenon_H1d8 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H192 zenon_H183 zenon_H6f zenon_H159 zenon_H141 zenon_H111 zenon_H13f zenon_He7 zenon_Hf0 zenon_H195 zenon_H54 zenon_H117 zenon_H1c6 zenon_H162 zenon_H26a zenon_H25b zenon_H24 zenon_H9f zenon_H13c zenon_H73 zenon_H153 zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H181. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.33 apply (zenon_L69_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.33 apply (zenon_L900_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.33 exact (zenon_H159 zenon_H10c). % 22.22/22.33 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.33 apply (zenon_L1700_); trivial. % 22.22/22.33 apply (zenon_L1521_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.33 apply (zenon_L184_); trivial. % 22.22/22.33 apply (zenon_L414_); trivial. % 22.22/22.33 (* end of lemma zenon_L1711_ *) % 22.22/22.33 assert (zenon_L1712_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> False). % 22.22/22.33 do 0 intro. intros zenon_H3a zenon_H9f zenon_H38. % 22.22/22.33 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.22/22.33 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.22/22.33 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.22/22.33 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.22/22.33 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.22/22.33 apply (zenon_L1568_); trivial. % 22.22/22.33 (* end of lemma zenon_L1712_ *) % 22.22/22.33 assert (zenon_L1713_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((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)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 22.22/22.33 do 0 intro. intros zenon_H1cf zenon_H177 zenon_Ha9 zenon_Hac zenon_H183 zenon_H156 zenon_Hef zenon_H8b zenon_H164 zenon_H195 zenon_H93 zenon_H163 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H77 zenon_H25 zenon_H68 zenon_Hfa zenon_H14c zenon_H104 zenon_H67 zenon_H7e. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.22/22.33 apply (zenon_L1575_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.22/22.33 apply (zenon_L100_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.22/22.33 exact (zenon_H8b zenon_H8a). % 22.22/22.33 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.22/22.33 apply (zenon_L456_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.22/22.33 apply (zenon_L828_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.22/22.33 apply (zenon_L257_); trivial. % 22.22/22.33 apply (zenon_L547_); trivial. % 22.22/22.33 (* end of lemma zenon_L1713_ *) % 22.22/22.33 assert (zenon_L1714_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.22/22.33 do 0 intro. intros zenon_H82 zenon_H68 zenon_H38 zenon_H13a zenon_Hb6 zenon_H3d zenon_Ha9 zenon_Ha0 zenon_H77 zenon_H139 zenon_H4e zenon_H5a zenon_H55 zenon_H53 zenon_H34 zenon_H48. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.33 apply (zenon_L1149_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.33 apply (zenon_L16_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.33 apply (zenon_L15_); trivial. % 22.22/22.33 apply (zenon_L456_); trivial. % 22.22/22.33 (* end of lemma zenon_L1714_ *) % 22.22/22.33 assert (zenon_L1715_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((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). % 22.22/22.33 do 0 intro. intros zenon_H15d zenon_H9f zenon_H34 zenon_H53 zenon_H55 zenon_H5a zenon_H4e zenon_H139 zenon_H77 zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H13a zenon_H68 zenon_H82 zenon_H73 zenon_H4d zenon_H38 zenon_H48. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.33 apply (zenon_L253_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.33 apply (zenon_L1714_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.33 apply (zenon_L184_); trivial. % 22.22/22.33 apply (zenon_L246_); trivial. % 22.22/22.33 (* end of lemma zenon_L1715_ *) % 22.22/22.33 assert (zenon_L1716_ : (~((e0) = (e3))) -> ((op (e0) (e0)) = (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 (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (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 (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((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) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (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 (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (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 (e2) (e3)) = (e2)) -> False). % 22.22/22.33 do 0 intro. intros zenon_Ha0 zenon_H9f zenon_H15d zenon_H73 zenon_H139 zenon_H68 zenon_Ha9 zenon_H38 zenon_H13a zenon_H77 zenon_H48 zenon_H55 zenon_H53 zenon_H1d5 zenon_H125 zenon_H1c6 zenon_H92 zenon_H1ef zenon_H131 zenon_H4d zenon_H13e zenon_H7b zenon_Hf0 zenon_H8b zenon_H16a zenon_H1cf zenon_Hfa zenon_H195 zenon_H163 zenon_H1bb zenon_Hc4 zenon_H20f zenon_H1b4 zenon_H18d zenon_H104 zenon_H164 zenon_H156 zenon_H177 zenon_H129 zenon_H183 zenon_H196 zenon_H141 zenon_H159 zenon_H82 zenon_Hb6 zenon_H5a zenon_H4e zenon_H1fe zenon_H93. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.22/22.33 exact (zenon_H16b zenon_H93). % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.22/22.33 apply (zenon_L41_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.33 apply (zenon_L253_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.33 apply (zenon_L1149_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.33 apply (zenon_L25_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.33 apply (zenon_L15_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.33 apply (zenon_L171_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.33 apply (zenon_L55_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.33 exact (zenon_H159 zenon_H10c). % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.33 apply (zenon_L113_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.33 apply (zenon_L1008_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.33 apply (zenon_L111_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.33 apply (zenon_L1713_); trivial. % 22.22/22.33 apply (zenon_L1162_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.33 apply (zenon_L59_); trivial. % 22.22/22.33 apply (zenon_L228_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.33 apply (zenon_L214_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.33 apply (zenon_L651_); trivial. % 22.22/22.33 apply (zenon_L165_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.33 apply (zenon_L184_); trivial. % 22.22/22.33 apply (zenon_L246_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.22/22.33 apply (zenon_L755_); trivial. % 22.22/22.33 apply (zenon_L1715_); trivial. % 22.22/22.33 (* end of lemma zenon_L1716_ *) % 22.22/22.33 assert (zenon_L1717_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (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 (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.22/22.33 do 0 intro. intros zenon_H61 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H93 zenon_H77 zenon_H1b7. % 22.22/22.33 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.22/22.33 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.22/22.33 apply (zenon_L1276_); trivial. % 22.22/22.33 (* end of lemma zenon_L1717_ *) % 22.22/22.33 assert (zenon_L1718_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.22/22.33 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H25 zenon_H77 zenon_H3f zenon_H160 zenon_H163 zenon_H93 zenon_H195. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.33 apply (zenon_L171_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.33 apply (zenon_L186_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.33 apply (zenon_L227_); trivial. % 22.22/22.33 apply (zenon_L228_); trivial. % 22.22/22.33 (* end of lemma zenon_L1718_ *) % 22.22/22.33 assert (zenon_L1719_ : (((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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((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))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.33 do 0 intro. intros zenon_H13c zenon_H9f zenon_H24 zenon_H1c6 zenon_H159 zenon_H38 zenon_H196 zenon_H164 zenon_H1cd zenon_H7d zenon_H24e zenon_H4d zenon_H192 zenon_H3d zenon_H12e zenon_H1b7 zenon_H68 zenon_H93 zenon_Ha0 zenon_Hfa zenon_H25 zenon_H77 zenon_H1bb zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H160 zenon_H163 zenon_H195 zenon_H19a zenon_H104 zenon_H1b4 zenon_H13f zenon_Hb6 zenon_H131 zenon_H141 zenon_H1c7. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.33 apply (zenon_L900_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.33 exact (zenon_H159 zenon_H10c). % 22.22/22.33 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.33 apply (zenon_L124_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.33 apply (zenon_L55_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.33 exact (zenon_H159 zenon_H10c). % 22.22/22.33 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.33 apply (zenon_L825_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.33 apply (zenon_L152_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.22/22.33 apply (zenon_L853_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.22/22.33 apply (zenon_L829_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.22/22.33 apply (zenon_L257_); trivial. % 22.22/22.33 apply (zenon_L411_); trivial. % 22.22/22.33 apply (zenon_L1162_); trivial. % 22.22/22.33 exact (zenon_H1c7 zenon_Hac). % 22.22/22.33 (* end of lemma zenon_L1719_ *) % 22.22/22.33 assert (zenon_L1720_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (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)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.22/22.33 do 0 intro. intros zenon_H18d zenon_H48 zenon_H1cb zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H68 zenon_H1c3 zenon_H99 zenon_H93 zenon_H77 zenon_H7e zenon_H18a. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.22/22.33 apply (zenon_L246_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.22/22.33 apply (zenon_L1352_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.22/22.33 apply (zenon_L218_); trivial. % 22.22/22.33 apply (zenon_L140_); trivial. % 22.22/22.33 (* end of lemma zenon_L1720_ *) % 22.22/22.33 assert (zenon_L1721_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (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) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.22/22.33 do 0 intro. intros zenon_Hfa zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_H77 zenon_H24e zenon_H189 zenon_H53 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H160 zenon_H163 zenon_H93 zenon_H195. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.33 apply (zenon_L24_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.33 apply (zenon_L1687_); trivial. % 22.22/22.33 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.33 apply (zenon_L227_); trivial. % 22.22/22.33 apply (zenon_L228_); trivial. % 22.22/22.33 (* end of lemma zenon_L1721_ *) % 22.22/22.33 assert (zenon_L1722_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((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 (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.22/22.33 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H153 zenon_H23c zenon_H195 zenon_H163 zenon_H160 zenon_H189 zenon_H24e zenon_H3c zenon_H5d zenon_H1cd zenon_H1c7 zenon_Hfa zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H93 zenon_H77 zenon_H1b7. % 22.22/22.33 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.22/22.33 apply (zenon_L738_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.22/22.34 apply (zenon_L492_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.22/22.34 apply (zenon_L1721_); trivial. % 22.22/22.34 apply (zenon_L1276_); trivial. % 22.22/22.34 (* end of lemma zenon_L1722_ *) % 22.22/22.34 assert (zenon_L1723_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (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)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (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)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.22/22.34 do 0 intro. intros zenon_H82 zenon_H13a zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H139 zenon_H1b7 zenon_H1c7 zenon_H1cd zenon_H5d zenon_H24e zenon_H189 zenon_H23c zenon_H1d8 zenon_He4 zenon_H153 zenon_H73 zenon_Hfa zenon_H25 zenon_H160 zenon_H163 zenon_H195 zenon_H100 zenon_Heb zenon_H18d zenon_H48 zenon_H1cb zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H68 zenon_H1c3 zenon_H99 zenon_H93 zenon_H77 zenon_H18a. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L1284_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_L1722_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.34 apply (zenon_L69_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.34 apply (zenon_L1718_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.34 apply (zenon_L184_); trivial. % 22.22/22.34 apply (zenon_L1352_); trivial. % 22.22/22.34 apply (zenon_L1720_); trivial. % 22.22/22.34 (* end of lemma zenon_L1723_ *) % 22.22/22.34 assert (zenon_L1724_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.22/22.34 do 0 intro. intros zenon_H12e zenon_H18a zenon_H77 zenon_H99 zenon_H1c3 zenon_H68 zenon_H129 zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H48 zenon_H18d zenon_H3d zenon_H192 zenon_H105 zenon_H104 zenon_H26a zenon_Ha0 zenon_H186 zenon_H133 zenon_H195 zenon_H93 zenon_H20f zenon_Hf5 zenon_H38 zenon_H25b zenon_Hc4. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.22/22.34 apply (zenon_L1720_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.22/22.34 apply (zenon_L146_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.22/22.34 apply (zenon_L72_); trivial. % 22.22/22.34 apply (zenon_L1699_); trivial. % 22.22/22.34 (* end of lemma zenon_L1724_ *) % 22.22/22.34 assert (zenon_L1725_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e3)) = (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (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 (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 22.22/22.34 do 0 intro. intros zenon_H13f zenon_H2d zenon_Hb6 zenon_H10d zenon_Hc4 zenon_H25b zenon_H38 zenon_Hf5 zenon_H20f zenon_H195 zenon_H133 zenon_H186 zenon_Ha0 zenon_H26a zenon_H104 zenon_H192 zenon_H3d zenon_H18d zenon_H48 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H129 zenon_H68 zenon_H1c3 zenon_H99 zenon_H18a zenon_H12e zenon_H77 zenon_H93. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.34 apply (zenon_L217_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.34 apply (zenon_L113_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.34 apply (zenon_L1724_); trivial. % 22.22/22.34 apply (zenon_L218_); trivial. % 22.22/22.34 (* end of lemma zenon_L1725_ *) % 22.22/22.34 assert (zenon_L1726_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> False). % 22.22/22.34 do 0 intro. intros zenon_H201 zenon_H1d8 zenon_H3d zenon_Hf3 zenon_H48 zenon_H53 zenon_H190 zenon_H77 zenon_H160. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.22/22.34 apply (zenon_L738_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.22/22.34 apply (zenon_L117_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.22/22.34 apply (zenon_L143_); trivial. % 22.22/22.34 apply (zenon_L367_); trivial. % 22.22/22.34 (* end of lemma zenon_L1726_ *) % 22.22/22.34 assert (zenon_L1727_ : (((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)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 22.22/22.34 do 0 intro. intros zenon_H13f zenon_H3c zenon_H100 zenon_H190 zenon_Hf3 zenon_H1d8 zenon_H201 zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_Ha0 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_Hef zenon_H109 zenon_H2d zenon_H164 zenon_Hb6 zenon_H12e zenon_H99 zenon_H1c3 zenon_H68 zenon_H1cb zenon_H3d zenon_H192 zenon_H104 zenon_H26a zenon_H186 zenon_H195 zenon_Hf5 zenon_H25b zenon_H67 zenon_H1a2 zenon_H77 zenon_H93. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.34 apply (zenon_L69_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.34 apply (zenon_L1726_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.22/22.34 apply (zenon_L446_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.22/22.34 apply (zenon_L1724_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.22/22.34 apply (zenon_L400_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.22/22.34 apply (zenon_L359_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.22/22.34 apply (zenon_L827_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.22/22.34 apply (zenon_L80_); trivial. % 22.22/22.34 apply (zenon_L560_); trivial. % 22.22/22.34 apply (zenon_L218_); trivial. % 22.22/22.34 (* end of lemma zenon_L1727_ *) % 22.22/22.34 assert (zenon_L1728_ : (((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) = (e3))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 22.22/22.34 do 0 intro. intros zenon_H13f zenon_H3c zenon_H100 zenon_Hb6 zenon_H11d zenon_Ha0 zenon_H10d zenon_H190 zenon_Ha5 zenon_H186 zenon_H67 zenon_H1a2 zenon_H77 zenon_H93. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.34 apply (zenon_L69_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.34 apply (zenon_L113_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.22/22.34 apply (zenon_L446_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.22/22.34 apply (zenon_L308_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.22/22.34 apply (zenon_L163_); trivial. % 22.22/22.34 apply (zenon_L80_); trivial. % 22.22/22.34 apply (zenon_L218_); trivial. % 22.22/22.34 (* end of lemma zenon_L1728_ *) % 22.22/22.34 assert (zenon_L1729_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (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)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.22/22.34 do 0 intro. intros zenon_H82 zenon_H13a zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H139 zenon_H1b7 zenon_Hfa zenon_H1c7 zenon_H1cd zenon_H5d zenon_H24e zenon_H189 zenon_H160 zenon_H163 zenon_H195 zenon_H23c zenon_H153 zenon_H1d8 zenon_He4 zenon_H2d zenon_H18d zenon_H48 zenon_H1cb zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H68 zenon_H1c3 zenon_H99 zenon_H93 zenon_H77 zenon_H18a. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L1284_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_L1722_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_L217_); trivial. % 22.22/22.34 apply (zenon_L1720_); trivial. % 22.22/22.34 (* end of lemma zenon_L1729_ *) % 22.22/22.34 assert (zenon_L1730_ : (((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)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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 (e0) (e1)) = (op (e3) (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 (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.22/22.34 do 0 intro. intros zenon_H15d zenon_H13c zenon_H9f zenon_H24 zenon_H1c6 zenon_H159 zenon_H1a2 zenon_H186 zenon_H190 zenon_H100 zenon_H13f zenon_H1ef zenon_H201 zenon_H212 zenon_H7d zenon_Hbc zenon_H209 zenon_H109 zenon_H164 zenon_H12e zenon_H192 zenon_H104 zenon_H26a zenon_Hf5 zenon_H25b zenon_H26d zenon_H140 zenon_H177 zenon_H18a zenon_H77 zenon_H93 zenon_H99 zenon_H1c3 zenon_H68 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H18d zenon_H2d zenon_He4 zenon_H1d8 zenon_H23c zenon_H195 zenon_H163 zenon_H160 zenon_H189 zenon_H24e zenon_H5d zenon_H1cd zenon_H1c7 zenon_Hfa zenon_H1b7 zenon_H139 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H82 zenon_H38 zenon_H48. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.34 apply (zenon_L253_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L1149_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.34 apply (zenon_L24_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.34 apply (zenon_L900_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.34 apply (zenon_L55_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.34 apply (zenon_L1725_); trivial. % 22.22/22.34 exact (zenon_H1c7 zenon_Hac). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.34 apply (zenon_L55_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.22/22.34 apply (zenon_L756_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.22/22.34 apply (zenon_L1727_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.22/22.34 apply (zenon_L405_); trivial. % 22.22/22.34 apply (zenon_L1728_); trivial. % 22.22/22.34 exact (zenon_H1c7 zenon_Hac). % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.34 apply (zenon_L227_); trivial. % 22.22/22.34 apply (zenon_L228_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.34 apply (zenon_L214_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.34 apply (zenon_L122_); trivial. % 22.22/22.34 apply (zenon_L165_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_L217_); trivial. % 22.22/22.34 apply (zenon_L1720_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.34 apply (zenon_L1729_); trivial. % 22.22/22.34 apply (zenon_L246_); trivial. % 22.22/22.34 (* end of lemma zenon_L1730_ *) % 22.22/22.34 assert (zenon_L1731_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (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) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.34 do 0 intro. intros zenon_H1c6 zenon_H1a3 zenon_H11a zenon_H9f zenon_H33 zenon_H121 zenon_H93 zenon_H77 zenon_H12e zenon_H18a zenon_H99 zenon_H1c3 zenon_H68 zenon_H129 zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H48 zenon_H18d zenon_H3d zenon_H192 zenon_H104 zenon_H26a zenon_Ha0 zenon_H186 zenon_H133 zenon_H195 zenon_H20f zenon_Hf5 zenon_H38 zenon_H25b zenon_Hc4 zenon_Hb6 zenon_H2d zenon_H13f zenon_H1c7. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.34 apply (zenon_L55_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.34 apply (zenon_L538_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.34 apply (zenon_L1725_); trivial. % 22.22/22.34 exact (zenon_H1c7 zenon_Hac). % 22.22/22.34 (* end of lemma zenon_L1731_ *) % 22.22/22.34 assert (zenon_L1732_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((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))) -> False). % 22.22/22.34 do 0 intro. intros zenon_H1c6 zenon_H3d zenon_H159 zenon_H93 zenon_H77 zenon_H1a2 zenon_H67 zenon_Hf3 zenon_Hb6 zenon_H164 zenon_H160 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H18a zenon_H1cb zenon_H12e zenon_Hef zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_Ha0 zenon_H162 zenon_H100 zenon_H3c zenon_H13f zenon_H1c7. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.34 apply (zenon_L55_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.34 apply (zenon_L69_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.34 apply (zenon_L113_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.22/22.34 apply (zenon_L446_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.22/22.34 apply (zenon_L162_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.22/22.34 apply (zenon_L400_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.22/22.34 apply (zenon_L1510_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.22/22.34 apply (zenon_L827_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.22/22.34 apply (zenon_L80_); trivial. % 22.22/22.34 exact (zenon_H162 zenon_H167). % 22.22/22.34 apply (zenon_L218_); trivial. % 22.22/22.34 exact (zenon_H1c7 zenon_Hac). % 22.22/22.34 (* end of lemma zenon_L1732_ *) % 22.22/22.34 assert (zenon_L1733_ : ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (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 (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.34 do 0 intro. intros zenon_H93 zenon_H77 zenon_H1a2 zenon_H67 zenon_H186 zenon_Ha5 zenon_H190 zenon_Ha0 zenon_Hb6 zenon_H100 zenon_H3c zenon_H13f zenon_H1ef zenon_H2d zenon_H1c6 zenon_H3d zenon_H159 zenon_H164 zenon_H160 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H18a zenon_H1cb zenon_H12e zenon_Hef zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H162 zenon_H26d zenon_H140 zenon_H1c7. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.34 apply (zenon_L55_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.22/22.34 apply (zenon_L756_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.22/22.34 apply (zenon_L1732_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.22/22.34 apply (zenon_L405_); trivial. % 22.22/22.34 apply (zenon_L1728_); trivial. % 22.22/22.34 exact (zenon_H1c7 zenon_Hac). % 22.22/22.34 (* end of lemma zenon_L1733_ *) % 22.22/22.34 assert (zenon_L1734_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (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) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e3) (e0)) = (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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) (e2)) = (op (e2) (e2)))) -> (((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 (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (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) (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 (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> False). % 22.22/22.34 do 0 intro. intros zenon_Hc8 zenon_Hcb zenon_He2 zenon_Hf0 zenon_H121 zenon_H11a zenon_H33 zenon_H1fe zenon_H26a zenon_H212 zenon_H109 zenon_H201 zenon_H140 zenon_H177 zenon_H125 zenon_H160 zenon_Hbc zenon_H93 zenon_H94 zenon_H68 zenon_H77 zenon_H82 zenon_H99 zenon_H18a zenon_H100 zenon_Hfa zenon_H195 zenon_H163 zenon_H13c zenon_H141 zenon_H196 zenon_H12e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H24e zenon_H192 zenon_H19a zenon_H18d zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H1bb zenon_H104 zenon_H164 zenon_H131 zenon_H13f zenon_H1c6 zenon_H159 zenon_H24 zenon_H284 zenon_H25e zenon_H281 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1a2 zenon_H1cb zenon_H16a zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H4e zenon_H1cf zenon_H283 zenon_H48 zenon_H13a zenon_H38 zenon_Ha9 zenon_Hb6 zenon_H139 zenon_H1d8 zenon_H23c zenon_He4 zenon_H9f zenon_Ha0 zenon_Hca. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.22/22.34 apply (zenon_L41_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.34 apply (zenon_L541_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L1149_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_L25_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.34 apply (zenon_L69_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.34 apply (zenon_L1718_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.34 apply (zenon_L1719_); trivial. % 22.22/22.34 apply (zenon_L1236_); trivial. % 22.22/22.34 apply (zenon_L1720_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.34 apply (zenon_L1723_); trivial. % 22.22/22.34 apply (zenon_L246_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.22/22.34 apply (zenon_L1730_); trivial. % 22.22/22.34 apply (zenon_L1510_); trivial. % 22.22/22.34 apply (zenon_L555_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.22/22.34 apply (zenon_L41_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.34 apply (zenon_L541_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L541_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_L25_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.22/22.34 apply (zenon_L316_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.34 apply (zenon_L69_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.34 apply (zenon_L1718_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.34 apply (zenon_L171_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.34 apply (zenon_L900_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.34 apply (zenon_L1244_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.34 apply (zenon_L55_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.34 apply (zenon_L825_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.34 apply (zenon_L152_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.34 apply (zenon_L883_); trivial. % 22.22/22.34 apply (zenon_L158_); trivial. % 22.22/22.34 exact (zenon_H1c7 zenon_Hac). % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.34 apply (zenon_L59_); trivial. % 22.22/22.34 apply (zenon_L228_); trivial. % 22.22/22.34 apply (zenon_L1236_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.22/22.34 apply (zenon_L1242_); trivial. % 22.22/22.34 apply (zenon_L828_); trivial. % 22.22/22.34 apply (zenon_L1720_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.34 apply (zenon_L1723_); trivial. % 22.22/22.34 apply (zenon_L246_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.34 apply (zenon_L253_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L253_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.34 apply (zenon_L24_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.34 apply (zenon_L900_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.34 apply (zenon_L1731_); trivial. % 22.22/22.34 apply (zenon_L1733_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.34 apply (zenon_L227_); trivial. % 22.22/22.34 apply (zenon_L228_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.34 apply (zenon_L214_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.34 apply (zenon_L122_); trivial. % 22.22/22.34 apply (zenon_L167_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_L217_); trivial. % 22.22/22.34 apply (zenon_L1720_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.34 apply (zenon_L1729_); trivial. % 22.22/22.34 apply (zenon_L246_); trivial. % 22.22/22.34 apply (zenon_L1510_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.22/22.34 apply (zenon_L41_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.34 apply (zenon_L541_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L541_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_L25_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.22/22.34 apply (zenon_L65_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.34 apply (zenon_L69_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.34 apply (zenon_L1718_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.34 apply (zenon_L171_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.34 apply (zenon_L900_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.34 apply (zenon_L1244_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.34 apply (zenon_L55_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.34 apply (zenon_L887_); trivial. % 22.22/22.34 exact (zenon_H1c7 zenon_Hac). % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.34 apply (zenon_L59_); trivial. % 22.22/22.34 apply (zenon_L228_); trivial. % 22.22/22.34 apply (zenon_L1236_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.22/22.34 apply (zenon_L1242_); trivial. % 22.22/22.34 apply (zenon_L828_); trivial. % 22.22/22.34 apply (zenon_L1720_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L1284_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_L1722_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.34 apply (zenon_L69_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.34 apply (zenon_L1718_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.34 apply (zenon_L184_); trivial. % 22.22/22.34 apply (zenon_L414_); trivial. % 22.22/22.34 apply (zenon_L211_); trivial. % 22.22/22.34 apply (zenon_L246_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.34 apply (zenon_L253_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L253_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.34 apply (zenon_L24_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.34 apply (zenon_L46_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.34 apply (zenon_L1700_); trivial. % 22.22/22.34 apply (zenon_L1733_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.34 apply (zenon_L227_); trivial. % 22.22/22.34 apply (zenon_L228_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.34 apply (zenon_L214_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.34 apply (zenon_L122_); trivial. % 22.22/22.34 apply (zenon_L165_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_L217_); trivial. % 22.22/22.34 apply (zenon_L1720_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L1284_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_L1722_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_L217_); trivial. % 22.22/22.34 apply (zenon_L211_); trivial. % 22.22/22.34 apply (zenon_L246_); trivial. % 22.22/22.34 apply (zenon_L870_); trivial. % 22.22/22.34 apply (zenon_L237_); trivial. % 22.22/22.34 (* end of lemma zenon_L1734_ *) % 22.22/22.34 assert (zenon_L1735_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.22/22.34 do 0 intro. intros zenon_H1a8 zenon_H77 zenon_H3d zenon_H1b3 zenon_H189 zenon_H93 zenon_Ha9 zenon_Hac. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.34 apply (zenon_L214_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.34 exact (zenon_H1b3 zenon_Hef). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.34 apply (zenon_L439_); trivial. % 22.22/22.34 apply (zenon_L371_); trivial. % 22.22/22.34 (* end of lemma zenon_L1735_ *) % 22.22/22.34 assert (zenon_L1736_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.22/22.34 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_H73 zenon_H153 zenon_H1bb zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_H93 zenon_Hc4. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.34 exact (zenon_H7a zenon_H3c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.34 exact (zenon_H40 zenon_H3f). % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.34 apply (zenon_L184_); trivial. % 22.22/22.34 apply (zenon_L413_); trivial. % 22.22/22.34 (* end of lemma zenon_L1736_ *) % 22.22/22.34 assert (zenon_L1737_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((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) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 22.22/22.34 do 0 intro. intros zenon_H169 zenon_Hb6 zenon_H9f zenon_H1a8 zenon_Hac zenon_Ha9 zenon_H189 zenon_H77 zenon_H73 zenon_H48 zenon_H15d zenon_H7a zenon_H40 zenon_H1bb zenon_Hc4 zenon_H93 zenon_H129 zenon_H20f zenon_H38 zenon_H1b4 zenon_Heb. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.22/22.34 apply (zenon_L1589_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.34 apply (zenon_L253_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.34 apply (zenon_L1735_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.34 apply (zenon_L1736_); trivial. % 22.22/22.34 apply (zenon_L246_); trivial. % 22.22/22.34 (* end of lemma zenon_L1737_ *) % 22.22/22.34 assert (zenon_L1738_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (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 (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 (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((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)) = (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) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (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))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 22.22/22.34 do 0 intro. intros zenon_H169 zenon_Ha0 zenon_H9f zenon_H1ec zenon_Ha5 zenon_H186 zenon_He3 zenon_H40 zenon_H156 zenon_H159 zenon_H158 zenon_H4e zenon_He2 zenon_Hac zenon_H55 zenon_H38 zenon_H1fb zenon_H1d5 zenon_H94 zenon_H125 zenon_H179 zenon_H5d zenon_Hfa zenon_H201 zenon_Hf0 zenon_H18d zenon_H141 zenon_H2c zenon_H117 zenon_H195 zenon_Hb6 zenon_Heb zenon_H12e zenon_H20f zenon_H1bb zenon_Hc4 zenon_H1cb zenon_H18a zenon_H192 zenon_H13a zenon_H1c3 zenon_H1b4 zenon_Hf5 zenon_H25e zenon_He4 zenon_H1b7 zenon_H1d8 zenon_H15d zenon_H100 zenon_H16a zenon_H1a2 zenon_H1cd zenon_H13f zenon_H48 zenon_H13b zenon_H82 zenon_H77 zenon_H173 zenon_H183 zenon_H93 zenon_H129 zenon_H177 zenon_Ha9 zenon_H68 zenon_H196 zenon_H139 zenon_H1fe. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.22/22.34 apply (zenon_L41_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.22/22.34 apply (zenon_L309_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.22/22.34 apply (zenon_L1594_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.34 apply (zenon_L1597_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L1597_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.34 apply (zenon_L297_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.34 exact (zenon_He3 zenon_He7). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.22/22.34 apply (zenon_L65_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.22/22.34 exact (zenon_He3 zenon_He7). % 22.22/22.34 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.34 apply (zenon_L1612_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.34 apply (zenon_L111_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.34 apply (zenon_L1669_); trivial. % 22.22/22.34 apply (zenon_L218_); trivial. % 22.22/22.34 apply (zenon_L1689_); trivial. % 22.22/22.34 apply (zenon_L90_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.34 apply (zenon_L306_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.34 apply (zenon_L1247_); trivial. % 22.22/22.34 apply (zenon_L167_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_L1613_); trivial. % 22.22/22.34 apply (zenon_L456_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.34 apply (zenon_L1605_); trivial. % 22.22/22.34 apply (zenon_L246_); trivial. % 22.22/22.34 apply (zenon_L1113_); trivial. % 22.22/22.34 (* end of lemma zenon_L1738_ *) % 22.22/22.34 assert (zenon_L1739_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (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)) = (op (e2) (e3)))) -> False). % 22.22/22.34 do 0 intro. intros zenon_Hc0 zenon_H13c zenon_H9f zenon_H24 zenon_H159 zenon_H163 zenon_H195. % 22.22/22.34 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.22/22.34 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.34 apply (zenon_L900_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.34 apply (zenon_L617_); trivial. % 22.22/22.34 apply (zenon_L172_); trivial. % 22.22/22.34 (* end of lemma zenon_L1739_ *) % 22.22/22.34 assert (zenon_L1740_ : ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (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) (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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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 (e1) (e1)) = (op (e1) (e3)))) -> (((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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((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)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (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) (e0)) = (op (e2) (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) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (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) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 22.22/22.34 do 0 intro. intros zenon_H38 zenon_H1fb zenon_H26d zenon_H179 zenon_H159 zenon_H33 zenon_H11a zenon_H121 zenon_H288 zenon_H164 zenon_H212 zenon_H1fe zenon_Hb2 zenon_H13f zenon_Hfa zenon_H140 zenon_Hbc zenon_He4 zenon_H231 zenon_H104 zenon_H18a zenon_H1f1 zenon_H183 zenon_H234 zenon_H82 zenon_H23c zenon_H26a zenon_H111 zenon_H1d8 zenon_H2c zenon_H177 zenon_H125 zenon_H283 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H158 zenon_H13a zenon_H13e zenon_H55 zenon_H6f zenon_H266 zenon_H1ef zenon_H139 zenon_H16a zenon_H68 zenon_H25b zenon_Hf5 zenon_H27e zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H13c zenon_H186 zenon_H190 zenon_H156 zenon_H7d zenon_H1b7 zenon_H24e zenon_H24 zenon_H189 zenon_H93 zenon_H1c6 zenon_H48 zenon_H201 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H1cb zenon_H18d zenon_H192 zenon_H163 zenon_H12e zenon_H1d5 zenon_H1a2 zenon_Ha9 zenon_H1c2 zenon_H1cd zenon_H1cf zenon_H196 zenon_H141 zenon_H1a8 zenon_H100 zenon_He2 zenon_Hf0 zenon_H13b zenon_Ha0 zenon_H109 zenon_H77 zenon_H9f zenon_Hb6. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.22/22.34 apply (zenon_L2_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.22/22.34 apply (zenon_L1146_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.22/22.34 apply (zenon_L1147_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.22/22.34 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.22/22.34 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.22/22.34 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.22/22.34 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.22/22.34 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.22/22.34 apply (zenon_L1691_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.34 apply (zenon_L253_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L253_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.34 apply (zenon_L25_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.34 apply (zenon_L24_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.34 apply (zenon_L1697_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.34 apply (zenon_L214_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.34 apply (zenon_L100_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.34 apply (zenon_L439_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.34 apply (zenon_L900_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.34 apply (zenon_L436_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.34 apply (zenon_L55_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.34 apply (zenon_L359_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.34 apply (zenon_L152_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.34 apply (zenon_L1698_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.34 apply (zenon_L1403_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.34 apply (zenon_L255_); trivial. % 22.22/22.34 apply (zenon_L1444_); trivial. % 22.22/22.34 apply (zenon_L1162_); trivial. % 22.22/22.34 exact (zenon_H1c7 zenon_Hac). % 22.22/22.34 apply (zenon_L228_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.22/22.34 apply (zenon_L65_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.34 apply (zenon_L24_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.34 apply (zenon_L1697_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.34 apply (zenon_L62_); trivial. % 22.22/22.34 apply (zenon_L228_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.22/22.34 apply (zenon_L1242_); trivial. % 22.22/22.34 apply (zenon_L1689_); trivial. % 22.22/22.34 apply (zenon_L663_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.34 apply (zenon_L214_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.34 apply (zenon_L1247_); trivial. % 22.22/22.34 apply (zenon_L167_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_L1698_); trivial. % 22.22/22.34 apply (zenon_L456_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L1284_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_L1523_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.34 apply (zenon_L1530_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.34 apply (zenon_L297_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.34 apply (zenon_L1523_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.34 apply (zenon_L1522_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.34 apply (zenon_L184_); trivial. % 22.22/22.34 apply (zenon_L414_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.34 apply (zenon_L1525_); trivial. % 22.22/22.34 apply (zenon_L663_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.34 apply (zenon_L94_); trivial. % 22.22/22.34 apply (zenon_L167_); trivial. % 22.22/22.34 apply (zenon_L456_); trivial. % 22.22/22.34 apply (zenon_L246_); trivial. % 22.22/22.34 apply (zenon_L555_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.22/22.34 apply (zenon_L1691_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.34 apply (zenon_L253_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.34 apply (zenon_L253_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.34 apply (zenon_L297_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.34 apply (zenon_L900_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.34 apply (zenon_L1700_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.34 apply (zenon_L55_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.34 apply (zenon_L359_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.34 apply (zenon_L152_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.34 apply (zenon_L1706_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.34 apply (zenon_L1403_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.34 apply (zenon_L255_); trivial. % 22.22/22.34 apply (zenon_L218_); trivial. % 22.22/22.34 apply (zenon_L886_); trivial. % 22.22/22.34 exact (zenon_H1c7 zenon_Hac). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.22/22.34 apply (zenon_L65_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.34 apply (zenon_L24_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.34 apply (zenon_L900_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.34 apply (zenon_L162_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.34 apply (zenon_L55_); trivial. % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.34 exact (zenon_H159 zenon_H10c). % 22.22/22.34 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.35 apply (zenon_L359_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.35 apply (zenon_L152_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.35 apply (zenon_L1706_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.35 apply (zenon_L1707_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.35 apply (zenon_L255_); trivial. % 22.22/22.35 apply (zenon_L218_); trivial. % 22.22/22.35 apply (zenon_L886_); trivial. % 22.22/22.35 exact (zenon_H1c7 zenon_Hac). % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.35 apply (zenon_L62_); trivial. % 22.22/22.35 apply (zenon_L228_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.22/22.35 apply (zenon_L1242_); trivial. % 22.22/22.35 apply (zenon_L1689_); trivial. % 22.22/22.35 apply (zenon_L663_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.35 apply (zenon_L1709_); trivial. % 22.22/22.35 apply (zenon_L211_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.35 apply (zenon_L1284_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.22/22.35 apply (zenon_L738_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.22/22.35 apply (zenon_L492_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.22/22.35 apply (zenon_L1710_); trivial. % 22.22/22.35 apply (zenon_L1276_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.35 apply (zenon_L297_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.35 apply (zenon_L1711_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.22/22.35 apply (zenon_L317_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.35 apply (zenon_L69_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.35 apply (zenon_L1708_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.35 apply (zenon_L184_); trivial. % 22.22/22.35 apply (zenon_L1236_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.35 apply (zenon_L69_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.35 apply (zenon_L1528_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.35 apply (zenon_L117_); trivial. % 22.22/22.35 apply (zenon_L414_); trivial. % 22.22/22.35 apply (zenon_L802_); trivial. % 22.22/22.35 apply (zenon_L663_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.35 apply (zenon_L1701_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.35 apply (zenon_L94_); trivial. % 22.22/22.35 apply (zenon_L167_); trivial. % 22.22/22.35 apply (zenon_L211_); trivial. % 22.22/22.35 apply (zenon_L246_); trivial. % 22.22/22.35 apply (zenon_L555_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.22/22.35 apply (zenon_L1712_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.22/22.35 apply (zenon_L11_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.22/22.35 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.22/22.35 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.22/22.35 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.22/22.35 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.22/22.35 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.22/22.35 apply (zenon_L1716_); trivial. % 22.22/22.35 apply (zenon_L1716_); trivial. % 22.22/22.35 apply (zenon_L1221_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.22/22.35 apply (zenon_L1717_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.22/22.35 apply (zenon_L1208_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.22/22.35 apply (zenon_L1209_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.22/22.35 apply (zenon_L37_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.22/22.35 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.22/22.35 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.22/22.35 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.22/22.35 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.22/22.35 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.22/22.35 apply (zenon_L1734_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.22/22.35 apply (zenon_L1353_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.22/22.35 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.22/22.35 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.22/22.35 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.22/22.35 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.22/22.35 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.22/22.35 apply (zenon_L1737_); trivial. % 22.22/22.35 apply (zenon_L1737_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.22/22.35 apply (zenon_L1738_); trivial. % 22.22/22.35 apply (zenon_L1738_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.22/22.35 apply (zenon_L1739_); trivial. % 22.22/22.35 apply (zenon_L51_); trivial. % 22.22/22.35 apply (zenon_L1212_); trivial. % 22.22/22.35 (* end of lemma zenon_L1740_ *) % 22.22/22.35 assert (zenon_L1741_ : ((op (e1) (e3)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (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) (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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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 (e1) (e1)) = (op (e1) (e3)))) -> (((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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((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)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (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) (e0)) = (op (e2) (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) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (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) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 22.22/22.35 do 0 intro. intros zenon_Ha5 zenon_H14c zenon_H54 zenon_H120 zenon_H4d zenon_H34 zenon_H181 zenon_H38 zenon_H1fb zenon_H26d zenon_H179 zenon_H159 zenon_H33 zenon_H11a zenon_H121 zenon_H288 zenon_H164 zenon_H212 zenon_H1fe zenon_Hb2 zenon_H13f zenon_Hfa zenon_H140 zenon_Hbc zenon_He4 zenon_H231 zenon_H104 zenon_H18a zenon_H1f1 zenon_H183 zenon_H234 zenon_H82 zenon_H23c zenon_H26a zenon_H111 zenon_H1d8 zenon_H2c zenon_H177 zenon_H125 zenon_H283 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H158 zenon_H13a zenon_H13e zenon_H55 zenon_H6f zenon_H266 zenon_H1ef zenon_H139 zenon_H16a zenon_H68 zenon_H25b zenon_Hf5 zenon_H27e zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H13c zenon_H186 zenon_H190 zenon_H156 zenon_H7d zenon_H1b7 zenon_H24e zenon_H24 zenon_H189 zenon_H1c6 zenon_H48 zenon_H201 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H1cb zenon_H18d zenon_H192 zenon_H163 zenon_H12e zenon_H1d5 zenon_H1a2 zenon_Ha9 zenon_H1c2 zenon_H1cd zenon_H1cf zenon_H196 zenon_H141 zenon_H1a8 zenon_H100 zenon_He2 zenon_Hf0 zenon_H13b zenon_Ha0 zenon_H109 zenon_H77 zenon_H9f zenon_Hb6. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.22/22.35 apply (zenon_L30_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.22/22.35 apply (zenon_L1090_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.22/22.35 apply (zenon_L1684_); trivial. % 22.22/22.35 apply (zenon_L1740_); trivial. % 22.22/22.35 (* end of lemma zenon_L1741_ *) % 22.22/22.35 assert (zenon_L1742_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((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 (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (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 (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 (e3) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.22/22.35 do 0 intro. intros zenon_Hef zenon_He7 zenon_Hb6 zenon_H9f zenon_H77 zenon_H109 zenon_Ha0 zenon_H13b zenon_Hf0 zenon_He2 zenon_H100 zenon_H1a8 zenon_H141 zenon_H1cf zenon_H1cd zenon_H1c2 zenon_Ha9 zenon_H1a2 zenon_H1d5 zenon_H12e zenon_H163 zenon_H192 zenon_H18d zenon_H1cb zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H201 zenon_H48 zenon_H1c6 zenon_H189 zenon_H24 zenon_H24e zenon_H1b7 zenon_H7d zenon_H156 zenon_H190 zenon_H186 zenon_H13c zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H27e zenon_Hf5 zenon_H25b zenon_H68 zenon_H16a zenon_H139 zenon_H1ef zenon_H266 zenon_H6f zenon_H55 zenon_H13e zenon_H13a zenon_H158 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H283 zenon_H125 zenon_H177 zenon_H2c zenon_H1d8 zenon_H111 zenon_H26a zenon_H23c zenon_H82 zenon_H234 zenon_H183 zenon_H1f1 zenon_H18a zenon_H104 zenon_H231 zenon_He4 zenon_Hbc zenon_H140 zenon_Hfa zenon_H13f zenon_Hb2 zenon_H1fe zenon_H212 zenon_H164 zenon_H288 zenon_H121 zenon_H11a zenon_H33 zenon_H159 zenon_H179 zenon_H26d zenon_H1fb zenon_H181 zenon_H34 zenon_H4d zenon_H120 zenon_H54 zenon_H196 zenon_H38. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.35 apply (zenon_L900_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.35 exact (zenon_H159 zenon_H10c). % 22.22/22.35 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.35 apply (zenon_L1244_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.35 apply (zenon_L217_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.35 apply (zenon_L929_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.35 apply (zenon_L1741_); trivial. % 22.22/22.35 apply (zenon_L1162_); trivial. % 22.22/22.35 (* end of lemma zenon_L1742_ *) % 22.22/22.35 assert (zenon_L1743_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e0) (e0)) = (e2)) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 22.22/22.35 do 0 intro. intros zenon_H36 zenon_H67 zenon_Hcb zenon_H209 zenon_He7 zenon_H3d zenon_H34 zenon_H159 zenon_H54 zenon_H181 zenon_H120 zenon_Hb2 zenon_H24e zenon_H1f1 zenon_H23c zenon_H26a zenon_H104 zenon_H231 zenon_H2c zenon_H109 zenon_H11a zenon_H1c2 zenon_H1cd zenon_H111 zenon_He2 zenon_H12e zenon_H100 zenon_H22d zenon_H191 zenon_H125 zenon_H141 zenon_H201 zenon_H164 zenon_H212 zenon_Hbc zenon_H179 zenon_H288 zenon_H192 zenon_H183 zenon_H18a zenon_Hfa zenon_H13b zenon_H1a8 zenon_H24 zenon_H121 zenon_H33 zenon_Hf0 zenon_H1d5 zenon_H1fe zenon_H82 zenon_H177 zenon_H1d8 zenon_H234 zenon_H7d zenon_He4 zenon_Hc4 zenon_H26d zenon_H38 zenon_H4e zenon_H13f zenon_H77 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H140 zenon_H9f zenon_Ha0. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.35 apply (zenon_L69_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.35 apply (zenon_L214_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.35 apply (zenon_L186_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.35 apply (zenon_L1647_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.35 apply (zenon_L900_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.35 exact (zenon_H159 zenon_H10c). % 22.22/22.35 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.35 apply (zenon_L1683_); trivial. % 22.22/22.35 apply (zenon_L1657_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.35 apply (zenon_L214_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.35 apply (zenon_L1742_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.35 apply (zenon_L1661_); trivial. % 22.22/22.35 apply (zenon_L965_); trivial. % 22.22/22.35 apply (zenon_L1627_); trivial. % 22.22/22.35 (* end of lemma zenon_L1743_ *) % 22.22/22.35 assert (zenon_L1744_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 22.22/22.35 do 0 intro. intros zenon_H201 zenon_H1d8 zenon_H3d zenon_H4e zenon_H3c zenon_H48 zenon_H14c zenon_H1a2 zenon_Ha9 zenon_H66 zenon_H186 zenon_Ha5 zenon_H190 zenon_H10d zenon_Hb6. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.22/22.35 apply (zenon_L738_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.22/22.35 apply (zenon_L14_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.22/22.35 apply (zenon_L255_); trivial. % 22.22/22.35 apply (zenon_L512_); trivial. % 22.22/22.35 (* end of lemma zenon_L1744_ *) % 22.22/22.35 assert (zenon_L1745_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (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 (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.35 do 0 intro. intros zenon_H24 zenon_Hf3 zenon_H13a zenon_H11a zenon_H3d zenon_H2c zenon_H111 zenon_H1f1 zenon_H23c zenon_He4 zenon_H26a zenon_H1d8 zenon_H82 zenon_H1b7 zenon_H1cd zenon_H7d zenon_H24e zenon_H104 zenon_H162 zenon_H19a zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H139 zenon_H1c6 zenon_H25b zenon_Hf5 zenon_H27e zenon_H189 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H18a zenon_H191 zenon_Hf0 zenon_H38 zenon_H196 zenon_H201 zenon_H1a2 zenon_H54 zenon_H141 zenon_H186 zenon_H16a zenon_H5c zenon_H195 zenon_H117 zenon_Hb6 zenon_Ha0 zenon_H13f zenon_H1c2 zenon_H121 zenon_H33 zenon_H9f zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_H1a3 zenon_H1c3 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1cb zenon_H109 zenon_H1c7. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.35 apply (zenon_L900_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.35 apply (zenon_L1306_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.35 apply (zenon_L162_); trivial. % 22.22/22.35 apply (zenon_L1541_); trivial. % 22.22/22.35 (* end of lemma zenon_L1745_ *) % 22.22/22.35 assert (zenon_L1746_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (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) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((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)) = (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) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (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) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.22/22.35 do 0 intro. intros zenon_Hf5 zenon_H100 zenon_H1a8 zenon_H1d5 zenon_Hfa zenon_H13a zenon_H11a zenon_H2c zenon_H111 zenon_H1f1 zenon_H23c zenon_He4 zenon_H26a zenon_H1d8 zenon_H82 zenon_H1b7 zenon_H1cd zenon_H7d zenon_H24e zenon_H104 zenon_H162 zenon_H19a zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H6f zenon_H266 zenon_H1ef zenon_H139 zenon_H25b zenon_H27e zenon_H189 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H18a zenon_H191 zenon_Hf0 zenon_H16a zenon_H195 zenon_H117 zenon_H13f zenon_H1c2 zenon_H34 zenon_H183 zenon_H1c3 zenon_H18d zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H109 zenon_He2 zenon_H177 zenon_H125 zenon_Hb2 zenon_H1fe zenon_H212 zenon_H164 zenon_H13b zenon_H288 zenon_H179 zenon_Hca zenon_H36 zenon_Hc2 zenon_H12e zenon_Hcb zenon_H234 zenon_H231 zenon_H192 zenon_Hbc zenon_H140 zenon_H1c7 zenon_H1a2 zenon_Ha9 zenon_H186 zenon_H190 zenon_H1a3 zenon_H159 zenon_H3d zenon_Hb6 zenon_H1c6 zenon_H196 zenon_H201 zenon_H77 zenon_H48 zenon_H121 zenon_H33 zenon_H9f zenon_Hc4 zenon_Ha0 zenon_H54 zenon_H141 zenon_H24 zenon_H13c zenon_H38 zenon_H68. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.35 apply (zenon_L297_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.35 apply (zenon_L69_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.35 apply (zenon_L1415_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.35 apply (zenon_L1416_); trivial. % 22.22/22.35 apply (zenon_L1542_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.35 apply (zenon_L69_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.35 apply (zenon_L1469_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.35 apply (zenon_L117_); trivial. % 22.22/22.35 apply (zenon_L1745_); trivial. % 22.22/22.35 apply (zenon_L663_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.35 apply (zenon_L214_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.35 apply (zenon_L1472_); trivial. % 22.22/22.35 apply (zenon_L165_); trivial. % 22.22/22.35 (* end of lemma zenon_L1746_ *) % 22.22/22.35 assert (zenon_L1747_ : (((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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((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) (e3)) = (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.22/22.35 do 0 intro. intros zenon_H139 zenon_H2c zenon_H162 zenon_H1cd zenon_H7d zenon_H24e zenon_H192 zenon_H183 zenon_Ha0 zenon_Ha9 zenon_H3d zenon_Hb6 zenon_H190 zenon_H1c3 zenon_H1cf zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H1b7 zenon_H117 zenon_H109 zenon_H6f zenon_H14c zenon_H13a zenon_H186 zenon_H1ef zenon_H65 zenon_H18a zenon_H34 zenon_H1d8 zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_H181 zenon_H1a2 zenon_Hc4 zenon_H104 zenon_H1c7 zenon_H33 zenon_H121 zenon_H18d zenon_H48 zenon_H5d zenon_H3c zenon_H1cb zenon_H38 zenon_H68. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.35 apply (zenon_L180_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.35 apply (zenon_L1701_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.22/22.35 apply (zenon_L1505_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.22/22.35 apply (zenon_L55_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.22/22.35 apply (zenon_L193_); trivial. % 22.22/22.35 apply (zenon_L156_); trivial. % 22.22/22.35 apply (zenon_L165_); trivial. % 22.22/22.35 (* end of lemma zenon_L1747_ *) % 22.22/22.35 assert (zenon_L1748_ : (((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)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.22/22.35 do 0 intro. intros zenon_H139 zenon_H2c zenon_H65 zenon_H181 zenon_H1bb zenon_H162 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_Hc4 zenon_H192 zenon_H183 zenon_H153 zenon_H77 zenon_H38 zenon_H68. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.35 apply (zenon_L180_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.35 apply (zenon_L1701_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.35 apply (zenon_L94_); trivial. % 22.22/22.35 apply (zenon_L165_); trivial. % 22.22/22.35 (* end of lemma zenon_L1748_ *) % 22.22/22.35 assert (zenon_L1749_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (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) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((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 (e3) (e3)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e0)) = (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)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.22/22.35 do 0 intro. intros zenon_H15d zenon_H24 zenon_H1cb zenon_H3c zenon_H5d zenon_H18d zenon_H121 zenon_H33 zenon_H104 zenon_H1a2 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1d8 zenon_H18a zenon_H1ef zenon_H186 zenon_H13a zenon_H14c zenon_H6f zenon_H109 zenon_H117 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H1c3 zenon_H190 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H68 zenon_H77 zenon_H183 zenon_H192 zenon_Hc4 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H162 zenon_H1bb zenon_H181 zenon_H65 zenon_H2c zenon_H139 zenon_H38 zenon_H48. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.35 apply (zenon_L1475_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.35 apply (zenon_L1747_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.35 apply (zenon_L1748_); trivial. % 22.22/22.35 apply (zenon_L246_); trivial. % 22.22/22.35 (* end of lemma zenon_L1749_ *) % 22.22/22.35 assert (zenon_L1750_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((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) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (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 (e0) (e3)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> False). % 22.22/22.35 do 0 intro. intros zenon_Hcb zenon_H162 zenon_H24e zenon_H1cd zenon_H7d zenon_H192 zenon_H15d zenon_H2c zenon_H65 zenon_H77 zenon_Ha9 zenon_H183 zenon_H38 zenon_H121 zenon_H13a zenon_Hb6 zenon_H23c zenon_H201 zenon_H6f zenon_Ha0 zenon_H18d zenon_H1cb zenon_H5d zenon_H117 zenon_H190 zenon_H13f zenon_H109 zenon_H1b7 zenon_H1f1 zenon_He4 zenon_H33 zenon_H186 zenon_H1ef zenon_H1bb zenon_H18a zenon_H1cf zenon_H1b4 zenon_H20f zenon_H129 zenon_H26a zenon_Hf5 zenon_H195 zenon_H25b zenon_H1a2 zenon_H1c3 zenon_H34 zenon_H68 zenon_H111 zenon_H1c7 zenon_H104 zenon_H14c zenon_H48 zenon_H4e zenon_H1d8 zenon_H139 zenon_H3c zenon_H24 zenon_Hc2. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.22/22.35 apply (zenon_L1476_); trivial. % 22.22/22.35 apply (zenon_L1476_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.22/22.35 apply (zenon_L1749_); trivial. % 22.22/22.35 apply (zenon_L1749_); trivial. % 22.22/22.35 (* end of lemma zenon_L1750_ *) % 22.22/22.35 assert (zenon_L1751_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((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)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.22/22.35 do 0 intro. intros zenon_Hfa zenon_H3c zenon_H6e zenon_H173 zenon_H1a3 zenon_Ha0 zenon_H14c zenon_Ha9 zenon_Hb6 zenon_H1a2 zenon_H1cf zenon_H153 zenon_H77 zenon_H186 zenon_H1ef zenon_H65 zenon_H1bb zenon_H162 zenon_H120 zenon_H1cb zenon_Hc4. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.35 apply (zenon_L24_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.35 apply (zenon_L226_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.35 apply (zenon_L1170_); trivial. % 22.22/22.35 apply (zenon_L1322_); trivial. % 22.22/22.35 (* end of lemma zenon_L1751_ *) % 22.22/22.35 assert (zenon_L1752_ : (((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)) = (e3))) -> (~((op (e3) (e2)) = (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 (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((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))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((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 (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.22/22.35 do 0 intro. intros zenon_H139 zenon_H2c zenon_Hc4 zenon_H1cb zenon_H120 zenon_H162 zenon_H1bb zenon_H65 zenon_H1ef zenon_H186 zenon_H1cf zenon_H1a2 zenon_Hb6 zenon_Ha9 zenon_H14c zenon_Ha0 zenon_H1a3 zenon_H173 zenon_H3c zenon_Hfa zenon_H153 zenon_H77 zenon_H38 zenon_H68. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.35 apply (zenon_L180_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.35 apply (zenon_L1751_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.35 apply (zenon_L94_); trivial. % 22.22/22.35 apply (zenon_L165_); trivial. % 22.22/22.35 (* end of lemma zenon_L1752_ *) % 22.22/22.35 assert (zenon_L1753_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((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)) = (op (e3) (e0)))) -> (~((op (e0) (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) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((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 (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((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)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.22/22.35 do 0 intro. intros zenon_H15d zenon_H24 zenon_H1d8 zenon_Hc2 zenon_Hcb zenon_H183 zenon_H1b7 zenon_H129 zenon_H1b4 zenon_H104 zenon_Hbc zenon_H231 zenon_H121 zenon_H34 zenon_H18a zenon_H13a zenon_H33 zenon_H6f zenon_H109 zenon_H117 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1c3 zenon_H26a zenon_H190 zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H18d zenon_H5d zenon_H68 zenon_H77 zenon_Hfa zenon_H3c zenon_H173 zenon_H1a3 zenon_Ha0 zenon_H14c zenon_Ha9 zenon_Hb6 zenon_H1a2 zenon_H1cf zenon_H186 zenon_H1ef zenon_H65 zenon_H1bb zenon_H162 zenon_H120 zenon_H1cb zenon_Hc4 zenon_H2c zenon_H139 zenon_H38 zenon_H48. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.35 apply (zenon_L1475_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.35 apply (zenon_L1325_); trivial. % 22.22/22.35 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.35 apply (zenon_L1752_); trivial. % 22.22/22.35 apply (zenon_L246_); trivial. % 22.22/22.35 (* end of lemma zenon_L1753_ *) % 22.22/22.35 assert (zenon_L1754_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (((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))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (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 (e0) (e3)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((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)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> False). % 22.22/22.36 do 0 intro. intros zenon_Hca zenon_H231 zenon_Hbc zenon_H173 zenon_Hfa zenon_Hc2 zenon_H24 zenon_H3c zenon_H139 zenon_H1d8 zenon_H4e zenon_H48 zenon_H14c zenon_H104 zenon_H111 zenon_H68 zenon_H34 zenon_H1c3 zenon_H1a2 zenon_H25b zenon_H195 zenon_Hf5 zenon_H26a zenon_H129 zenon_H20f zenon_H1b4 zenon_H1cf zenon_H18a zenon_H1bb zenon_H1ef zenon_H186 zenon_H33 zenon_He4 zenon_H1f1 zenon_H1b7 zenon_H109 zenon_H13f zenon_H190 zenon_H117 zenon_H5d zenon_H1cb zenon_H18d zenon_Ha0 zenon_H6f zenon_H201 zenon_H23c zenon_Hb6 zenon_H13a zenon_H121 zenon_H38 zenon_H183 zenon_Ha9 zenon_H77 zenon_H65 zenon_H2c zenon_H15d zenon_H192 zenon_H7d zenon_H1cd zenon_H24e zenon_H162 zenon_Hcb. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.22/22.36 apply (zenon_L1750_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.22/22.36 apply (zenon_L1753_); trivial. % 22.22/22.36 apply (zenon_L1753_); trivial. % 22.22/22.36 apply (zenon_L434_); trivial. % 22.22/22.36 (* end of lemma zenon_L1754_ *) % 22.22/22.36 assert (zenon_L1755_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (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) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e3)) = (op (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((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)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (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 (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (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)))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.22/22.36 do 0 intro. intros zenon_H16a zenon_Hcb zenon_H162 zenon_H24e zenon_H192 zenon_H15d zenon_H13a zenon_H23c zenon_H201 zenon_H6f zenon_H18d zenon_H5d zenon_H190 zenon_H13f zenon_H1b7 zenon_H1f1 zenon_He4 zenon_H186 zenon_H1ef zenon_H1bb zenon_H1cf zenon_H1b4 zenon_H129 zenon_H26a zenon_Hf5 zenon_H25b zenon_H1a2 zenon_H111 zenon_H4e zenon_H1d8 zenon_H139 zenon_Hc2 zenon_H173 zenon_Hca zenon_H171 zenon_He7 zenon_H1c3 zenon_Hc4 zenon_H1a3 zenon_H183 zenon_H68 zenon_H20f zenon_H33 zenon_H121 zenon_H1c2 zenon_H14c zenon_H104 zenon_H7d zenon_H18a zenon_H231 zenon_Hbc zenon_H1cd zenon_H1cb zenon_H212 zenon_H12e zenon_Hfa zenon_H77 zenon_H24 zenon_H38 zenon_H196 zenon_H117 zenon_H9f zenon_H2c zenon_Hb6 zenon_H53 zenon_Ha0 zenon_H48 zenon_H109 zenon_H34 zenon_H141 zenon_Ha9 zenon_H159 zenon_H3c zenon_H13c zenon_H195. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.22/22.36 apply (zenon_L1754_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.22/22.36 apply (zenon_L56_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.22/22.36 apply (zenon_L1411_); trivial. % 22.22/22.36 apply (zenon_L1496_); trivial. % 22.22/22.36 (* end of lemma zenon_L1755_ *) % 22.22/22.36 assert (zenon_L1756_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((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 (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (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 (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((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)) = (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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.22/22.36 do 0 intro. intros zenon_H82 zenon_H1f1 zenon_H13f zenon_H186 zenon_Hfa zenon_Hca zenon_H173 zenon_Hc2 zenon_H4e zenon_H111 zenon_H25b zenon_H26a zenon_H1ef zenon_H5d zenon_H18d zenon_H6f zenon_H201 zenon_H23c zenon_H15d zenon_H162 zenon_Hcb zenon_H68 zenon_H38 zenon_H77 zenon_H153 zenon_H121 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H33 zenon_H13a zenon_H1c7 zenon_H1a3 zenon_Hc4 zenon_H13b zenon_H179 zenon_H141 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_H1c3 zenon_H190 zenon_H1cf zenon_H196 zenon_H140 zenon_Hbc zenon_H183 zenon_H192 zenon_H231 zenon_H1cd zenon_H1a8 zenon_H55 zenon_H234 zenon_H1d8 zenon_He4 zenon_H73 zenon_H1b7 zenon_H24e zenon_H11a zenon_H109 zenon_Hf0 zenon_H1c2 zenon_H1d5 zenon_H12e zenon_H212 zenon_H18a zenon_H7d zenon_H104 zenon_H9f zenon_H117 zenon_H195 zenon_H159 zenon_H24 zenon_H13c zenon_H139 zenon_H2c zenon_H16a zenon_H100 zenon_Heb zenon_H191 zenon_H1a2 zenon_Hf5 zenon_H34 zenon_H48. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.36 apply (zenon_L1284_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.36 apply (zenon_L25_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.22/22.36 apply (zenon_L738_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.22/22.36 apply (zenon_L492_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.36 apply (zenon_L24_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.36 apply (zenon_L1405_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.36 apply (zenon_L1473_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.36 apply (zenon_L1409_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.36 apply (zenon_L1455_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.36 apply (zenon_L56_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.36 apply (zenon_L359_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.36 apply (zenon_L111_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.36 apply (zenon_L1755_); trivial. % 22.22/22.36 apply (zenon_L1162_); trivial. % 22.22/22.36 apply (zenon_L1484_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.36 apply (zenon_L1265_); trivial. % 22.22/22.36 apply (zenon_L663_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.36 apply (zenon_L1409_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.36 apply (zenon_L94_); trivial. % 22.22/22.36 apply (zenon_L165_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.36 apply (zenon_L1485_); trivial. % 22.22/22.36 apply (zenon_L456_); trivial. % 22.22/22.36 (* end of lemma zenon_L1756_ *) % 22.22/22.36 assert (zenon_L1757_ : (((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) (e3)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.22/22.36 do 0 intro. intros zenon_H141 zenon_H68 zenon_He7 zenon_Hf0 zenon_Hc4 zenon_Hb6 zenon_H1c7 zenon_H1cf zenon_Ha0 zenon_Ha9 zenon_He4 zenon_H23c zenon_H190 zenon_H4e zenon_H201 zenon_H13f zenon_H77 zenon_H1f1 zenon_H1b7 zenon_H3c zenon_H5d zenon_H48 zenon_H18d zenon_H117 zenon_H109 zenon_H6f zenon_H33 zenon_H13a zenon_Hf7 zenon_H186 zenon_H1ef zenon_H65 zenon_H1bb zenon_H18a zenon_H34 zenon_H1cb zenon_H121 zenon_H133 zenon_H3d zenon_H1d8 zenon_H196 zenon_H38. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.36 apply (zenon_L27_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.36 apply (zenon_L929_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.36 apply (zenon_L1503_); trivial. % 22.22/22.36 apply (zenon_L1162_); trivial. % 22.22/22.36 (* end of lemma zenon_L1757_ *) % 22.22/22.36 assert (zenon_L1758_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (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) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((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 (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((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 (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (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)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.22/22.36 do 0 intro. intros zenon_H15d zenon_H24 zenon_H196 zenon_H117 zenon_H190 zenon_H186 zenon_H1a2 zenon_H195 zenon_Hf0 zenon_He7 zenon_H109 zenon_H34 zenon_H141 zenon_H1cf zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H1b7 zenon_H3c zenon_H5d zenon_H18d zenon_H6f zenon_H1ef zenon_H1bb zenon_H18a zenon_H1cb zenon_H1d8 zenon_H11a zenon_H13c zenon_H73 zenon_Hfa zenon_H68 zenon_H77 zenon_H121 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H33 zenon_H13a zenon_H1c7 zenon_H1a3 zenon_Hc4 zenon_H65 zenon_H2c zenon_H139 zenon_H38 zenon_H48. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.36 apply (zenon_L1475_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.36 apply (zenon_L180_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.36 apply (zenon_L214_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.36 apply (zenon_L24_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.36 apply (zenon_L1453_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.36 apply (zenon_L22_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.36 apply (zenon_L46_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.36 apply (zenon_L1248_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.36 apply (zenon_L1757_); trivial. % 22.22/22.36 apply (zenon_L1452_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.22/22.36 apply (zenon_L55_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.22/22.36 apply (zenon_L193_); trivial. % 22.22/22.36 apply (zenon_L156_); trivial. % 22.22/22.36 apply (zenon_L165_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.36 apply (zenon_L1410_); trivial. % 22.22/22.36 apply (zenon_L246_); trivial. % 22.22/22.36 (* end of lemma zenon_L1758_ *) % 22.22/22.36 assert (zenon_L1759_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (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))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((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 (e3) (e3)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e0)) = (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)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.22/22.36 do 0 intro. intros zenon_H15d zenon_H24 zenon_H196 zenon_H190 zenon_H1c3 zenon_H1cf zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H117 zenon_H109 zenon_H6f zenon_H13a zenon_H186 zenon_H1ef zenon_H18a zenon_H1d8 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1a2 zenon_H104 zenon_H33 zenon_H121 zenon_H18d zenon_H5d zenon_H3c zenon_H1cb zenon_Hf0 zenon_He7 zenon_H141 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H68 zenon_H77 zenon_H183 zenon_H192 zenon_Hc4 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H162 zenon_H1bb zenon_H181 zenon_H65 zenon_H2c zenon_H139 zenon_H38 zenon_H48. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.36 apply (zenon_L1475_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.36 apply (zenon_L1632_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.36 apply (zenon_L1748_); trivial. % 22.22/22.36 apply (zenon_L246_); trivial. % 22.22/22.36 (* end of lemma zenon_L1759_ *) % 22.22/22.36 assert (zenon_L1760_ : (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (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) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.22/22.36 do 0 intro. intros zenon_H1d8 zenon_H3d zenon_Hc2 zenon_Hcb zenon_H183 zenon_H1b7 zenon_H18d zenon_H48 zenon_H129 zenon_H1b4 zenon_H1bb zenon_H120 zenon_H133 zenon_H162 zenon_H104 zenon_Hbc zenon_H231 zenon_H121 zenon_H1cb zenon_H34 zenon_H18a zenon_H65 zenon_H1ef zenon_H13a zenon_H33 zenon_Hb6 zenon_H14c zenon_H6f zenon_H109 zenon_H117 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H68 zenon_H1c3 zenon_H77 zenon_H26a zenon_Ha0 zenon_H1a3 zenon_H10d zenon_H190 zenon_H186 zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H195 zenon_H20f zenon_H3c zenon_H5d zenon_Hf5 zenon_H38 zenon_H25b zenon_Hc4. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.22/22.36 apply (zenon_L738_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.22/22.36 apply (zenon_L14_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.22/22.36 apply (zenon_L1321_); trivial. % 22.22/22.36 apply (zenon_L1324_); trivial. % 22.22/22.36 (* end of lemma zenon_L1760_ *) % 22.22/22.36 assert (zenon_L1761_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((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)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 22.22/22.36 do 0 intro. intros zenon_H201 zenon_Hc4 zenon_H120 zenon_H65 zenon_H1ef zenon_H186 zenon_H1cf zenon_Hb6 zenon_H133 zenon_Hcb zenon_H231 zenon_H162 zenon_H1cb zenon_H1bb zenon_H104 zenon_Hbc zenon_Hc2 zenon_Hca zenon_H183 zenon_H68 zenon_H34 zenon_Hac zenon_Ha9 zenon_H77 zenon_Hf7 zenon_H20f. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.22/22.36 apply (zenon_L1322_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.22/22.36 apply (zenon_L124_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.22/22.36 apply (zenon_L1547_); trivial. % 22.22/22.36 apply (zenon_L1153_); trivial. % 22.22/22.36 (* end of lemma zenon_L1761_ *) % 22.22/22.36 assert (zenon_L1762_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (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) (e3)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((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 (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 (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((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)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (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) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 22.22/22.36 do 0 intro. intros zenon_H13c zenon_H20f zenon_H77 zenon_H34 zenon_H68 zenon_H183 zenon_Hca zenon_Hc2 zenon_Hbc zenon_H104 zenon_H1bb zenon_H1cb zenon_H162 zenon_H231 zenon_Hcb zenon_Hb6 zenon_H1cf zenon_H186 zenon_H1ef zenon_H65 zenon_H120 zenon_Hc4 zenon_H201 zenon_H141 zenon_H25b zenon_Hf5 zenon_H5d zenon_H3c zenon_H195 zenon_H1a2 zenon_H66 zenon_H190 zenon_H1a3 zenon_Ha0 zenon_H26a zenon_H1c3 zenon_He4 zenon_H23c zenon_H4e zenon_H13f zenon_H1f1 zenon_H117 zenon_H109 zenon_H6f zenon_H33 zenon_H13a zenon_H18a zenon_H121 zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_H1b7 zenon_H3d zenon_H1d8 zenon_H196 zenon_H38 zenon_H11a zenon_H1c6 zenon_Ha9 zenon_Hf7. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.36 apply (zenon_L46_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.36 apply (zenon_L1248_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.36 apply (zenon_L55_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.36 apply (zenon_L1248_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.36 apply (zenon_L27_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.36 apply (zenon_L152_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.36 apply (zenon_L1760_); trivial. % 22.22/22.36 apply (zenon_L1162_); trivial. % 22.22/22.36 apply (zenon_L1761_); trivial. % 22.22/22.36 apply (zenon_L299_); trivial. % 22.22/22.36 (* end of lemma zenon_L1762_ *) % 22.22/22.36 assert (zenon_L1763_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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)) = (op (e3) (e3)))) -> (((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 (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (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) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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 (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((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))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((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 (e0) (e3)) = (op (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 (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.22/22.36 do 0 intro. intros zenon_H15d zenon_H24 zenon_H1c6 zenon_H11a zenon_H1d8 zenon_H1b7 zenon_H18d zenon_H129 zenon_H1b4 zenon_H121 zenon_H18a zenon_H13a zenon_H33 zenon_H6f zenon_H117 zenon_H1f1 zenon_H13f zenon_H4e zenon_H23c zenon_He4 zenon_H1c3 zenon_H26a zenon_H190 zenon_H195 zenon_H5d zenon_Hf5 zenon_H25b zenon_H201 zenon_Hcb zenon_H231 zenon_H104 zenon_Hbc zenon_Hc2 zenon_Hca zenon_H183 zenon_H20f zenon_H13c zenon_H73 zenon_H68 zenon_H77 zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_Hc4 zenon_H1cb zenon_H120 zenon_H162 zenon_H1bb zenon_H65 zenon_H1ef zenon_H186 zenon_H1cf zenon_H1a2 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H1a3 zenon_H173 zenon_H3c zenon_Hfa zenon_H196 zenon_H2c zenon_H139 zenon_H38 zenon_H48. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.36 apply (zenon_L1475_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.36 apply (zenon_L180_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.36 apply (zenon_L214_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.36 apply (zenon_L24_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.36 apply (zenon_L1453_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.36 apply (zenon_L22_); trivial. % 22.22/22.36 apply (zenon_L1762_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.22/22.36 apply (zenon_L55_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.22/22.36 apply (zenon_L193_); trivial. % 22.22/22.36 apply (zenon_L156_); trivial. % 22.22/22.36 apply (zenon_L165_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.36 apply (zenon_L180_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.36 apply (zenon_L359_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.36 apply (zenon_L929_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.36 apply (zenon_L1751_); trivial. % 22.22/22.36 apply (zenon_L1162_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.36 apply (zenon_L94_); trivial. % 22.22/22.36 apply (zenon_L165_); trivial. % 22.22/22.36 apply (zenon_L246_); trivial. % 22.22/22.36 (* end of lemma zenon_L1763_ *) % 22.22/22.36 assert (zenon_L1764_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (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) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 22.22/22.36 do 0 intro. intros zenon_H24 zenon_H3c zenon_H139 zenon_Hfa zenon_H13a zenon_H1c6 zenon_Hca zenon_H1c3 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1cf zenon_H1ef zenon_H23c zenon_H201 zenon_H6f zenon_H18d zenon_H5d zenon_H48 zenon_H13f zenon_H1b7 zenon_H1f1 zenon_He4 zenon_H18a zenon_H26a zenon_Hf5 zenon_H25b zenon_H183 zenon_Hc2 zenon_Hbc zenon_H104 zenon_H1bb zenon_H1cb zenon_H120 zenon_H162 zenon_H231 zenon_Hcb zenon_H4e zenon_H1d8 zenon_H73 zenon_Hb6 zenon_H121 zenon_H1a3 zenon_H11a zenon_H33 zenon_H141 zenon_H38 zenon_H196 zenon_He7 zenon_Hf0 zenon_H68 zenon_Ha9 zenon_H1a2 zenon_H190 zenon_H186 zenon_Ha0 zenon_H195 zenon_H117 zenon_H34 zenon_H109 zenon_H13c zenon_H77 zenon_H65 zenon_H2c zenon_H173 zenon_H15d. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.22/22.36 apply (zenon_L1763_); trivial. % 22.22/22.36 apply (zenon_L1763_); trivial. % 22.22/22.36 (* end of lemma zenon_L1764_ *) % 22.22/22.36 assert (zenon_L1765_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (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 (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((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 (e0) (e2)))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (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) (e0)) = (op (e3) (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((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)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 22.22/22.36 do 0 intro. intros zenon_H36 zenon_H1c6 zenon_H26a zenon_Hf5 zenon_H25b zenon_Hbc zenon_H231 zenon_H173 zenon_H24 zenon_H3c zenon_H139 zenon_Hfa zenon_H13a zenon_H1d8 zenon_H48 zenon_H23c zenon_H201 zenon_H6f zenon_H18d zenon_H1cb zenon_H5d zenon_H4e zenon_H13f zenon_H1b7 zenon_H1f1 zenon_He4 zenon_H1ef zenon_H1bb zenon_H18a zenon_H1cf zenon_H73 zenon_Hb6 zenon_H121 zenon_H11a zenon_H33 zenon_H141 zenon_H196 zenon_He7 zenon_Hf0 zenon_H68 zenon_Ha9 zenon_H1a2 zenon_H190 zenon_H186 zenon_Ha0 zenon_H195 zenon_H117 zenon_H109 zenon_H13c zenon_H77 zenon_H65 zenon_H2c zenon_H15d zenon_H104 zenon_H1c3 zenon_H129 zenon_H20f zenon_H1b4 zenon_H192 zenon_H7d zenon_H1cd zenon_H24e zenon_H162 zenon_H183. % 22.22/22.36 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.22/22.36 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.22/22.36 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.22/22.36 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.22/22.36 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.22/22.36 apply (zenon_L1758_); trivial. % 22.22/22.36 apply (zenon_L1758_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.22/22.36 apply (zenon_L1759_); trivial. % 22.22/22.36 apply (zenon_L1759_); trivial. % 22.22/22.36 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.22/22.36 apply (zenon_L1764_); trivial. % 22.22/22.36 apply (zenon_L434_); trivial. % 22.22/22.36 (* end of lemma zenon_L1765_ *) % 22.22/22.36 assert (zenon_L1766_ : (((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 (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((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 (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((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 (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)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.22/22.36 do 0 intro. intros zenon_H125 zenon_H1d5 zenon_H66 zenon_H38 zenon_Hf5 zenon_He2 zenon_H3d zenon_H183 zenon_H162 zenon_H24e zenon_H1cd zenon_H7d zenon_H192 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1c3 zenon_H104 zenon_H15d zenon_H2c zenon_H77 zenon_H109 zenon_H186 zenon_H190 zenon_H1a2 zenon_Hf0 zenon_H196 zenon_H141 zenon_H11a zenon_Hb6 zenon_H73 zenon_H1cf zenon_H18a zenon_H1bb zenon_H1ef zenon_He4 zenon_H1f1 zenon_H1b7 zenon_H13f zenon_H4e zenon_H5d zenon_H1cb zenon_H18d zenon_H6f zenon_H201 zenon_H23c zenon_H48 zenon_H1d8 zenon_H13a zenon_Hfa zenon_H139 zenon_H3c zenon_H173 zenon_H231 zenon_Hbc zenon_H25b zenon_H26a zenon_H1c6 zenon_H36 zenon_H195 zenon_H191 zenon_Ha9 zenon_H117 zenon_H159 zenon_H24 zenon_H13c zenon_H121 zenon_H33 zenon_H9f zenon_Ha0 zenon_H1a3 zenon_Hc4 zenon_H179 zenon_H13b zenon_H34 zenon_H68. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.22/22.37 apply (zenon_L252_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.22/22.37 apply (zenon_L24_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.37 apply (zenon_L297_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.37 apply (zenon_L1765_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.22/22.37 apply (zenon_L65_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.22/22.37 apply (zenon_L1765_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.22/22.37 apply (zenon_L1460_); trivial. % 22.22/22.37 apply (zenon_L1401_); trivial. % 22.22/22.37 apply (zenon_L663_); trivial. % 22.22/22.37 apply (zenon_L291_); trivial. % 22.22/22.37 (* end of lemma zenon_L1766_ *) % 22.22/22.37 assert (zenon_L1767_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H183 zenon_H68 zenon_H77 zenon_H7f zenon_Hc4 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H162 zenon_H1bb zenon_H181. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.22/22.37 apply (zenon_L291_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.22/22.37 apply (zenon_L169_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.22/22.37 apply (zenon_L870_); trivial. % 22.22/22.37 exact (zenon_H181 zenon_H17c). % 22.22/22.37 (* end of lemma zenon_L1767_ *) % 22.22/22.37 assert (zenon_L1768_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (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)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (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)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.22/22.37 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H153 zenon_H23c zenon_H38 zenon_H196 zenon_H117 zenon_H9f zenon_H2c zenon_Hb6 zenon_Ha0 zenon_H195 zenon_H48 zenon_H109 zenon_H141 zenon_Hf3 zenon_H159 zenon_H3c zenon_H13c zenon_H183 zenon_H68 zenon_H77 zenon_Hc4 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H162 zenon_H1bb zenon_H181. % 22.22/22.37 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.22/22.37 apply (zenon_L738_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.22/22.37 apply (zenon_L492_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.22/22.37 apply (zenon_L1498_); trivial. % 22.22/22.37 apply (zenon_L1767_); trivial. % 22.22/22.37 (* end of lemma zenon_L1768_ *) % 22.22/22.37 assert (zenon_L1769_ : (((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((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))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (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))))) -> (((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 (e2) (e1)) = (op (e3) (e1)))) -> (((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) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((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))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.22/22.37 do 0 intro. intros zenon_H13b zenon_H179 zenon_H1a8 zenon_Hf0 zenon_H12e zenon_H18a zenon_H1cb zenon_H1b4 zenon_H129 zenon_H18d zenon_H26a zenon_H186 zenon_H20f zenon_H25b zenon_H24 zenon_H104 zenon_H177 zenon_Hca zenon_H231 zenon_Hbc zenon_H173 zenon_Hfa zenon_Hc2 zenon_H139 zenon_H4e zenon_H111 zenon_H1c3 zenon_H1a2 zenon_H1cf zenon_H1ef zenon_H33 zenon_H1f1 zenon_H13f zenon_H190 zenon_H5d zenon_H6f zenon_H201 zenon_H13a zenon_H121 zenon_Ha9 zenon_H15d zenon_H192 zenon_Hcb zenon_H16a zenon_H181 zenon_H1bb zenon_H162 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_Hc4 zenon_H77 zenon_H68 zenon_H183 zenon_H13c zenon_H3c zenon_H159 zenon_H141 zenon_H109 zenon_H48 zenon_H195 zenon_Ha0 zenon_Hb6 zenon_H2c zenon_H9f zenon_H117 zenon_H196 zenon_H23c zenon_H153 zenon_H1d8 zenon_He4 zenon_Hf5 zenon_H38. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.37 apply (zenon_L297_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.22/22.37 apply (zenon_L738_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.22/22.37 apply (zenon_L492_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.22/22.37 apply (zenon_L24_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.22/22.37 apply (zenon_L1405_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.22/22.37 apply (zenon_L1473_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.37 apply (zenon_L1701_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.37 apply (zenon_L1455_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.37 apply (zenon_L56_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.37 apply (zenon_L359_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.37 apply (zenon_L111_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.22/22.37 apply (zenon_L1754_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.22/22.37 apply (zenon_L56_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.22/22.37 apply (zenon_L1495_); trivial. % 22.22/22.37 apply (zenon_L1710_); trivial. % 22.22/22.37 apply (zenon_L1162_); trivial. % 22.22/22.37 apply (zenon_L1767_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.37 apply (zenon_L1768_); trivial. % 22.22/22.37 apply (zenon_L663_); trivial. % 22.22/22.37 (* end of lemma zenon_L1769_ *) % 22.22/22.37 assert (zenon_L1770_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (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)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((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 (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H1cf zenon_H1d5 zenon_H67 zenon_H38 zenon_H196 zenon_H117 zenon_Hb6 zenon_H54 zenon_Ha9 zenon_Ha0 zenon_H195 zenon_H68 zenon_H48 zenon_H141 zenon_H159 zenon_H24 zenon_H9f zenon_H13c zenon_H190 zenon_H6d zenon_H1bb zenon_H162 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H181 zenon_Hc4. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.22/22.37 apply (zenon_L252_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.22/22.37 apply (zenon_L1481_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.22/22.37 apply (zenon_L366_); trivial. % 22.22/22.37 apply (zenon_L870_); trivial. % 22.22/22.37 (* end of lemma zenon_L1770_ *) % 22.22/22.37 assert (zenon_L1771_ : (((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 (e2) (e2)))) -> ((op (e0) (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 (e3) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (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 (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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 (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (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 (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (((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 (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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) (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H16a zenon_H2c zenon_H190 zenon_H67 zenon_H1d5 zenon_H1cf zenon_H171 zenon_H177 zenon_Heb zenon_H100 zenon_H1c7 zenon_H1a2 zenon_H186 zenon_Hbc zenon_H18a zenon_H104 zenon_H231 zenon_H1cb zenon_H18d zenon_H36 zenon_H12e zenon_H48 zenon_H11a zenon_H288 zenon_Hf5 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H196 zenon_H1fb zenon_H25e zenon_H13a zenon_H1d8 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H192 zenon_H183 zenon_H6f zenon_H159 zenon_H141 zenon_H111 zenon_H13f zenon_He7 zenon_Hf0 zenon_H195 zenon_H54 zenon_H117 zenon_H1c6 zenon_H162 zenon_H26a zenon_H25b zenon_H24 zenon_H9f zenon_H13c zenon_H73 zenon_H153 zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H181. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.22/22.37 apply (zenon_L180_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.22/22.37 apply (zenon_L1770_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.22/22.37 apply (zenon_L1495_); trivial. % 22.22/22.37 apply (zenon_L1711_); trivial. % 22.22/22.37 (* end of lemma zenon_L1771_ *) % 22.22/22.37 assert (zenon_L1772_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> (~((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))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> (((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 (e2) (e2)))) -> ((op (e0) (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 (e0) (e2)) = (op (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) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (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 (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (((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 (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.22/22.37 do 0 intro. intros zenon_H109 zenon_H10d zenon_Hc4 zenon_Hb6 zenon_H1c7 zenon_H9f zenon_H33 zenon_H121 zenon_H48 zenon_H12e zenon_H34 zenon_H3d zenon_H192 zenon_H163 zenon_He7 zenon_H171 zenon_H16a zenon_H2c zenon_H190 zenon_H67 zenon_H1d5 zenon_H1cf zenon_H177 zenon_Heb zenon_H100 zenon_H1a2 zenon_H186 zenon_Hbc zenon_H18a zenon_H104 zenon_H231 zenon_H1cb zenon_H18d zenon_H36 zenon_H11a zenon_H288 zenon_Hf5 zenon_Ha0 zenon_Ha9 zenon_H1fb zenon_H25e zenon_H13a zenon_H1d8 zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H183 zenon_H6f zenon_H159 zenon_H141 zenon_H111 zenon_H13f zenon_Hf0 zenon_H195 zenon_H54 zenon_H117 zenon_H1c6 zenon_H162 zenon_H26a zenon_H25b zenon_H24 zenon_H13c zenon_H73 zenon_H1c3 zenon_H68 zenon_H77 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H181 zenon_H201 zenon_H196 zenon_H38. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.37 apply (zenon_L359_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.37 apply (zenon_L152_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.22/22.37 apply (zenon_L1771_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.22/22.37 apply (zenon_L965_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.22/22.37 apply (zenon_L255_); trivial. % 22.22/22.37 apply (zenon_L1414_); trivial. % 22.22/22.37 apply (zenon_L1162_); trivial. % 22.22/22.37 (* end of lemma zenon_L1772_ *) % 22.22/22.37 assert (zenon_L1773_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H16a zenon_H38 zenon_H192 zenon_Hc4 zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H162 zenon_H1bb zenon_H2c zenon_H139 zenon_Ha9 zenon_H10d zenon_H171 zenon_He7 zenon_H177 zenon_H153 zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H104 zenon_H181 zenon_H48 zenon_H12e zenon_Hf7 zenon_H195. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.22/22.37 apply (zenon_L1748_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.22/22.37 apply (zenon_L289_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.22/22.37 apply (zenon_L1495_); trivial. % 22.22/22.37 apply (zenon_L228_); trivial. % 22.22/22.37 (* end of lemma zenon_L1773_ *) % 22.22/22.37 assert (zenon_L1774_ : (((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)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (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))))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (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 (e1) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (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 (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 22.22/22.37 do 0 intro. intros zenon_H13c zenon_H24 zenon_H1c7 zenon_H141 zenon_H109 zenon_Ha0 zenon_Hc4 zenon_Hb6 zenon_H9f zenon_H33 zenon_H121 zenon_H48 zenon_H16a zenon_H192 zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H162 zenon_H1bb zenon_H2c zenon_H139 zenon_H171 zenon_He7 zenon_H177 zenon_H183 zenon_H68 zenon_H34 zenon_H77 zenon_H104 zenon_H181 zenon_H12e zenon_H195 zenon_H201 zenon_H196 zenon_H38 zenon_H159 zenon_H3d zenon_H1c6 zenon_Ha9 zenon_Hf7. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.37 apply (zenon_L900_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.37 exact (zenon_H159 zenon_H10c). % 22.22/22.37 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.37 apply (zenon_L55_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.37 exact (zenon_H159 zenon_H10c). % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.37 apply (zenon_L359_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.37 apply (zenon_L152_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.22/22.37 apply (zenon_L1773_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.22/22.37 apply (zenon_L124_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.22/22.37 apply (zenon_L255_); trivial. % 22.22/22.37 apply (zenon_L1414_); trivial. % 22.22/22.37 apply (zenon_L1162_); trivial. % 22.22/22.37 exact (zenon_H1c7 zenon_Hac). % 22.22/22.37 apply (zenon_L299_); trivial. % 22.22/22.37 (* end of lemma zenon_L1774_ *) % 22.22/22.37 assert (zenon_L1775_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e2) (e1)) = (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) (e3)) = (e0)) -> (~((op (e0) (e3)) = (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)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (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)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.22/22.37 do 0 intro. intros zenon_He4 zenon_Hdd zenon_H1c6 zenon_H23c zenon_H38 zenon_H196 zenon_H117 zenon_H9f zenon_H2c zenon_Hb6 zenon_Ha0 zenon_H195 zenon_H48 zenon_H109 zenon_H141 zenon_Hf3 zenon_H159 zenon_H3c zenon_H13c zenon_H183 zenon_H68 zenon_H77 zenon_Hc4 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H162 zenon_H1bb zenon_H181. % 22.22/22.37 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.22/22.37 apply (zenon_L1242_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.22/22.37 apply (zenon_L492_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.22/22.37 apply (zenon_L1498_); trivial. % 22.22/22.37 apply (zenon_L1767_); trivial. % 22.22/22.37 (* end of lemma zenon_L1775_ *) % 22.22/22.37 assert (zenon_L1776_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H26a zenon_H9f zenon_Ha9 zenon_H115 zenon_H1bb zenon_H181 zenon_H1c2 zenon_H8a zenon_H5c zenon_H77 zenon_H19a zenon_H68 zenon_H48 zenon_Ha0 zenon_H162 zenon_H1c3 zenon_Hc4. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H9e | zenon_intro zenon_H26b ]. % 22.22/22.37 apply (zenon_L209_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H26c ]. % 22.22/22.37 apply (zenon_L886_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc3 ]. % 22.22/22.37 apply (zenon_L208_); trivial. % 22.22/22.37 exact (zenon_Hc4 zenon_Hc3). % 22.22/22.37 (* end of lemma zenon_L1776_ *) % 22.22/22.37 assert (zenon_L1777_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H1c3 zenon_Ha0 zenon_H48 zenon_H68 zenon_H19a zenon_H77 zenon_H5c zenon_H8a zenon_H1c2 zenon_H181 zenon_H1bb zenon_Ha9 zenon_H9f zenon_H26a zenon_H162. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.22/22.37 apply (zenon_L414_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.22/22.37 apply (zenon_L157_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.22/22.37 apply (zenon_L1776_); trivial. % 22.22/22.37 exact (zenon_H162 zenon_H167). % 22.22/22.37 (* end of lemma zenon_L1777_ *) % 22.22/22.37 assert (zenon_L1778_ : (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (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 (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (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) (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 (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (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) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H68 zenon_H38 zenon_H77 zenon_H153 zenon_H183 zenon_H192 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_Hb6 zenon_H9f zenon_H24 zenon_H121 zenon_H11a zenon_H33 zenon_H141 zenon_H2c zenon_H1d8 zenon_H111 zenon_H26a zenon_He4 zenon_H1f1 zenon_H109 zenon_H13f zenon_H23c zenon_H82 zenon_H186 zenon_Hf0 zenon_H191 zenon_H104 zenon_H1c2 zenon_H19a zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H201 zenon_H48 zenon_H1a8 zenon_Hcb zenon_Hfa zenon_H140 zenon_Hbc zenon_H231 zenon_H12e zenon_H234 zenon_Hc2 zenon_H1d5 zenon_H36 zenon_Hca zenon_H5d zenon_H13a zenon_Ha0 zenon_Ha9 zenon_H139 zenon_H13b zenon_H179 zenon_H288 zenon_H164 zenon_H212 zenon_H1fe zenon_Hb2 zenon_H125 zenon_H177 zenon_H159 zenon_H100 zenon_Hf5 zenon_H1bb zenon_H162 zenon_H18a zenon_H181 zenon_Hc4. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.37 apply (zenon_L1284_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.37 apply (zenon_L1769_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.37 apply (zenon_L297_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.37 apply (zenon_L69_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.37 apply (zenon_L1701_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.37 apply (zenon_L186_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.37 apply (zenon_L1770_); trivial. % 22.22/22.37 apply (zenon_L1771_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.37 apply (zenon_L184_); trivial. % 22.22/22.37 apply (zenon_L414_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.37 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.37 apply (zenon_L69_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.37 apply (zenon_L1642_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.37 apply (zenon_L184_); trivial. % 22.22/22.37 apply (zenon_L1556_); trivial. % 22.22/22.37 apply (zenon_L663_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.22/22.37 apply (zenon_L1701_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.22/22.37 apply (zenon_L94_); trivial. % 22.22/22.37 apply (zenon_L165_); trivial. % 22.22/22.37 apply (zenon_L211_); trivial. % 22.22/22.37 (* end of lemma zenon_L1778_ *) % 22.22/22.37 assert (zenon_L1779_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> (~((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 (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) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((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) (e3)) = (e3))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H82 zenon_H68 zenon_H38 zenon_H1cb zenon_H5d zenon_H48 zenon_H18d zenon_H121 zenon_H33 zenon_H1c7 zenon_H104 zenon_H1a2 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1d8 zenon_H34 zenon_H1ef zenon_H186 zenon_H13a zenon_H14c zenon_H6f zenon_H109 zenon_H117 zenon_H1b7 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H1c3 zenon_H190 zenon_Hb6 zenon_H3d zenon_Ha9 zenon_Ha0 zenon_H183 zenon_H192 zenon_H24e zenon_H7d zenon_H1cd zenon_H2c zenon_H139 zenon_H65 zenon_H77 zenon_H1bb zenon_H162 zenon_H18a zenon_H181 zenon_Hc4. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.37 apply (zenon_L1287_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.37 apply (zenon_L1747_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.37 apply (zenon_L30_); trivial. % 22.22/22.37 apply (zenon_L211_); trivial. % 22.22/22.37 (* end of lemma zenon_L1779_ *) % 22.22/22.37 assert (zenon_L1780_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((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)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (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)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H1c6 zenon_H159 zenon_H181 zenon_H12e zenon_H48 zenon_H3d zenon_H192 zenon_H4d zenon_H163 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_He7 zenon_H68 zenon_H183 zenon_Hb6 zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H93 zenon_H77 zenon_H162 zenon_H18a zenon_H13a zenon_H104 zenon_H33 zenon_H121 zenon_H111 zenon_Ha0 zenon_H141 zenon_H54 zenon_Hef zenon_H196 zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H1c7. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.37 apply (zenon_L55_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.37 exact (zenon_H159 zenon_H10c). % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.37 apply (zenon_L1704_); trivial. % 22.22/22.37 exact (zenon_H1c7 zenon_Hac). % 22.22/22.37 (* end of lemma zenon_L1780_ *) % 22.22/22.37 assert (zenon_L1781_ : ((op (e0) (e0)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((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))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((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) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H67 zenon_Ha5 zenon_H16a zenon_H139 zenon_H2c zenon_H162 zenon_H1bb zenon_H1ef zenon_H186 zenon_H1cf zenon_H1a2 zenon_Hb6 zenon_Ha0 zenon_H173 zenon_H3c zenon_Hfa zenon_H5d zenon_H18d zenon_H25b zenon_Hf5 zenon_H195 zenon_H190 zenon_H26a zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H117 zenon_H109 zenon_H6f zenon_H13a zenon_H1b4 zenon_H129 zenon_H1b7 zenon_Hcb zenon_Hc2 zenon_H1d8 zenon_H24 zenon_H15d zenon_Hf0 zenon_Hef zenon_H120 zenon_H1c3 zenon_H38 zenon_Hc4 zenon_H1a3 zenon_H183 zenon_H68 zenon_H34 zenon_Ha9 zenon_H20f zenon_H9f zenon_H33 zenon_H121 zenon_H1c2 zenon_H14c zenon_H104 zenon_H7d zenon_H18a zenon_H231 zenon_Hbc zenon_H1cd zenon_H1cb zenon_H212 zenon_H48 zenon_H12e zenon_H77. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.37 apply (zenon_L1644_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.37 apply (zenon_L1403_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.37 apply (zenon_L255_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.22/22.37 apply (zenon_L1753_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.22/22.37 apply (zenon_L61_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.22/22.37 apply (zenon_L1643_); trivial. % 22.22/22.37 apply (zenon_L218_); trivial. % 22.22/22.37 (* end of lemma zenon_L1781_ *) % 22.22/22.37 assert (zenon_L1782_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H1cf zenon_H77 zenon_H1a3 zenon_Ha0 zenon_H14c zenon_Ha9 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H190 zenon_H6d zenon_Hc2 zenon_H162 zenon_H120 zenon_H1cb zenon_H1bb. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.22/22.37 apply (zenon_L94_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.22/22.37 apply (zenon_L1170_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.22/22.37 apply (zenon_L366_); trivial. % 22.22/22.37 apply (zenon_L238_); trivial. % 22.22/22.37 (* end of lemma zenon_L1782_ *) % 22.22/22.37 assert (zenon_L1783_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H1a2 zenon_H67 zenon_H105 zenon_H72 zenon_H1ef zenon_Ha8 zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_Ha9 zenon_H6d zenon_H1cd. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.22/22.37 apply (zenon_L446_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.22/22.37 apply (zenon_L436_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.22/22.37 apply (zenon_L282_); trivial. % 22.22/22.37 apply (zenon_L1111_); trivial. % 22.22/22.37 (* end of lemma zenon_L1783_ *) % 22.22/22.37 assert (zenon_L1784_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.22/22.37 do 0 intro. intros zenon_H117 zenon_H1cd zenon_H159 zenon_H3d zenon_Hb6 zenon_H1c6 zenon_H1ef zenon_H72 zenon_H105 zenon_H67 zenon_H1a2 zenon_Ha9 zenon_H6d zenon_H14c zenon_Ha0 zenon_Ha5 zenon_H195. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.22/22.37 apply (zenon_L1783_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.22/22.37 apply (zenon_L289_); trivial. % 22.22/22.37 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.22/22.38 apply (zenon_L278_); trivial. % 22.22/22.38 apply (zenon_L172_); trivial. % 22.22/22.38 (* end of lemma zenon_L1784_ *) % 22.22/22.38 assert (zenon_L1785_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((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))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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 (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((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)) = (op (e2) (e1)))) -> (((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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (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)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e0)) = (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> ((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)) = (op (e2) (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 (e1) (e2)) = (op (e1) (e3)))) -> (((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) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (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) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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 (e3) (e0)) = (op (e3) (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)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 22.22/22.38 do 0 intro. intros zenon_Hb2 zenon_H111 zenon_He2 zenon_H100 zenon_H22d zenon_H125 zenon_H164 zenon_H179 zenon_H288 zenon_H13b zenon_H1fe zenon_H177 zenon_H212 zenon_H12e zenon_H159 zenon_H67 zenon_H234 zenon_H192 zenon_H27e zenon_Hf0 zenon_He7 zenon_H1d5 zenon_Hfa zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H1fb zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H189 zenon_H266 zenon_H55 zenon_H13e zenon_H158 zenon_H173 zenon_H1ec zenon_H73 zenon_H163 zenon_H283 zenon_Ha9 zenon_H141 zenon_H68 zenon_H195 zenon_H48 zenon_H117 zenon_Hb6 zenon_Ha0 zenon_H13f zenon_H196 zenon_H38 zenon_H156 zenon_H3d zenon_H1a8 zenon_H54 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H1c3 zenon_H1a3 zenon_H183 zenon_H34 zenon_H9f zenon_H33 zenon_H121 zenon_H1c2 zenon_H16a zenon_H1a2 zenon_H186 zenon_H201 zenon_H140 zenon_H26d zenon_H36 zenon_H131 zenon_H191 zenon_H162 zenon_H19a zenon_H120 zenon_H24e zenon_H7d zenon_H1cd zenon_H1b7 zenon_H11a zenon_H82 zenon_H1d8 zenon_Hc2 zenon_Hcb zenon_H104 zenon_H231 zenon_H18a zenon_H1ef zenon_H13a zenon_H6f zenon_H109 zenon_H1f1 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H26a zenon_H190 zenon_Hf5 zenon_H25b zenon_H5d zenon_H2c zenon_H139 zenon_Hbc zenon_H1c6 zenon_H24 zenon_H13c zenon_H77. % 22.22/22.38 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.22/22.38 apply (zenon_L69_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.22/22.38 apply (zenon_L1653_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.22/22.38 apply (zenon_L1654_); trivial. % 22.22/22.38 apply (zenon_L1546_); trivial. % 22.22/22.38 (* end of lemma zenon_L1785_ *) % 22.22/22.38 assert (zenon_L1786_ : (((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))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (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) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (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) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.22/22.38 do 0 intro. intros zenon_H82 zenon_H13a zenon_H68 zenon_H38 zenon_H153 zenon_Hfa zenon_H173 zenon_H1a3 zenon_Ha0 zenon_H14c zenon_Ha9 zenon_Hb6 zenon_H1a2 zenon_H1cf zenon_H186 zenon_H1ef zenon_H1bb zenon_H162 zenon_H120 zenon_H1cb zenon_Hc4 zenon_H2c zenon_H139 zenon_H65 zenon_H77 zenon_H34 zenon_H48. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.22/22.38 apply (zenon_L1284_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.22/22.38 apply (zenon_L1752_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.22/22.38 apply (zenon_L30_); trivial. % 22.22/22.38 apply (zenon_L456_); trivial. % 22.22/22.38 (* end of lemma zenon_L1786_ *) % 22.22/22.38 assert (zenon_L1787_ : (~((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)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (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) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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 (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (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)) = (e0)) -> False). % 22.22/22.38 do 0 intro. intros zenon_H195 zenon_H13c zenon_H3c zenon_H159 zenon_Ha9 zenon_H141 zenon_H34 zenon_H109 zenon_H48 zenon_Ha0 zenon_H53 zenon_Hb6 zenon_H2c zenon_H9f zenon_H117 zenon_H24 zenon_H77 zenon_Hfa zenon_H191 zenon_H12e zenon_H1b7 zenon_H5d zenon_H18d zenon_H1c2 zenon_H121 zenon_H33 zenon_H20f zenon_H68 zenon_H183 zenon_H1a3 zenon_Hc4 zenon_H1c3 zenon_H120 zenon_H82 zenon_H13a zenon_H153 zenon_H173 zenon_H1a2 zenon_H1cf zenon_H186 zenon_H1ef zenon_H1bb zenon_H162 zenon_H1cb zenon_H139 zenon_H16a zenon_H196 zenon_H38. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.38 apply (zenon_L359_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.38 apply (zenon_L111_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.22/22.38 apply (zenon_L1786_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.22/22.38 apply (zenon_L56_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.22/22.38 apply (zenon_L1065_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.22/22.38 apply (zenon_L113_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.22/22.38 exact (zenon_H191 zenon_H110). % 22.22/22.38 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.22/22.38 apply (zenon_L456_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.22/22.38 apply (zenon_L1290_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.22/22.38 apply (zenon_L1158_); trivial. % 22.22/22.38 exact (zenon_H120 zenon_H11f). % 22.22/22.38 apply (zenon_L1496_); trivial. % 22.22/22.38 apply (zenon_L1162_); trivial. % 22.22/22.38 (* end of lemma zenon_L1787_ *) % 22.22/22.38 assert (zenon_L1788_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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 (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)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (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) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e2) (e1)) = (op (e3) (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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.22/22.38 do 0 intro. intros zenon_He4 zenon_H177 zenon_H11a zenon_H1c3 zenon_H20f zenon_H1c2 zenon_H18d zenon_H5d zenon_H1b7 zenon_H12e zenon_H191 zenon_H24 zenon_H117 zenon_H159 zenon_H13c zenon_H195 zenon_H141 zenon_H109 zenon_He7 zenon_Hf0 zenon_H77 zenon_H183 zenon_H68 zenon_H34 zenon_H104 zenon_H121 zenon_H33 zenon_H9f zenon_H7d zenon_H18a zenon_H231 zenon_Hbc zenon_H1cd zenon_H1cb zenon_H212 zenon_H1a3 zenon_Hc4 zenon_H6e zenon_H6f zenon_H82 zenon_H13a zenon_H153 zenon_Hfa zenon_H173 zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H1a2 zenon_H1cf zenon_H186 zenon_H1ef zenon_H1bb zenon_H162 zenon_H120 zenon_H2c zenon_H139 zenon_H48 zenon_H16a zenon_Hc2 zenon_H1f1 zenon_H100 zenon_H3c zenon_H13f zenon_H196 zenon_H38. % 22.22/22.38 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.22/22.38 apply (zenon_L214_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.22/22.38 apply (zenon_L1648_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.22/22.38 apply (zenon_L1787_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.38 apply (zenon_L359_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.38 apply (zenon_L929_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.38 apply (zenon_L69_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.38 apply (zenon_L284_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.38 apply (zenon_L477_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.22/22.38 apply (zenon_L1786_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.22/22.38 apply (zenon_L21_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.22/22.38 apply (zenon_L1168_); trivial. % 22.22/22.38 apply (zenon_L218_); trivial. % 22.22/22.38 apply (zenon_L1162_); trivial. % 22.22/22.38 (* end of lemma zenon_L1788_ *) % 22.22/22.38 assert (zenon_L1789_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (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) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((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)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.22/22.38 do 0 intro. intros zenon_H13b zenon_H77 zenon_H141 zenon_H34 zenon_H109 zenon_Hf0 zenon_H1bb zenon_H1cb zenon_H120 zenon_H162 zenon_Hc2 zenon_H190 zenon_Ha9 zenon_H1cf zenon_H196 zenon_H140 zenon_H48 zenon_Hbc zenon_He4 zenon_H177 zenon_H11a zenon_H1c3 zenon_H20f zenon_H1c2 zenon_H18d zenon_H5d zenon_H1b7 zenon_H12e zenon_H24 zenon_H117 zenon_H159 zenon_H13c zenon_H195 zenon_H183 zenon_H68 zenon_H104 zenon_H121 zenon_H33 zenon_H9f zenon_H7d zenon_H18a zenon_H231 zenon_H1cd zenon_H212 zenon_Hc4 zenon_H6f zenon_H82 zenon_H13a zenon_Hfa zenon_H173 zenon_H186 zenon_H1ef zenon_H2c zenon_H139 zenon_H16a zenon_H1f1 zenon_H100 zenon_H3c zenon_H13f zenon_H1a8 zenon_H23c zenon_H1d8 zenon_H1a3 zenon_H191 zenon_Ha0 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_Hf5 zenon_H38. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.22/22.38 apply (zenon_L25_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.22/22.38 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.22/22.38 apply (zenon_L738_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.22/22.38 apply (zenon_L492_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.22/22.38 apply (zenon_L1787_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.22/22.38 apply (zenon_L1788_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.22/22.38 apply (zenon_L1316_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.38 apply (zenon_L359_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.38 apply (zenon_L929_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.38 apply (zenon_L1782_); trivial. % 22.22/22.38 apply (zenon_L1162_); trivial. % 22.22/22.38 apply (zenon_L169_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.22/22.38 apply (zenon_L1265_); trivial. % 22.22/22.38 apply (zenon_L663_); trivial. % 22.22/22.38 (* end of lemma zenon_L1789_ *) % 22.22/22.38 assert (zenon_L1790_ : ((op (e0) (e3)) = (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (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) (e0)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (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) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (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 (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (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) (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))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (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 (e1) (e3)) = (op (e3) (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))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 22.22/22.38 do 0 intro. intros zenon_H38 zenon_H196 zenon_H1c6 zenon_H25b zenon_H26a zenon_H4e zenon_Hcb zenon_H24e zenon_H19a zenon_H131 zenon_H36 zenon_H26d zenon_H129 zenon_H1b4 zenon_H156 zenon_H283 zenon_H73 zenon_H1ec zenon_H158 zenon_H13e zenon_H55 zenon_H266 zenon_H189 zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1fb zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H1d5 zenon_H27e zenon_H234 zenon_H67 zenon_H1fe zenon_H288 zenon_H179 zenon_H164 zenon_H125 zenon_H22d zenon_He2 zenon_H111 zenon_Hb2 zenon_H201 zenon_Hf5 zenon_H1a2 zenon_Hb6 zenon_Ha0 zenon_H191 zenon_H1d8 zenon_H23c zenon_H1a8 zenon_H13f zenon_H3c zenon_H100 zenon_H1f1 zenon_H16a zenon_H139 zenon_H2c zenon_H1ef zenon_H186 zenon_H173 zenon_Hfa zenon_H13a zenon_H82 zenon_H6f zenon_H212 zenon_H1cd zenon_H231 zenon_H18a zenon_H7d zenon_H104 zenon_H195 zenon_H13c zenon_H159 zenon_H117 zenon_H24 zenon_H5d zenon_H18d zenon_H1c2 zenon_H11a zenon_H177 zenon_He4 zenon_Hbc zenon_H140 zenon_H1cf zenon_H190 zenon_Hc2 zenon_H162 zenon_H120 zenon_H1cb zenon_H1bb zenon_Hf0 zenon_H109 zenon_H141 zenon_H13b zenon_He7 zenon_H163 zenon_H192 zenon_H3d zenon_H12e zenon_H48 zenon_H1c3 zenon_Hc4 zenon_H1a3 zenon_H183 zenon_H68 zenon_H34 zenon_H20f zenon_H9f zenon_H33 zenon_H121 zenon_H77 zenon_H1b7 zenon_Ha9 zenon_H171. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.22/22.38 apply (zenon_L55_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.22/22.38 exact (zenon_H159 zenon_H10c). % 22.22/22.38 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.22/22.38 apply (zenon_L359_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.22/22.38 apply (zenon_L152_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.22/22.38 apply (zenon_L1785_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.22/22.38 apply (zenon_L113_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.22/22.38 apply (zenon_L255_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.22/22.38 apply (zenon_L1789_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.22/22.38 apply (zenon_L965_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.22/22.38 apply (zenon_L255_); trivial. % 22.22/22.38 apply (zenon_L1651_); trivial. % 22.22/22.38 apply (zenon_L1162_); trivial. % 22.22/22.38 apply (zenon_L371_); trivial. % 22.22/22.38 (* end of lemma zenon_L1790_ *) % 22.22/22.38 assert (zenon_L1791_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 22.22/22.38 do 0 intro. intros zenon_H13c zenon_Ha0 zenon_H25 zenon_H159 zenon_Hb6 zenon_H4d zenon_Ha9 zenon_Hf7. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.22/22.38 apply (zenon_L116_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.22/22.38 exact (zenon_H159 zenon_H10c). % 22.22/22.38 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.22/22.38 apply (zenon_L124_); trivial. % 22.22/22.38 apply (zenon_L299_); trivial. % 22.22/22.38 (* end of lemma zenon_L1791_ *) % 22.22/22.38 assert (zenon_L1792_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((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) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (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))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((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). % 22.22/22.38 do 0 intro. intros zenon_H1fe zenon_He2 zenon_H13c zenon_H24 zenon_H141 zenon_H92 zenon_Hf0 zenon_H195 zenon_H2c zenon_H117 zenon_H16a zenon_H7b zenon_Hfa zenon_H1c6 zenon_H159 zenon_H191 zenon_H8b zenon_H131 zenon_H1ef zenon_H13e zenon_H15d zenon_H9f zenon_H53 zenon_H55 zenon_H5a zenon_H4e zenon_H139 zenon_H77 zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H13a zenon_H68 zenon_H82 zenon_H73 zenon_H4d zenon_H38 zenon_H48. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.22/22.38 apply (zenon_L41_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.22/22.38 apply (zenon_L253_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.22/22.38 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.22/22.38 apply (zenon_L65_); trivial. % 22.22/22.38 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.32/22.39 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.32/22.39 apply (zenon_L171_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.39 apply (zenon_L900_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.39 exact (zenon_H159 zenon_H10c). % 22.32/22.39 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.39 apply (zenon_L124_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.32/22.39 apply (zenon_L1008_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.32/22.39 apply (zenon_L929_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.32/22.39 apply (zenon_L1403_); trivial. % 22.32/22.39 apply (zenon_L766_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.32/22.39 apply (zenon_L59_); trivial. % 22.32/22.39 apply (zenon_L1791_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.32/22.39 apply (zenon_L111_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.32/22.39 apply (zenon_L55_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.32/22.39 exact (zenon_H159 zenon_H10c). % 22.32/22.39 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.32/22.39 apply (zenon_L113_); trivial. % 22.32/22.39 apply (zenon_L107_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.39 apply (zenon_L184_); trivial. % 22.32/22.39 apply (zenon_L246_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.39 apply (zenon_L755_); trivial. % 22.32/22.39 apply (zenon_L1715_); trivial. % 22.32/22.39 (* end of lemma zenon_L1792_ *) % 22.32/22.39 assert (zenon_L1793_ : ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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 (e2) (e0)) = (op (e3) (e0)))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (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 (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (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) (e1)) = (op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((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) (e0)) = (op (e3) (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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (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) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((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) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (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 (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> False). % 22.32/22.39 do 0 intro. intros zenon_H38 zenon_H1fb zenon_H26d zenon_Hb6 zenon_H9f zenon_H13b zenon_Hf5 zenon_Hfa zenon_H4e zenon_H1ef zenon_He2 zenon_H13c zenon_H109 zenon_H201 zenon_H117 zenon_H195 zenon_H183 zenon_H129 zenon_H27e zenon_H1c2 zenon_H18a zenon_H1c3 zenon_H18d zenon_H1cb zenon_H1b4 zenon_H20f zenon_H1bb zenon_H16a zenon_H186 zenon_H1a2 zenon_Hf0 zenon_H196 zenon_H141 zenon_H173 zenon_H121 zenon_H177 zenon_H11a zenon_H33 zenon_H48 zenon_H15d zenon_H24 zenon_H189 zenon_H191 zenon_H13f zenon_H190 zenon_H1cf zenon_H82 zenon_H1d8 zenon_H234 zenon_H55 zenon_H1a8 zenon_H140 zenon_H192 zenon_H231 zenon_H1cd zenon_Hbc zenon_He4 zenon_H1c6 zenon_H179 zenon_H288 zenon_H164 zenon_H212 zenon_H1fe zenon_Hb2 zenon_H125 zenon_H104 zenon_H12e zenon_H7d zenon_H24e zenon_H1f1 zenon_H23c zenon_H26a zenon_H2c zenon_H1d5 zenon_H111 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_Hcc zenon_H282 zenon_Heb zenon_H236 zenon_H25b zenon_H1b7 zenon_H266 zenon_H6f zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H283 zenon_H5c zenon_H5d zenon_H77 zenon_H13a zenon_Ha0 zenon_Ha9 zenon_H68 zenon_H139 zenon_H100 zenon_H22d. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 22.32/22.39 apply (zenon_L1627_); trivial. % 22.32/22.39 apply (zenon_L1235_); trivial. % 22.32/22.39 (* end of lemma zenon_L1793_ *) % 22.32/22.39 assert (zenon_L1794_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (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) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((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)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (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 (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (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 (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) (e0)) = (op (e2) (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) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.32/22.39 do 0 intro. intros zenon_H22d zenon_H100 zenon_H139 zenon_H68 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H77 zenon_H5d zenon_H5c zenon_H283 zenon_H163 zenon_H131 zenon_H73 zenon_H1ec zenon_H156 zenon_H158 zenon_H13e zenon_H6f zenon_H266 zenon_H1b7 zenon_H25b zenon_H236 zenon_Heb zenon_H282 zenon_Hcc zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_H1d5 zenon_H2c zenon_H26a zenon_H23c zenon_H1f1 zenon_H24e zenon_H7d zenon_H12e zenon_H104 zenon_H125 zenon_Hb2 zenon_H1fe zenon_H212 zenon_H164 zenon_H288 zenon_H179 zenon_H1c6 zenon_He4 zenon_Hbc zenon_H1cd zenon_H231 zenon_H192 zenon_H140 zenon_H1a8 zenon_H55 zenon_H234 zenon_H1d8 zenon_H82 zenon_H1cf zenon_H190 zenon_H13f zenon_H189 zenon_H24 zenon_H15d zenon_H48 zenon_H33 zenon_H11a zenon_H177 zenon_H121 zenon_H173 zenon_H141 zenon_H196 zenon_Hf0 zenon_H1a2 zenon_H186 zenon_H16a zenon_H1bb zenon_H20f zenon_H1b4 zenon_H1cb zenon_H18d zenon_H1c3 zenon_H18a zenon_H1c2 zenon_H27e zenon_H129 zenon_H183 zenon_H195 zenon_H117 zenon_H201 zenon_H109 zenon_H13c zenon_He2 zenon_H1ef zenon_H4e zenon_Hfa zenon_Hf5 zenon_H13b zenon_H9f zenon_Hb6 zenon_H26d zenon_H1fb zenon_H38. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H191 | zenon_intro zenon_H93 ]. % 22.32/22.39 apply (zenon_L1793_); trivial. % 22.32/22.39 apply (zenon_L1236_); trivial. % 22.32/22.39 (* end of lemma zenon_L1794_ *) % 22.32/22.39 assert (zenon_L1795_ : (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (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) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((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)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (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 (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (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 (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) (e0)) = (op (e2) (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) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.32/22.39 do 0 intro. intros zenon_H7a zenon_H40 zenon_H72 zenon_H22d zenon_H100 zenon_H139 zenon_H68 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H77 zenon_H5d zenon_H283 zenon_H163 zenon_H131 zenon_H73 zenon_H1ec zenon_H156 zenon_H158 zenon_H13e zenon_H6f zenon_H266 zenon_H1b7 zenon_H25b zenon_H236 zenon_Heb zenon_H282 zenon_Hcc zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_H1d5 zenon_H2c zenon_H26a zenon_H23c zenon_H1f1 zenon_H24e zenon_H7d zenon_H12e zenon_H104 zenon_H125 zenon_Hb2 zenon_H1fe zenon_H212 zenon_H164 zenon_H288 zenon_H179 zenon_H1c6 zenon_He4 zenon_Hbc zenon_H1cd zenon_H231 zenon_H192 zenon_H140 zenon_H1a8 zenon_H55 zenon_H234 zenon_H1d8 zenon_H82 zenon_H1cf zenon_H190 zenon_H13f zenon_H189 zenon_H24 zenon_H15d zenon_H48 zenon_H33 zenon_H11a zenon_H177 zenon_H121 zenon_H173 zenon_H141 zenon_H196 zenon_Hf0 zenon_H1a2 zenon_H186 zenon_H16a zenon_H1bb zenon_H20f zenon_H1b4 zenon_H1cb zenon_H18d zenon_H1c3 zenon_H18a zenon_H1c2 zenon_H27e zenon_H129 zenon_H183 zenon_H195 zenon_H117 zenon_H201 zenon_H109 zenon_H13c zenon_He2 zenon_H1ef zenon_H4e zenon_Hfa zenon_Hf5 zenon_H13b zenon_H9f zenon_Hb6 zenon_H26d zenon_H1fb zenon_H38. % 22.32/22.39 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.32/22.39 exact (zenon_H7a zenon_H3c). % 22.32/22.39 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.32/22.39 exact (zenon_H40 zenon_H3f). % 22.32/22.39 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.32/22.39 apply (zenon_L59_); trivial. % 22.32/22.39 apply (zenon_L1794_); trivial. % 22.32/22.39 (* end of lemma zenon_L1795_ *) % 22.32/22.39 assert (zenon_L1796_ : (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e2)) = (e2)) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (((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 (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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) (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 (e0) (e3)) = (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))))) -> (~((e0) = (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 (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 (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (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))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (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) (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> False). % 22.32/22.39 do 0 intro. intros zenon_H40 zenon_H66 zenon_H3e zenon_H1fe zenon_H13b zenon_Hb1 zenon_H2c zenon_H109 zenon_H179 zenon_Hb6 zenon_H177 zenon_H82 zenon_He4 zenon_H7d zenon_H125 zenon_H1d5 zenon_Hfa zenon_H156 zenon_H1a8 zenon_H201 zenon_H141 zenon_H196 zenon_H195 zenon_H117 zenon_H48 zenon_H13f zenon_H183 zenon_H129 zenon_H27e zenon_H11a zenon_H1c2 zenon_H18a zenon_H1c3 zenon_H18d zenon_H1cb zenon_H1b4 zenon_H20f zenon_Hc4 zenon_H1bb zenon_H16a zenon_H186 zenon_Ha5 zenon_H191 zenon_H1cd zenon_Hac zenon_H1a2 zenon_H1d8 zenon_Hf0 zenon_H111 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H189 zenon_Hf5 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H7a zenon_H77 zenon_H13a zenon_H38 zenon_Ha9 zenon_H68 zenon_H139 zenon_H9f zenon_Ha0 zenon_H169. % 22.32/22.39 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.32/22.39 exact (zenon_H7a zenon_H3c). % 22.32/22.39 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.32/22.39 exact (zenon_H40 zenon_H3f). % 22.32/22.39 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.32/22.39 apply (zenon_L379_); trivial. % 22.32/22.39 apply (zenon_L1593_); trivial. % 22.32/22.39 (* end of lemma zenon_L1796_ *) % 22.32/22.39 assert (zenon_L1797_ : (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (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) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((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)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (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 (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (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 (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) (e0)) = (op (e2) (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) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.32/22.39 do 0 intro. intros zenon_H7a zenon_H40 zenon_Hf3 zenon_H22d zenon_H100 zenon_H139 zenon_H68 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H77 zenon_H5d zenon_H283 zenon_H163 zenon_H131 zenon_H73 zenon_H1ec zenon_H156 zenon_H158 zenon_H13e zenon_H6f zenon_H266 zenon_H1b7 zenon_H25b zenon_H236 zenon_Heb zenon_H282 zenon_Hcc zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_H1d5 zenon_H2c zenon_H26a zenon_H23c zenon_H1f1 zenon_H24e zenon_H7d zenon_H12e zenon_H104 zenon_H125 zenon_Hb2 zenon_H1fe zenon_H212 zenon_H164 zenon_H288 zenon_H179 zenon_H1c6 zenon_He4 zenon_Hbc zenon_H1cd zenon_H231 zenon_H192 zenon_H140 zenon_H1a8 zenon_H55 zenon_H234 zenon_H1d8 zenon_H82 zenon_H1cf zenon_H190 zenon_H13f zenon_H189 zenon_H24 zenon_H15d zenon_H48 zenon_H33 zenon_H11a zenon_H177 zenon_H121 zenon_H173 zenon_H141 zenon_H196 zenon_Hf0 zenon_H1a2 zenon_H186 zenon_H16a zenon_H1bb zenon_H20f zenon_H1b4 zenon_H1cb zenon_H18d zenon_H1c3 zenon_H18a zenon_H1c2 zenon_H27e zenon_H129 zenon_H183 zenon_H195 zenon_H117 zenon_H201 zenon_H109 zenon_H13c zenon_He2 zenon_H1ef zenon_H4e zenon_Hfa zenon_Hf5 zenon_H13b zenon_H9f zenon_Hb6 zenon_H26d zenon_H1fb zenon_H38. % 22.32/22.39 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.32/22.39 exact (zenon_H7a zenon_H3c). % 22.32/22.39 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.32/22.39 exact (zenon_H40 zenon_H3f). % 22.32/22.39 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.32/22.39 apply (zenon_L117_); trivial. % 22.32/22.39 apply (zenon_L1794_); trivial. % 22.32/22.39 (* end of lemma zenon_L1797_ *) % 22.32/22.39 assert (zenon_L1798_ : (((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.32/22.39 do 0 intro. intros zenon_H82 zenon_H13a zenon_H139 zenon_H7a zenon_Hac zenon_Ha9 zenon_H141 zenon_H68 zenon_H195 zenon_Ha5 zenon_Ha0 zenon_Hb6 zenon_H117 zenon_H196 zenon_H38 zenon_H1b3 zenon_H3d zenon_H77 zenon_H1a8 zenon_H34 zenon_H48. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.39 apply (zenon_L1149_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.39 exact (zenon_H7a zenon_H3c). % 22.32/22.39 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.32/22.39 apply (zenon_L214_); trivial. % 22.32/22.39 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.32/22.39 exact (zenon_H1b3 zenon_Hef). % 22.32/22.39 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.32/22.39 apply (zenon_L1393_); trivial. % 22.32/22.39 apply (zenon_L371_); trivial. % 22.32/22.39 apply (zenon_L456_); trivial. % 22.32/22.39 (* end of lemma zenon_L1798_ *) % 22.32/22.40 assert (zenon_L1799_ : (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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) (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 (e0) (e3)) = (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))))) -> (~((e0) = (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 (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 (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (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))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (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) (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (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 (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> False). % 22.32/22.40 do 0 intro. intros zenon_Ha0 zenon_H9f zenon_Hb6 zenon_H177 zenon_H82 zenon_He4 zenon_H7d zenon_H125 zenon_H1d5 zenon_Hfa zenon_H156 zenon_H1a8 zenon_H201 zenon_H141 zenon_H196 zenon_H195 zenon_H117 zenon_H48 zenon_H13f zenon_H183 zenon_H129 zenon_H27e zenon_H11a zenon_H1c2 zenon_H18a zenon_H1c3 zenon_H18d zenon_H1cb zenon_H1b4 zenon_H20f zenon_Hc4 zenon_H1bb zenon_H16a zenon_H186 zenon_Ha5 zenon_H191 zenon_H1cd zenon_Hac zenon_H1a2 zenon_H1d8 zenon_Hf0 zenon_H111 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H189 zenon_Hf5 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H77 zenon_H13a zenon_H38 zenon_Ha9 zenon_H68 zenon_H139 zenon_H40 zenon_H7a zenon_H169 zenon_H179 zenon_H109 zenon_H2c zenon_Hb1 zenon_H13b zenon_H1fe zenon_H3e zenon_H22d zenon_H100 zenon_H26a zenon_H23c zenon_H1f1 zenon_H24e zenon_H12e zenon_H104 zenon_Hb2 zenon_H212 zenon_H164 zenon_H288 zenon_Hbc zenon_H231 zenon_H192 zenon_H140 zenon_H234 zenon_H24 zenon_H33 zenon_H121 zenon_He2. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.40 apply (zenon_L41_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.32/22.40 exact (zenon_H7a zenon_H3c). % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.32/22.40 exact (zenon_H40 zenon_H3f). % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.32/22.40 exact (zenon_H1d4 zenon_H4d). % 22.32/22.40 apply (zenon_L1582_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.40 apply (zenon_L253_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.32/22.40 exact (zenon_H7a zenon_H3c). % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.32/22.40 exact (zenon_H40 zenon_H3f). % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.32/22.40 exact (zenon_H1d4 zenon_H4d). % 22.32/22.40 apply (zenon_L1574_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.40 apply (zenon_L214_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.40 apply (zenon_L1796_); trivial. % 22.32/22.40 apply (zenon_L165_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.40 apply (zenon_L1439_); trivial. % 22.32/22.40 apply (zenon_L246_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.40 apply (zenon_L253_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.40 apply (zenon_L1149_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.40 exact (zenon_H7a zenon_H3c). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.32/22.40 apply (zenon_L297_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.32/22.40 exact (zenon_H7a zenon_H3c). % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.32/22.40 exact (zenon_H40 zenon_H3f). % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.32/22.40 exact (zenon_H1d4 zenon_H4d). % 22.32/22.40 apply (zenon_L1584_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.32/22.40 apply (zenon_L1797_); trivial. % 22.32/22.40 apply (zenon_L90_); trivial. % 22.32/22.40 apply (zenon_L456_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.40 apply (zenon_L1439_); trivial. % 22.32/22.40 apply (zenon_L461_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.40 apply (zenon_L41_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.32/22.40 exact (zenon_H7a zenon_H3c). % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.32/22.40 exact (zenon_H40 zenon_H3f). % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.32/22.40 apply (zenon_L923_); trivial. % 22.32/22.40 apply (zenon_L1794_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.40 apply (zenon_L355_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.32/22.40 exact (zenon_H7a zenon_H3c). % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.32/22.40 exact (zenon_H40 zenon_H3f). % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.32/22.40 apply (zenon_L214_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.32/22.40 exact (zenon_H1b3 zenon_Hef). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.32/22.40 apply (zenon_L1393_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.32/22.40 apply (zenon_L56_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.32/22.40 apply (zenon_L128_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.32/22.40 apply (zenon_L67_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.32/22.40 apply (zenon_L289_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.32/22.40 exact (zenon_H191 zenon_H110). % 22.32/22.40 apply (zenon_L182_); trivial. % 22.32/22.40 apply (zenon_L371_); trivial. % 22.32/22.40 apply (zenon_L1593_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.40 apply (zenon_L1439_); trivial. % 22.32/22.40 apply (zenon_L246_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.40 apply (zenon_L253_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.40 apply (zenon_L1798_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.40 apply (zenon_L1439_); trivial. % 22.32/22.40 apply (zenon_L246_); trivial. % 22.32/22.40 (* end of lemma zenon_L1799_ *) % 22.32/22.40 assert (zenon_L1800_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (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))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (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 (e0) (e1)) = (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (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) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((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)) = (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 (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H169 zenon_H11a zenon_Ha0 zenon_H9f zenon_H1ec zenon_Ha5 zenon_H186 zenon_He3 zenon_H40 zenon_H156 zenon_H159 zenon_H158 zenon_H4e zenon_He2 zenon_Hac zenon_H55 zenon_H38 zenon_H1fb zenon_H139 zenon_H68 zenon_Ha9 zenon_H13a zenon_H77 zenon_H1d5 zenon_H125 zenon_H48 zenon_H7d zenon_H201 zenon_Hf0 zenon_H18d zenon_H141 zenon_H173 zenon_H2c zenon_H117 zenon_H195 zenon_Heb zenon_H196 zenon_H177 zenon_H129 zenon_H183 zenon_H12e zenon_H20f zenon_H1bb zenon_Hc4 zenon_H1cb zenon_H18a zenon_H192 zenon_H1c3 zenon_H1b4 zenon_Hf5 zenon_H25e zenon_He4 zenon_H1b7 zenon_H1d8 zenon_H15d zenon_H100 zenon_H16a zenon_H13c zenon_H109 zenon_H1a2 zenon_H1cd zenon_H191 zenon_H13f zenon_H13b zenon_H82 zenon_Hb6 zenon_H1fe. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.40 apply (zenon_L41_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.40 apply (zenon_L309_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.40 apply (zenon_L1594_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.40 apply (zenon_L253_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.40 apply (zenon_L1149_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.32/22.40 apply (zenon_L25_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.32/22.40 exact (zenon_He3 zenon_He7). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.32/22.40 apply (zenon_L65_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.32/22.40 exact (zenon_He3 zenon_He7). % 22.32/22.40 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.32/22.40 apply (zenon_L1612_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.32/22.40 apply (zenon_L1498_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.32/22.40 apply (zenon_L1669_); trivial. % 22.32/22.40 apply (zenon_L1670_); trivial. % 22.32/22.40 apply (zenon_L802_); trivial. % 22.32/22.40 apply (zenon_L663_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.40 apply (zenon_L306_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.32/22.40 apply (zenon_L252_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.32/22.40 apply (zenon_L24_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.32/22.40 apply (zenon_L316_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.32/22.40 exact (zenon_He3 zenon_He7). % 22.32/22.40 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.32/22.40 apply (zenon_L1459_); trivial. % 22.32/22.40 apply (zenon_L107_); trivial. % 22.32/22.40 apply (zenon_L291_); trivial. % 22.32/22.40 apply (zenon_L165_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.40 apply (zenon_L1613_); trivial. % 22.32/22.40 apply (zenon_L456_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.40 apply (zenon_L1439_); trivial. % 22.32/22.40 apply (zenon_L246_); trivial. % 22.32/22.40 apply (zenon_L373_); trivial. % 22.32/22.40 (* end of lemma zenon_L1800_ *) % 22.32/22.40 assert (zenon_L1801_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H11a zenon_He7 zenon_He0. % 22.32/22.40 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 22.32/22.40 intro zenon_D_pnotp. % 22.32/22.40 apply zenon_H11a. % 22.32/22.40 rewrite <- zenon_D_pnotp. % 22.32/22.40 exact zenon_He7. % 22.32/22.40 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 22.32/22.40 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 22.32/22.40 congruence. % 22.32/22.40 apply zenon_H10f. apply refl_equal. % 22.32/22.40 apply zenon_H1f2. apply sym_equal. exact zenon_He0. % 22.32/22.40 (* end of lemma zenon_L1801_ *) % 22.32/22.40 assert (zenon_L1802_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H1fe zenon_H1f zenon_H48 zenon_H3c zenon_H68 zenon_H65 zenon_H167 zenon_H18a. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.40 exact (zenon_H1f zenon_H1e). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.40 apply (zenon_L25_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.40 apply (zenon_L27_); trivial. % 22.32/22.40 apply (zenon_L416_); trivial. % 22.32/22.40 (* end of lemma zenon_L1802_ *) % 22.32/22.40 assert (zenon_L1803_ : (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H48 zenon_H11f zenon_H167. % 22.32/22.40 cut (((op (e3) (e3)) = (e1)) = ((e0) = (e1))). % 22.32/22.40 intro zenon_D_pnotp. % 22.32/22.40 apply zenon_H48. % 22.32/22.40 rewrite <- zenon_D_pnotp. % 22.32/22.40 exact zenon_H11f. % 22.32/22.40 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 22.32/22.40 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 22.32/22.40 congruence. % 22.32/22.40 exact (zenon_H162 zenon_H167). % 22.32/22.40 apply zenon_H4a. apply refl_equal. % 22.32/22.40 (* end of lemma zenon_L1803_ *) % 22.32/22.40 assert (zenon_L1804_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H16a zenon_H18a zenon_H68 zenon_H1f zenon_H1fe zenon_H1ba zenon_H8b zenon_H18d zenon_H9e zenon_Hb6 zenon_H5d zenon_H3c zenon_H77 zenon_H48 zenon_H167. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.40 apply (zenon_L1802_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.40 exact (zenon_H1ba zenon_H6d). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.40 exact (zenon_H8b zenon_H8a). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.32/22.40 apply (zenon_L115_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.32/22.40 apply (zenon_L17_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.32/22.40 apply (zenon_L218_); trivial. % 22.32/22.40 apply (zenon_L1803_); trivial. % 22.32/22.40 (* end of lemma zenon_L1804_ *) % 22.32/22.40 assert (zenon_L1805_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H125 zenon_H47 zenon_H77 zenon_H3c zenon_H68 zenon_H2f zenon_Ha9 zenon_H9d. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.32/22.40 apply (zenon_L251_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.32/22.40 apply (zenon_L24_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.32/22.40 apply (zenon_L28_); trivial. % 22.32/22.40 apply (zenon_L91_); trivial. % 22.32/22.40 (* end of lemma zenon_L1805_ *) % 22.32/22.40 assert (zenon_L1806_ : (((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)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H13a zenon_H33 zenon_H9d zenon_H3d zenon_Ha0 zenon_H31 zenon_H16a zenon_H18a zenon_H68 zenon_H1f zenon_H1fe zenon_H1ba zenon_H8b zenon_H18d zenon_Hb6 zenon_H5d zenon_H3c zenon_H77 zenon_H48 zenon_H167. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.40 apply (zenon_L245_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.40 apply (zenon_L55_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.40 apply (zenon_L68_); trivial. % 22.32/22.40 apply (zenon_L1804_); trivial. % 22.32/22.40 (* end of lemma zenon_L1806_ *) % 22.32/22.40 assert (zenon_L1807_ : (((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 (e2) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H13a zenon_H33 zenon_H9d zenon_H6f zenon_H1ba zenon_H89 zenon_H13d zenon_H190 zenon_H191 zenon_H13e zenon_H55 zenon_H2d zenon_H266 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H155. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.40 apply (zenon_L245_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.40 apply (zenon_L1076_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.40 apply (zenon_L68_); trivial. % 22.32/22.40 apply (zenon_L115_); trivial. % 22.32/22.40 (* end of lemma zenon_L1807_ *) % 22.32/22.40 assert (zenon_L1808_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H92 zenon_H125 zenon_Ha9 zenon_H2f zenon_H89 zenon_H13d zenon_H190 zenon_H13e zenon_H15d zenon_H33 zenon_H9d zenon_He4 zenon_H1f1 zenon_H68 zenon_H77 zenon_H8b zenon_H16a zenon_H55 zenon_H2d zenon_Hf0 zenon_H1ba zenon_H6f zenon_H266 zenon_Hb6 zenon_Ha0 zenon_H31 zenon_H5d zenon_H18d zenon_H1f zenon_H48 zenon_H3c zenon_H18a zenon_H167 zenon_H1fe zenon_H13a. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.40 apply (zenon_L245_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.40 apply (zenon_L705_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.40 apply (zenon_L68_); trivial. % 22.32/22.40 apply (zenon_L1804_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.40 apply (zenon_L1805_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.40 apply (zenon_L1806_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.40 apply (zenon_L239_); trivial. % 22.32/22.40 apply (zenon_L1807_); trivial. % 22.32/22.40 (* end of lemma zenon_L1808_ *) % 22.32/22.40 assert (zenon_L1809_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H16a zenon_H18a zenon_H167 zenon_H68 zenon_H3c zenon_H48 zenon_H1f zenon_H1fe zenon_Hf0 zenon_Hef zenon_H8b zenon_H16b. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.40 apply (zenon_L1802_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.40 apply (zenon_L61_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.40 exact (zenon_H8b zenon_H8a). % 22.32/22.40 exact (zenon_H16b zenon_H93). % 22.32/22.40 (* end of lemma zenon_L1809_ *) % 22.32/22.40 assert (zenon_L1810_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H18d zenon_Hb6 zenon_H5d zenon_H3c zenon_H68 zenon_H77 zenon_H10c zenon_Ha9 zenon_H9e zenon_H1c3 zenon_H48 zenon_H167. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.32/22.40 apply (zenon_L115_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.32/22.40 apply (zenon_L17_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.32/22.40 apply (zenon_L296_); trivial. % 22.32/22.40 apply (zenon_L1803_); trivial. % 22.32/22.40 (* end of lemma zenon_L1810_ *) % 22.32/22.40 assert (zenon_L1811_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H13c zenon_H167 zenon_H48 zenon_H1c3 zenon_H77 zenon_H68 zenon_H3c zenon_H5d zenon_Hb6 zenon_H18d zenon_Ha9 zenon_H72 zenon_H9e zenon_Hf5. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.40 apply (zenon_L46_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.40 apply (zenon_L1810_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.40 apply (zenon_L436_); trivial. % 22.32/22.40 apply (zenon_L262_); trivial. % 22.32/22.40 (* end of lemma zenon_L1811_ *) % 22.32/22.40 assert (zenon_L1812_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H13a zenon_H33 zenon_Ha0 zenon_H31 zenon_Hfa zenon_Hf0 zenon_H1fe zenon_H1f zenon_H18a zenon_Hf5 zenon_H18d zenon_H5d zenon_H3c zenon_H77 zenon_H1c3 zenon_H48 zenon_H13c zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H167 zenon_H16b zenon_H8b zenon_Ha9 zenon_H2d zenon_H68 zenon_H16a zenon_H9d zenon_H7d. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.40 apply (zenon_L245_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.40 apply (zenon_L55_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.40 apply (zenon_L68_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.32/22.40 apply (zenon_L24_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.32/22.40 apply (zenon_L1809_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.32/22.40 apply (zenon_L1811_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.32/22.40 apply (zenon_L55_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.32/22.40 apply (zenon_L294_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.32/22.40 apply (zenon_L715_); trivial. % 22.32/22.40 apply (zenon_L44_); trivial. % 22.32/22.40 (* end of lemma zenon_L1812_ *) % 22.32/22.40 assert (zenon_L1813_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H92 zenon_H190 zenon_H13e zenon_H16a zenon_H8b zenon_H53 zenon_H77 zenon_H68 zenon_H48 zenon_H13d zenon_H129 zenon_H167 zenon_H141. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.32/22.40 apply (zenon_L327_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.32/22.40 apply (zenon_L111_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.32/22.40 exact (zenon_H13d zenon_H14c). % 22.32/22.40 apply (zenon_L298_); trivial. % 22.32/22.40 apply (zenon_L144_); trivial. % 22.32/22.40 (* end of lemma zenon_L1813_ *) % 22.32/22.40 assert (zenon_L1814_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((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) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H89 zenon_H141 zenon_H167 zenon_H129 zenon_H13d zenon_H48 zenon_H68 zenon_H77 zenon_H53 zenon_H16a zenon_H13e zenon_H190 zenon_H92. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.32/22.40 apply (zenon_L1813_); trivial. % 22.32/22.40 apply (zenon_L1813_); trivial. % 22.32/22.40 (* end of lemma zenon_L1814_ *) % 22.32/22.40 assert (zenon_L1815_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H183 zenon_H9d zenon_Ha9 zenon_H77 zenon_H7f zenon_H72 zenon_H163 zenon_H68 zenon_H167. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.32/22.40 apply (zenon_L91_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.32/22.40 apply (zenon_L169_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.32/22.40 apply (zenon_L227_); trivial. % 22.32/22.40 apply (zenon_L295_); trivial. % 22.32/22.40 (* end of lemma zenon_L1815_ *) % 22.32/22.40 assert (zenon_L1816_ : (((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)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> (((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 (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (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) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H13a zenon_H33 zenon_H18a zenon_H9d zenon_Ha9 zenon_H26a zenon_H1bf zenon_H1f1 zenon_H100 zenon_H3c zenon_H13f zenon_H183 zenon_H77 zenon_H163 zenon_H68 zenon_H167 zenon_H16a zenon_H48 zenon_H1f zenon_H1fe zenon_Hf0 zenon_H8b zenon_H16b zenon_Hfa zenon_H89 zenon_H141 zenon_H129 zenon_H13d zenon_H13e zenon_H190 zenon_H92 zenon_H23c zenon_He4 zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H155. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.40 apply (zenon_L245_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.32/22.40 apply (zenon_L55_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.32/22.40 apply (zenon_L492_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.32/22.40 apply (zenon_L1814_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.32/22.40 apply (zenon_L24_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.32/22.40 apply (zenon_L1809_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.32/22.40 apply (zenon_L1815_); trivial. % 22.32/22.40 apply (zenon_L748_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.40 apply (zenon_L68_); trivial. % 22.32/22.40 apply (zenon_L115_); trivial. % 22.32/22.40 (* end of lemma zenon_L1816_ *) % 22.32/22.40 assert (zenon_L1817_ : (~((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)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (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 (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (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) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((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))))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H1ef zenon_H125 zenon_H9d zenon_Ha9 zenon_H68 zenon_H2f zenon_H3c zenon_H77 zenon_H13a zenon_H16a zenon_H8b zenon_Hf0 zenon_H1f zenon_H48 zenon_H18a zenon_H167 zenon_H1fe zenon_H13c zenon_Hf5 zenon_H5d zenon_H1c3 zenon_H18d zenon_H1c6 zenon_H7d zenon_H2d zenon_Hfa zenon_H31 zenon_Ha0 zenon_Hb6 zenon_H33 zenon_H23c zenon_H89 zenon_H141 zenon_H129 zenon_H13d zenon_H13e zenon_H190 zenon_H92 zenon_H100 zenon_H1f1 zenon_H1bf zenon_H26a zenon_H13f zenon_H163 zenon_H183 zenon_He4 zenon_H15d. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.40 apply (zenon_L1805_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.40 apply (zenon_L1812_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.40 apply (zenon_L239_); trivial. % 22.32/22.40 apply (zenon_L1816_); trivial. % 22.32/22.40 apply (zenon_L644_); trivial. % 22.32/22.40 (* end of lemma zenon_L1817_ *) % 22.32/22.40 assert (zenon_L1818_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> False). % 22.32/22.40 do 0 intro. intros zenon_Hc8 zenon_H167 zenon_H9d. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.32/22.40 exact (zenon_H209 zenon_H9d). % 22.32/22.40 exact (zenon_H162 zenon_H167). % 22.32/22.40 (* end of lemma zenon_L1818_ *) % 22.32/22.40 assert (zenon_L1819_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H36 zenon_H167 zenon_H9d. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.32/22.40 apply (zenon_L1818_); trivial. % 22.32/22.40 (* end of lemma zenon_L1819_ *) % 22.32/22.40 assert (zenon_L1820_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H18d zenon_H38 zenon_H5d zenon_H3a zenon_H93 zenon_H77 zenon_H48 zenon_H167. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.32/22.40 apply (zenon_L246_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.32/22.40 apply (zenon_L1206_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.32/22.40 apply (zenon_L218_); trivial. % 22.32/22.40 apply (zenon_L1803_); trivial. % 22.32/22.40 (* end of lemma zenon_L1820_ *) % 22.32/22.40 assert (zenon_L1821_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H1c3 zenon_H10c zenon_H48 zenon_H77 zenon_H3a zenon_H5d zenon_H38 zenon_H18d zenon_H68 zenon_H167. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 22.32/22.40 apply (zenon_L165_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 22.32/22.40 apply (zenon_L294_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 22.32/22.40 apply (zenon_L1820_); trivial. % 22.32/22.40 apply (zenon_L295_); trivial. % 22.32/22.40 (* end of lemma zenon_L1821_ *) % 22.32/22.40 assert (zenon_L1822_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H1c3 zenon_H38 zenon_Ha5 zenon_Ha9 zenon_H128 zenon_H77 zenon_H68 zenon_H167. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 22.32/22.40 apply (zenon_L165_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 22.32/22.40 apply (zenon_L299_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 22.32/22.40 apply (zenon_L218_); trivial. % 22.32/22.40 apply (zenon_L295_); trivial. % 22.32/22.40 (* end of lemma zenon_L1822_ *) % 22.32/22.40 assert (zenon_L1823_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H18d zenon_H5d zenon_H3c zenon_H68 zenon_H77 zenon_Ha9 zenon_Ha5 zenon_H38 zenon_H1c3 zenon_H48 zenon_H167. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.32/22.40 apply (zenon_L246_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.32/22.40 apply (zenon_L17_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.32/22.40 apply (zenon_L1822_); trivial. % 22.32/22.40 apply (zenon_L1803_); trivial. % 22.32/22.40 (* end of lemma zenon_L1823_ *) % 22.32/22.40 assert (zenon_L1824_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H23b zenon_H3a zenon_H13a zenon_Ha0 zenon_H3c zenon_H1c3 zenon_H5d zenon_H77 zenon_H18d zenon_H167 zenon_H68 zenon_H73 zenon_Ha9 zenon_H13c zenon_Hb6 zenon_H1f zenon_H48 zenon_H3d zenon_H237 zenon_H236. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.40 apply (zenon_L487_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.40 exact (zenon_H1f zenon_H1e). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.40 apply (zenon_L318_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.40 exact (zenon_H237 zenon_H31). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.40 exact (zenon_Ha4 zenon_H9f). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.40 apply (zenon_L55_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.40 apply (zenon_L46_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.40 apply (zenon_L1821_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.40 apply (zenon_L89_); trivial. % 22.32/22.40 apply (zenon_L1823_); trivial. % 22.32/22.40 apply (zenon_L156_); trivial. % 22.32/22.40 (* end of lemma zenon_L1824_ *) % 22.32/22.40 assert (zenon_L1825_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H125 zenon_H6c zenon_H77 zenon_H18a zenon_H167 zenon_H68 zenon_H3c zenon_H48 zenon_H1f zenon_H1fe zenon_Ha9 zenon_H9d. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.32/22.40 exact (zenon_H6c zenon_H67). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.32/22.40 apply (zenon_L24_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.32/22.40 apply (zenon_L1802_); trivial. % 22.32/22.40 apply (zenon_L91_); trivial. % 22.32/22.40 (* end of lemma zenon_L1825_ *) % 22.32/22.40 assert (zenon_L1826_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H1fe zenon_H18a zenon_H9d zenon_H125 zenon_H236 zenon_H48 zenon_H1f zenon_Hb6 zenon_H13c zenon_Ha9 zenon_H73 zenon_H68 zenon_H167 zenon_H18d zenon_H77 zenon_H5d zenon_H1c3 zenon_Ha0 zenon_H13a zenon_H3a. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.40 apply (zenon_L1824_); trivial. % 22.32/22.40 apply (zenon_L1825_); trivial. % 22.32/22.40 (* end of lemma zenon_L1826_ *) % 22.32/22.40 assert (zenon_L1827_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H13b zenon_Hec zenon_H77 zenon_H40 zenon_H48 zenon_Heb zenon_He3 zenon_H72 zenon_H68 zenon_H167 zenon_H20f. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.32/22.40 apply (zenon_L60_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.32/22.40 exact (zenon_He3 zenon_He7). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.32/22.40 apply (zenon_L62_); trivial. % 22.32/22.40 apply (zenon_L421_); trivial. % 22.32/22.40 (* end of lemma zenon_L1827_ *) % 22.32/22.40 assert (zenon_L1828_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H15c zenon_H158 zenon_H156 zenon_H3e zenon_Heb zenon_H72 zenon_H77 zenon_H40 zenon_H48 zenon_He3 zenon_H68 zenon_H20f zenon_H167 zenon_H13b. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.32/22.40 apply (zenon_L1827_); trivial. % 22.32/22.40 apply (zenon_L102_); trivial. % 22.32/22.40 (* end of lemma zenon_L1828_ *) % 22.32/22.40 assert (zenon_L1829_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/(~((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) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H13b zenon_H167 zenon_H20f zenon_H68 zenon_He3 zenon_H48 zenon_H77 zenon_H72 zenon_Heb zenon_H3e zenon_H156 zenon_H158 zenon_H15c. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.32/22.40 apply (zenon_L1828_); trivial. % 22.32/22.40 apply (zenon_L1828_); trivial. % 22.32/22.40 (* end of lemma zenon_L1829_ *) % 22.32/22.40 assert (zenon_L1830_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H87 zenon_H158 zenon_H156 zenon_Heb zenon_H77 zenon_H48 zenon_H68 zenon_H20f zenon_H167 zenon_H13b zenon_H3c. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.32/22.40 exact (zenon_H7a zenon_H3c). % 22.32/22.40 apply (zenon_L1829_); trivial. % 22.32/22.40 (* end of lemma zenon_L1830_ *) % 22.32/22.40 assert (zenon_L1831_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H99 zenon_H167 zenon_H9d. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.32/22.40 apply (zenon_L1818_); trivial. % 22.32/22.40 (* end of lemma zenon_L1831_ *) % 22.32/22.40 assert (zenon_L1832_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H13c zenon_H167 zenon_H48 zenon_H1c3 zenon_Ha9 zenon_H77 zenon_H68 zenon_H3c zenon_H5d zenon_Hb6 zenon_H18d zenon_Ha0 zenon_Hf3 zenon_H9e zenon_Hf5. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.40 apply (zenon_L46_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.40 apply (zenon_L1810_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.40 apply (zenon_L162_); trivial. % 22.32/22.40 apply (zenon_L262_); trivial. % 22.32/22.40 (* end of lemma zenon_L1832_ *) % 22.32/22.40 assert (zenon_L1833_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H13b zenon_H2a zenon_H173 zenon_Hf5 zenon_H9e zenon_Ha0 zenon_H18d zenon_Hb6 zenon_H5d zenon_H3c zenon_H68 zenon_H77 zenon_Ha9 zenon_H1c3 zenon_H48 zenon_H13c zenon_H167 zenon_H20f. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.32/22.40 apply (zenon_L25_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.32/22.40 apply (zenon_L272_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.32/22.40 apply (zenon_L1832_); trivial. % 22.32/22.40 apply (zenon_L421_); trivial. % 22.32/22.40 (* end of lemma zenon_L1833_ *) % 22.32/22.40 assert (zenon_L1834_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((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)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H236 zenon_H1f zenon_H20f zenon_H167 zenon_H13c zenon_H48 zenon_H1c3 zenon_Ha9 zenon_H77 zenon_H68 zenon_H3c zenon_H5d zenon_Hb6 zenon_H18d zenon_Hf5 zenon_H173 zenon_H13b zenon_H237 zenon_H9e zenon_Ha0. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.40 exact (zenon_H1f zenon_H1e). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.40 apply (zenon_L1833_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.40 exact (zenon_H237 zenon_H31). % 22.32/22.40 apply (zenon_L156_); trivial. % 22.32/22.40 (* end of lemma zenon_L1834_ *) % 22.32/22.40 assert (zenon_L1835_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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)) = (e0))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (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)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((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)) = (e0))) -> (((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)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 22.32/22.40 do 0 intro. intros zenon_Hcc zenon_H266 zenon_H6f zenon_Hf0 zenon_H55 zenon_H16a zenon_H1f1 zenon_He4 zenon_H33 zenon_H15d zenon_H13e zenon_H190 zenon_H13d zenon_H183 zenon_H163 zenon_H13f zenon_H26a zenon_H100 zenon_H129 zenon_H141 zenon_H23c zenon_Hfa zenon_H1c6 zenon_H1ef zenon_H13a zenon_H73 zenon_H4e zenon_Heb zenon_H156 zenon_H158 zenon_H236 zenon_H48 zenon_H3c zenon_H173 zenon_H13c zenon_Hf5 zenon_Ha0 zenon_H5d zenon_H1c3 zenon_H68 zenon_H77 zenon_H167 zenon_Ha9 zenon_H18d zenon_Hb6 zenon_H20f zenon_H13b zenon_H1f zenon_H125 zenon_H18a zenon_H1fe zenon_H7d zenon_Hbc zenon_H9d. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.32/22.40 apply (zenon_L2_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.32/22.40 apply (zenon_L26_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.32/22.40 apply (zenon_L1808_); trivial. % 22.32/22.40 apply (zenon_L1808_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.32/22.40 apply (zenon_L1817_); trivial. % 22.32/22.40 apply (zenon_L1817_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.32/22.40 apply (zenon_L1819_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.32/22.40 apply (zenon_L1826_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.32/22.40 apply (zenon_L11_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.32/22.40 apply (zenon_L16_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.32/22.40 apply (zenon_L18_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.32/22.40 apply (zenon_L1802_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.32/22.40 apply (zenon_L1830_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.32/22.40 apply (zenon_L37_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.32/22.40 apply (zenon_L1831_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.40 apply (zenon_L1834_); trivial. % 22.32/22.40 apply (zenon_L1825_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.32/22.40 apply (zenon_L221_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.32/22.40 apply (zenon_L201_); trivial. % 22.32/22.40 apply (zenon_L51_); trivial. % 22.32/22.40 (* end of lemma zenon_L1835_ *) % 22.32/22.40 assert (zenon_L1836_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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)) = (e0))) -> (~((e2) = (e3))) -> (((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) (e2)) = (op (e3) (e2)))) -> (((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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (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)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H1c0 zenon_H3c zenon_H48 zenon_H13a zenon_H1fe zenon_H18a zenon_H1f zenon_H18d zenon_H5d zenon_Ha0 zenon_Hb6 zenon_H266 zenon_H6f zenon_Hf0 zenon_H55 zenon_H16a zenon_H77 zenon_H68 zenon_H1f1 zenon_He4 zenon_H33 zenon_H15d zenon_H13e zenon_H190 zenon_H13d zenon_Ha9 zenon_H125 zenon_H183 zenon_H163 zenon_H13f zenon_H26a zenon_H100 zenon_H129 zenon_H141 zenon_H23c zenon_Hfa zenon_H7d zenon_H1c6 zenon_H1c3 zenon_Hf5 zenon_H13c zenon_H1ef zenon_H73 zenon_H236 zenon_H4e zenon_H13b zenon_H20f zenon_Heb zenon_H156 zenon_H158 zenon_H173 zenon_Hbc zenon_Hcc zenon_H167. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 22.32/22.40 exact (zenon_H162 zenon_H167). % 22.32/22.40 apply (zenon_L1835_); trivial. % 22.32/22.40 (* end of lemma zenon_L1836_ *) % 22.32/22.40 assert (zenon_L1837_ : (((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 (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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)) = (e0))) -> (~((e2) = (e3))) -> (((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) (e2)) = (op (e3) (e2)))) -> (((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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (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)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H164 zenon_H2d zenon_H109 zenon_He7 zenon_H11a zenon_H31 zenon_H177 zenon_H1c0 zenon_H3c zenon_H48 zenon_H13a zenon_H1fe zenon_H18a zenon_H1f zenon_H18d zenon_H5d zenon_Ha0 zenon_Hb6 zenon_H266 zenon_H6f zenon_Hf0 zenon_H55 zenon_H16a zenon_H77 zenon_H68 zenon_H1f1 zenon_He4 zenon_H33 zenon_H15d zenon_H13e zenon_H190 zenon_H13d zenon_Ha9 zenon_H125 zenon_H183 zenon_H163 zenon_H13f zenon_H26a zenon_H100 zenon_H129 zenon_H141 zenon_H23c zenon_Hfa zenon_H7d zenon_H1c6 zenon_H1c3 zenon_Hf5 zenon_H13c zenon_H1ef zenon_H73 zenon_H236 zenon_H4e zenon_H13b zenon_H20f zenon_Heb zenon_H156 zenon_H158 zenon_H173 zenon_Hbc zenon_Hcc. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.32/22.40 apply (zenon_L359_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.32/22.40 apply (zenon_L1801_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.32/22.40 apply (zenon_L406_); trivial. % 22.32/22.40 apply (zenon_L1836_); trivial. % 22.32/22.40 (* end of lemma zenon_L1837_ *) % 22.32/22.40 assert (zenon_L1838_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (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 (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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)) = (e0))) -> (~((e2) = (e3))) -> (((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) (e2)) = (op (e3) (e2)))) -> (((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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (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)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H2f zenon_H164 zenon_H109 zenon_He7 zenon_H11a zenon_H177 zenon_H1c0 zenon_H3c zenon_H48 zenon_H13a zenon_H1fe zenon_H18a zenon_H1f zenon_H18d zenon_H5d zenon_Ha0 zenon_Hb6 zenon_H266 zenon_H6f zenon_Hf0 zenon_H55 zenon_H16a zenon_H77 zenon_H68 zenon_H1f1 zenon_He4 zenon_H33 zenon_H15d zenon_H13e zenon_H190 zenon_H13d zenon_Ha9 zenon_H125 zenon_H183 zenon_H163 zenon_H13f zenon_H26a zenon_H100 zenon_H129 zenon_H141 zenon_H23c zenon_Hfa zenon_H7d zenon_H1c6 zenon_H1c3 zenon_Hf5 zenon_H13c zenon_H1ef zenon_H73 zenon_H236 zenon_H4e zenon_H13b zenon_H20f zenon_Heb zenon_H156 zenon_H158 zenon_H173 zenon_Hbc zenon_Hcc. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.32/22.40 apply (zenon_L1837_); trivial. % 22.32/22.40 (* end of lemma zenon_L1838_ *) % 22.32/22.40 assert (zenon_L1839_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((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). % 22.32/22.40 do 0 intro. intros zenon_H141 zenon_H34 zenon_H109 zenon_He7 zenon_Hf0 zenon_H13d zenon_H196 zenon_H38. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.32/22.40 apply (zenon_L359_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.32/22.40 apply (zenon_L929_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.32/22.40 exact (zenon_H13d zenon_H14c). % 22.32/22.40 apply (zenon_L1162_); trivial. % 22.32/22.40 (* end of lemma zenon_L1839_ *) % 22.32/22.40 assert (zenon_L1840_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H36 zenon_H141 zenon_H109 zenon_He7 zenon_Hf0 zenon_H13d zenon_H196. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.32/22.40 apply (zenon_L1839_); trivial. % 22.32/22.40 (* end of lemma zenon_L1840_ *) % 22.32/22.40 assert (zenon_L1841_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_H67 zenon_H105 zenon_H38 zenon_Ha0. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.40 exact (zenon_Ha4 zenon_H9f). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.40 apply (zenon_L55_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.40 apply (zenon_L446_); trivial. % 22.32/22.40 apply (zenon_L156_); trivial. % 22.32/22.40 (* end of lemma zenon_L1841_ *) % 22.32/22.40 assert (zenon_L1842_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_H111 zenon_H110 zenon_H38 zenon_Ha0. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.40 exact (zenon_Ha4 zenon_H9f). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.40 apply (zenon_L55_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.40 apply (zenon_L75_); trivial. % 22.32/22.40 apply (zenon_L156_); trivial. % 22.32/22.40 (* end of lemma zenon_L1842_ *) % 22.32/22.40 assert (zenon_L1843_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H3a zenon_Hb6 zenon_H111 zenon_H110 zenon_Ha0 zenon_H13a zenon_H38. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.32/22.40 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.40 exact (zenon_H238 zenon_H38). % 22.32/22.40 apply (zenon_L1842_); trivial. % 22.32/22.40 (* end of lemma zenon_L1843_ *) % 22.32/22.40 assert (zenon_L1844_ : (((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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (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) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H117 zenon_H109 zenon_H9d zenon_H10c zenon_Hf0 zenon_H13a zenon_Ha0 zenon_H111 zenon_H3a zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_Hb6 zenon_H106 zenon_H1cb. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.32/22.40 apply (zenon_L73_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.32/22.40 apply (zenon_L74_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.32/22.40 apply (zenon_L1843_); trivial. % 22.32/22.40 apply (zenon_L1151_); trivial. % 22.32/22.40 (* end of lemma zenon_L1844_ *) % 22.32/22.40 assert (zenon_L1845_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (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)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (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) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H201 zenon_Hfe zenon_H4e zenon_H67 zenon_H3d zenon_Ha4 zenon_H117 zenon_H109 zenon_H9d zenon_H10c zenon_Hf0 zenon_H13a zenon_Ha0 zenon_H111 zenon_H3a zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_Hb6 zenon_H1cb. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.40 apply (zenon_L95_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.40 apply (zenon_L14_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.40 apply (zenon_L1841_); trivial. % 22.32/22.40 apply (zenon_L1844_); trivial. % 22.32/22.40 (* end of lemma zenon_L1845_ *) % 22.32/22.40 assert (zenon_L1846_ : (((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)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_H160 zenon_H77 zenon_Hf6 zenon_H9f. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.32/22.40 apply (zenon_L456_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.32/22.40 apply (zenon_L146_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.32/22.40 apply (zenon_L367_); trivial. % 22.32/22.40 apply (zenon_L673_); trivial. % 22.32/22.40 (* end of lemma zenon_L1846_ *) % 22.32/22.40 assert (zenon_L1847_ : (((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) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H125 zenon_H6c zenon_H77 zenon_H3c zenon_H6d zenon_H55 zenon_H34 zenon_H68. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.32/22.40 exact (zenon_H6c zenon_H67). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.32/22.40 apply (zenon_L24_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.32/22.40 apply (zenon_L34_); trivial. % 22.32/22.40 apply (zenon_L291_); trivial. % 22.32/22.40 (* end of lemma zenon_L1847_ *) % 22.32/22.40 assert (zenon_L1848_ : (((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 (e1) (e2)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Ha9 zenon_H72 zenon_H105 zenon_H12e zenon_H48 zenon_H34 zenon_H77 zenon_H171 zenon_Hb6 zenon_Hf6 zenon_H9f. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.32/22.40 apply (zenon_L68_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.32/22.40 apply (zenon_L436_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.32/22.40 apply (zenon_L400_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.32/22.40 apply (zenon_L456_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.32/22.40 apply (zenon_L169_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.32/22.40 apply (zenon_L363_); trivial. % 22.32/22.40 apply (zenon_L673_); trivial. % 22.32/22.40 (* end of lemma zenon_L1848_ *) % 22.32/22.40 assert (zenon_L1849_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H1cf zenon_H68 zenon_H31 zenon_Ha9 zenon_H133 zenon_H1ef zenon_H65 zenon_H77 zenon_H106. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.32/22.40 apply (zenon_L264_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.32/22.40 apply (zenon_L436_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.32/22.40 apply (zenon_L533_); trivial. % 22.32/22.40 apply (zenon_L367_); trivial. % 22.32/22.40 (* end of lemma zenon_L1849_ *) % 22.32/22.40 assert (zenon_L1850_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H1a2 zenon_Ha0 zenon_H77 zenon_H65 zenon_H1ef zenon_Ha9 zenon_H31 zenon_H68 zenon_H1cf zenon_H190 zenon_H10d zenon_Hb6 zenon_H106. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.32/22.40 apply (zenon_L68_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.32/22.40 apply (zenon_L1849_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.32/22.40 apply (zenon_L163_); trivial. % 22.32/22.40 apply (zenon_L363_); trivial. % 22.32/22.40 (* end of lemma zenon_L1850_ *) % 22.32/22.40 assert (zenon_L1851_ : (((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) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H266 zenon_He7 zenon_Hf0 zenon_H128 zenon_H189 zenon_H68 zenon_H34 zenon_H55 zenon_H3c zenon_H77 zenon_H6c zenon_H125 zenon_H110 zenon_H190. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_Hdd | zenon_intro zenon_H267 ]. % 22.32/22.40 apply (zenon_L929_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H53 | zenon_intro zenon_H268 ]. % 22.32/22.40 apply (zenon_L139_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H6d | zenon_intro zenon_H10d ]. % 22.32/22.40 apply (zenon_L1847_); trivial. % 22.32/22.40 apply (zenon_L163_); trivial. % 22.32/22.40 (* end of lemma zenon_L1851_ *) % 22.32/22.40 assert (zenon_L1852_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H201 zenon_H1d8 zenon_H3d zenon_H4e zenon_H48 zenon_H12e zenon_H72 zenon_H117 zenon_H1cf zenon_H31 zenon_H1ef zenon_H65 zenon_Ha0 zenon_H1a2 zenon_H1cb zenon_H266 zenon_He7 zenon_Hf0 zenon_H189 zenon_H68 zenon_H34 zenon_H55 zenon_H3c zenon_H77 zenon_H6c zenon_H125 zenon_H190 zenon_H5d zenon_Hf6 zenon_H18d zenon_H121 zenon_H33 zenon_H9f zenon_H171 zenon_Ha9 zenon_Hb6 zenon_H129. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.40 apply (zenon_L738_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.40 apply (zenon_L14_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.40 apply (zenon_L1848_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.32/22.40 apply (zenon_L43_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.32/22.40 apply (zenon_L1850_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.32/22.40 apply (zenon_L98_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.32/22.40 apply (zenon_L17_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.32/22.40 apply (zenon_L1851_); trivial. % 22.32/22.40 apply (zenon_L846_); trivial. % 22.32/22.40 apply (zenon_L493_); trivial. % 22.32/22.40 (* end of lemma zenon_L1852_ *) % 22.32/22.40 assert (zenon_L1853_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 22.32/22.40 do 0 intro. intros zenon_H139 zenon_H6c zenon_H77 zenon_H3d zenon_H68 zenon_H31 zenon_Ha9 zenon_H9e. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.40 exact (zenon_H6c zenon_H67). % 22.32/22.40 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.40 apply (zenon_L214_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.40 apply (zenon_L264_); trivial. % 22.32/22.40 apply (zenon_L92_); trivial. % 22.32/22.40 (* end of lemma zenon_L1853_ *) % 22.32/22.40 assert (zenon_L1854_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (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 (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (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) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (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) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 22.32/22.40 do 0 intro. intros zenon_H13a zenon_Hf6 zenon_Hf5 zenon_H1a8 zenon_H156 zenon_H201 zenon_H1d8 zenon_H4e zenon_H48 zenon_H12e zenon_H117 zenon_H1cf zenon_H1ef zenon_H65 zenon_H1a2 zenon_H1cb zenon_H266 zenon_He7 zenon_Hf0 zenon_H189 zenon_H34 zenon_H55 zenon_H3c zenon_H125 zenon_H190 zenon_H5d zenon_H18d zenon_H121 zenon_H33 zenon_H129 zenon_H192 zenon_Hfa zenon_Hb6 zenon_Ha0 zenon_H139 zenon_H6c zenon_H77 zenon_H3d zenon_H68 zenon_H31 zenon_Ha9. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.32/22.40 apply (zenon_L24_); trivial. % 22.32/22.40 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.32/22.40 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.32/22.40 apply (zenon_L264_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.32/22.41 apply (zenon_L100_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.32/22.41 apply (zenon_L1132_); trivial. % 22.32/22.41 apply (zenon_L1846_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.32/22.41 apply (zenon_L214_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.32/22.41 apply (zenon_L100_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.32/22.41 apply (zenon_L1847_); trivial. % 22.32/22.41 apply (zenon_L1852_); trivial. % 22.32/22.41 apply (zenon_L63_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.41 apply (zenon_L55_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.41 apply (zenon_L68_); trivial. % 22.32/22.41 apply (zenon_L1853_); trivial. % 22.32/22.41 (* end of lemma zenon_L1854_ *) % 22.32/22.41 assert (zenon_L1855_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 22.32/22.41 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_Ha0 zenon_H31 zenon_Ha9 zenon_Hf6. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.41 exact (zenon_Ha4 zenon_H9f). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.41 apply (zenon_L55_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.41 apply (zenon_L68_); trivial. % 22.32/22.41 apply (zenon_L92_); trivial. % 22.32/22.41 (* end of lemma zenon_L1855_ *) % 22.32/22.41 assert (zenon_L1856_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H139 zenon_H6c zenon_H77 zenon_H68 zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_Ha0 zenon_H31 zenon_Ha9. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.41 exact (zenon_H6c zenon_H67). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.41 apply (zenon_L214_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.41 apply (zenon_L264_); trivial. % 22.32/22.41 apply (zenon_L1855_); trivial. % 22.32/22.41 (* end of lemma zenon_L1856_ *) % 22.32/22.41 assert (zenon_L1857_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H139 zenon_H6c zenon_H77 zenon_Ha0 zenon_Ha9 zenon_H3d zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H38 zenon_H68. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.41 exact (zenon_H6c zenon_H67). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.41 apply (zenon_L214_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.41 apply (zenon_L488_); trivial. % 22.32/22.41 apply (zenon_L165_); trivial. % 22.32/22.41 (* end of lemma zenon_L1857_ *) % 22.32/22.41 assert (zenon_L1858_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H236 zenon_H1f zenon_H205 zenon_H139 zenon_H6c zenon_H77 zenon_Ha0 zenon_Ha9 zenon_H3d zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H68. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.41 exact (zenon_H205 zenon_H2a). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.41 apply (zenon_L1856_); trivial. % 22.32/22.41 apply (zenon_L1857_); trivial. % 22.32/22.41 (* end of lemma zenon_L1858_ *) % 22.32/22.41 assert (zenon_L1859_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> False). % 22.32/22.41 do 0 intro. intros zenon_H23d zenon_H1f zenon_H4c zenon_H6c zenon_H11f zenon_Hf6. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1e | zenon_intro zenon_H23e ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H47 | zenon_intro zenon_H23f ]. % 22.32/22.41 exact (zenon_H4c zenon_H47). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H67 | zenon_intro zenon_H9f ]. % 22.32/22.41 exact (zenon_H6c zenon_H67). % 22.32/22.41 apply (zenon_L673_); trivial. % 22.32/22.41 (* end of lemma zenon_L1859_ *) % 22.32/22.41 assert (zenon_L1860_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H236 zenon_H48 zenon_H3a zenon_H11f zenon_H6c zenon_H4c zenon_H1f zenon_H23d zenon_H68 zenon_H3d zenon_H77 zenon_H139 zenon_H238. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.41 apply (zenon_L318_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.41 exact (zenon_H6c zenon_H67). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.41 apply (zenon_L214_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.41 apply (zenon_L264_); trivial. % 22.32/22.41 apply (zenon_L1859_); trivial. % 22.32/22.41 exact (zenon_H238 zenon_H38). % 22.32/22.41 (* end of lemma zenon_L1860_ *) % 22.32/22.41 assert (zenon_L1861_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H23d zenon_H1f zenon_H4c zenon_H6c zenon_Ha4. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1e | zenon_intro zenon_H23e ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H47 | zenon_intro zenon_H23f ]. % 22.32/22.41 exact (zenon_H4c zenon_H47). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H67 | zenon_intro zenon_H9f ]. % 22.32/22.41 exact (zenon_H6c zenon_H67). % 22.32/22.41 exact (zenon_Ha4 zenon_H9f). % 22.32/22.41 (* end of lemma zenon_L1861_ *) % 22.32/22.41 assert (zenon_L1862_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H23b zenon_H1f zenon_H3a zenon_H48 zenon_H139 zenon_H4c zenon_H11f zenon_H23d zenon_H68 zenon_H3d zenon_H77 zenon_H6c zenon_H236. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.41 apply (zenon_L1860_); trivial. % 22.32/22.41 apply (zenon_L1861_); trivial. % 22.32/22.41 (* end of lemma zenon_L1862_ *) % 22.32/22.41 assert (zenon_L1863_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((e0) = (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) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H12e zenon_H34 zenon_H192 zenon_H160 zenon_H23b zenon_H1f zenon_H3a zenon_H48 zenon_H139 zenon_H4c zenon_H23d zenon_H68 zenon_H3d zenon_H77 zenon_H6c zenon_H236. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.32/22.41 apply (zenon_L456_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.32/22.41 apply (zenon_L146_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.32/22.41 apply (zenon_L367_); trivial. % 22.32/22.41 apply (zenon_L1862_); trivial. % 22.32/22.41 (* end of lemma zenon_L1863_ *) % 22.32/22.41 assert (zenon_L1864_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((e0) = (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) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H1cf zenon_H31 zenon_H156 zenon_Hef zenon_H1ef zenon_H65 zenon_H12e zenon_H34 zenon_H192 zenon_H23b zenon_H1f zenon_H3a zenon_H48 zenon_H139 zenon_H4c zenon_H23d zenon_H68 zenon_H3d zenon_H77 zenon_H6c zenon_H236. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.32/22.41 apply (zenon_L264_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.32/22.41 apply (zenon_L100_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.32/22.41 apply (zenon_L533_); trivial. % 22.32/22.41 apply (zenon_L1863_); trivial. % 22.32/22.41 (* end of lemma zenon_L1864_ *) % 22.32/22.41 assert (zenon_L1865_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (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 (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (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 (e1) (e1)) = (op (e1) (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) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H240 zenon_H3c zenon_Hfa zenon_Hf5 zenon_H55 zenon_H201 zenon_H190 zenon_H18d zenon_H1cb zenon_Hf0 zenon_He7 zenon_H189 zenon_H125 zenon_H266 zenon_H5d zenon_H121 zenon_H129 zenon_H33 zenon_H117 zenon_H1a2 zenon_H4e zenon_H1d8 zenon_H1a8 zenon_H156 zenon_H1ef zenon_H12e zenon_H23d zenon_H4c zenon_H3a zenon_H192 zenon_H1cf zenon_H1fe zenon_H236 zenon_H3d zenon_H48 zenon_H1f zenon_H2c zenon_H65 zenon_H77 zenon_H13a zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H68 zenon_H139 zenon_H23b. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.41 apply (zenon_L491_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.41 apply (zenon_L65_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.41 apply (zenon_L25_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.41 apply (zenon_L27_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.41 exact (zenon_H6c zenon_H67). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.41 apply (zenon_L214_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.41 apply (zenon_L264_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.32/22.41 apply (zenon_L24_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.32/22.41 apply (zenon_L1864_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.32/22.41 apply (zenon_L214_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.32/22.41 apply (zenon_L1864_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.32/22.41 apply (zenon_L34_); trivial. % 22.32/22.41 apply (zenon_L1852_); trivial. % 22.32/22.41 apply (zenon_L63_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.41 apply (zenon_L55_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.41 apply (zenon_L68_); trivial. % 22.32/22.41 apply (zenon_L92_); trivial. % 22.32/22.41 exact (zenon_H238 zenon_H38). % 22.32/22.41 apply (zenon_L1861_); trivial. % 22.32/22.41 (* end of lemma zenon_L1865_ *) % 22.32/22.41 assert (zenon_L1866_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e3)) = (e0))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H236 zenon_H1f zenon_H205 zenon_H68 zenon_H66 zenon_H238. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.41 exact (zenon_H205 zenon_H2a). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.41 apply (zenon_L264_); trivial. % 22.32/22.41 exact (zenon_H238 zenon_H38). % 22.32/22.41 (* end of lemma zenon_L1866_ *) % 22.32/22.41 assert (zenon_L1867_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H23b zenon_H237 zenon_H15d zenon_H48 zenon_H77 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H3c zenon_H24 zenon_H1f zenon_H205 zenon_H68 zenon_H66 zenon_H236. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.41 apply (zenon_L1866_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.41 exact (zenon_H205 zenon_H2a). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.41 exact (zenon_H237 zenon_H31). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.41 apply (zenon_L1475_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.41 apply (zenon_L488_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.41 apply (zenon_L94_); trivial. % 22.32/22.41 apply (zenon_L246_); trivial. % 22.32/22.41 (* end of lemma zenon_L1867_ *) % 22.32/22.41 assert (zenon_L1868_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H240 zenon_H139 zenon_H236 zenon_H66 zenon_H68 zenon_H205 zenon_H1f zenon_H24 zenon_H3c zenon_H13a zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H77 zenon_H48 zenon_H15d zenon_H23b. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.41 apply (zenon_L1867_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.41 apply (zenon_L1866_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.41 exact (zenon_H205 zenon_H2a). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.41 apply (zenon_L264_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.41 apply (zenon_L1475_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.41 apply (zenon_L1857_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.41 apply (zenon_L94_); trivial. % 22.32/22.41 apply (zenon_L246_); trivial. % 22.32/22.41 (* end of lemma zenon_L1868_ *) % 22.32/22.41 assert (zenon_L1869_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e3)) = (e0))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H236 zenon_H1f zenon_He7 zenon_H173 zenon_H68 zenon_H66 zenon_H238. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.41 apply (zenon_L272_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.41 apply (zenon_L264_); trivial. % 22.32/22.41 exact (zenon_H238 zenon_H38). % 22.32/22.41 (* end of lemma zenon_L1869_ *) % 22.32/22.41 assert (zenon_L1870_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (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) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> (((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))))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H63 zenon_He7 zenon_H173 zenon_H23d zenon_H1d5 zenon_H15d zenon_H48 zenon_H77 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H3c zenon_H24 zenon_H1f zenon_H68 zenon_H236 zenon_H139. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.32/22.41 apply (zenon_L1868_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.41 apply (zenon_L1869_); trivial. % 22.32/22.41 apply (zenon_L601_); trivial. % 22.32/22.41 (* end of lemma zenon_L1870_ *) % 22.32/22.41 assert (zenon_L1871_ : ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> False). % 22.32/22.41 do 0 intro. intros zenon_H44 zenon_He7 zenon_H3c. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.32/22.41 exact (zenon_H7a zenon_H3c). % 22.32/22.41 exact (zenon_He3 zenon_He7). % 22.32/22.41 (* end of lemma zenon_L1871_ *) % 22.32/22.41 assert (zenon_L1872_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> False). % 22.32/22.41 do 0 intro. intros zenon_H87 zenon_He7 zenon_H3c. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.32/22.41 apply (zenon_L1871_); trivial. % 22.32/22.41 (* end of lemma zenon_L1872_ *) % 22.32/22.41 assert (zenon_L1873_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H236 zenon_H1f zenon_H205 zenon_H237 zenon_H9e zenon_Ha0. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.41 exact (zenon_H205 zenon_H2a). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.41 exact (zenon_H237 zenon_H31). % 22.32/22.41 apply (zenon_L156_); trivial. % 22.32/22.41 (* end of lemma zenon_L1873_ *) % 22.32/22.41 assert (zenon_L1874_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H139 zenon_H6c zenon_H77 zenon_H68 zenon_H13a zenon_H33 zenon_H9d zenon_Hb6 zenon_H3d zenon_Ha0 zenon_H31 zenon_Ha9. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.41 exact (zenon_H6c zenon_H67). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.41 apply (zenon_L214_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.41 apply (zenon_L264_); trivial. % 22.32/22.41 apply (zenon_L708_); trivial. % 22.32/22.41 (* end of lemma zenon_L1874_ *) % 22.32/22.41 assert (zenon_L1875_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H240 zenon_H15d zenon_H48 zenon_H77 zenon_H68 zenon_H13a zenon_Ha9 zenon_Hb6 zenon_H9d zenon_H33 zenon_H139 zenon_H3c zenon_H24 zenon_H9b zenon_H1f zenon_H205 zenon_Ha0 zenon_H9e zenon_H236. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.41 apply (zenon_L1873_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.41 exact (zenon_H205 zenon_H2a). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.41 apply (zenon_L1475_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.41 apply (zenon_L1874_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.41 apply (zenon_L239_); trivial. % 22.32/22.41 apply (zenon_L115_); trivial. % 22.32/22.41 apply (zenon_L1353_); trivial. % 22.32/22.41 (* end of lemma zenon_L1875_ *) % 22.32/22.41 assert (zenon_L1876_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H240 zenon_H33 zenon_H9d zenon_H23d zenon_H1f zenon_H15d zenon_Hb6 zenon_H2c zenon_H65 zenon_H68 zenon_H77 zenon_Ha9 zenon_H9e zenon_H139 zenon_H48 zenon_H4c zenon_Ha0 zenon_H236. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.41 apply (zenon_L499_); trivial. % 22.32/22.41 apply (zenon_L611_); trivial. % 22.32/22.41 (* end of lemma zenon_L1876_ *) % 22.32/22.41 assert (zenon_L1877_ : ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H65 zenon_H2c zenon_H23d zenon_H236 zenon_Ha0 zenon_H1f zenon_H9b zenon_H24 zenon_H3c zenon_H139 zenon_H33 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H68 zenon_H77 zenon_H48 zenon_H15d. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.32/22.41 apply (zenon_L1875_); trivial. % 22.32/22.41 apply (zenon_L1876_); trivial. % 22.32/22.41 (* end of lemma zenon_L1877_ *) % 22.32/22.41 assert (zenon_L1878_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> False). % 22.32/22.41 do 0 intro. intros zenon_Hb1 zenon_He7 zenon_H3c. % 22.32/22.41 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.32/22.41 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.32/22.41 apply (zenon_L1871_); trivial. % 22.32/22.41 (* end of lemma zenon_L1878_ *) % 22.32/22.41 assert (zenon_L1879_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H13a zenon_H33 zenon_H9d zenon_Hb6 zenon_H3d zenon_Ha9 zenon_H66 zenon_H38 zenon_Ha0. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.41 apply (zenon_L245_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.41 apply (zenon_L55_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.41 apply (zenon_L193_); trivial. % 22.32/22.41 apply (zenon_L156_); trivial. % 22.32/22.41 (* end of lemma zenon_L1879_ *) % 22.32/22.41 assert (zenon_L1880_ : (((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)) = (e2)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H139 zenon_H2c zenon_H65 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H9d zenon_H33 zenon_H13a zenon_H153 zenon_H77 zenon_H38 zenon_H68. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.41 apply (zenon_L180_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.41 apply (zenon_L1408_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.41 apply (zenon_L94_); trivial. % 22.32/22.41 apply (zenon_L165_); trivial. % 22.32/22.41 (* end of lemma zenon_L1880_ *) % 22.32/22.41 assert (zenon_L1881_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H23b zenon_H1f zenon_H205 zenon_H139 zenon_H33 zenon_H9d zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H68 zenon_H3d zenon_H77 zenon_H6c zenon_H236. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.41 exact (zenon_H205 zenon_H2a). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.41 apply (zenon_L1874_); trivial. % 22.32/22.41 exact (zenon_H238 zenon_H38). % 22.32/22.41 apply (zenon_L1858_); trivial. % 22.32/22.41 (* end of lemma zenon_L1881_ *) % 22.32/22.41 assert (zenon_L1882_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H240 zenon_H9d zenon_H33 zenon_H205 zenon_H236 zenon_H3d zenon_H48 zenon_H1f zenon_H2c zenon_H65 zenon_H77 zenon_H13a zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H68 zenon_H139 zenon_H23b. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.41 apply (zenon_L491_); trivial. % 22.32/22.41 apply (zenon_L1881_); trivial. % 22.32/22.41 (* end of lemma zenon_L1882_ *) % 22.32/22.41 assert (zenon_L1883_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H204 zenon_H23d zenon_H23b zenon_H139 zenon_H68 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H77 zenon_H65 zenon_H2c zenon_H1f zenon_H48 zenon_H3d zenon_H236 zenon_H33 zenon_H9d zenon_H240. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.32/22.41 apply (zenon_L1882_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.41 apply (zenon_L491_); trivial. % 22.32/22.41 apply (zenon_L611_); trivial. % 22.32/22.41 (* end of lemma zenon_L1883_ *) % 22.32/22.41 assert (zenon_L1884_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> False). % 22.32/22.41 do 0 intro. intros zenon_H3a zenon_H23d zenon_H139 zenon_H68 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H77 zenon_H65 zenon_H2c zenon_H1f zenon_H48 zenon_H236 zenon_H33 zenon_H9d. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.32/22.41 apply (zenon_L1883_); trivial. % 22.32/22.41 (* end of lemma zenon_L1884_ *) % 22.32/22.41 assert (zenon_L1885_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((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)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H23b zenon_H1d5 zenon_H23d zenon_H1f zenon_H15d zenon_H33 zenon_H9d zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H13a zenon_H66 zenon_H77 zenon_H48 zenon_H4c zenon_H237 zenon_H236. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.41 apply (zenon_L590_); trivial. % 22.32/22.41 apply (zenon_L601_); trivial. % 22.32/22.41 (* end of lemma zenon_L1885_ *) % 22.32/22.41 assert (zenon_L1886_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H240 zenon_H236 zenon_H4c zenon_H48 zenon_H77 zenon_H66 zenon_H13a zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H9d zenon_H33 zenon_H15d zenon_H1f zenon_H23d zenon_H1d5 zenon_H23b. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.41 apply (zenon_L1885_); trivial. % 22.32/22.41 apply (zenon_L611_); trivial. % 22.32/22.41 (* end of lemma zenon_L1886_ *) % 22.32/22.41 assert (zenon_L1887_ : ((~((op (e0) (e1)) = (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)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H204 zenon_H1d5 zenon_H23d zenon_H33 zenon_H9d zenon_H23b zenon_H15d zenon_H48 zenon_H77 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H3c zenon_H24 zenon_H1f zenon_H68 zenon_H66 zenon_H236 zenon_H139 zenon_H240. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.32/22.41 apply (zenon_L1868_); trivial. % 22.32/22.41 apply (zenon_L1886_); trivial. % 22.32/22.41 (* end of lemma zenon_L1887_ *) % 22.32/22.41 assert (zenon_L1888_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((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)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> (((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))))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H63 zenon_H1d5 zenon_H23d zenon_H33 zenon_H9d zenon_H15d zenon_H48 zenon_H77 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H3c zenon_H24 zenon_H1f zenon_H68 zenon_H236 zenon_H139. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.32/22.41 apply (zenon_L1887_); trivial. % 22.32/22.41 (* end of lemma zenon_L1888_ *) % 22.32/22.41 assert (zenon_L1889_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((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 (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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) (e1)) = (op (e2) (e3)))) -> (((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 (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> False). % 22.32/22.41 do 0 intro. intros zenon_H1c0 zenon_H3c zenon_H48 zenon_H65 zenon_H68 zenon_H183 zenon_H24e zenon_H1cd zenon_H7d zenon_H192 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1c3 zenon_H104 zenon_H15d zenon_H2c zenon_H77 zenon_H13c zenon_H109 zenon_H117 zenon_H195 zenon_Ha0 zenon_H186 zenon_H190 zenon_H1a2 zenon_Ha9 zenon_Hf0 zenon_He7 zenon_H196 zenon_H141 zenon_H33 zenon_H11a zenon_H121 zenon_Hb6 zenon_H73 zenon_H1cf zenon_H18a zenon_H1bb zenon_H1ef zenon_He4 zenon_H1f1 zenon_H1b7 zenon_H13f zenon_H4e zenon_H5d zenon_H1cb zenon_H18d zenon_H6f zenon_H201 zenon_H23c zenon_H1d8 zenon_H13a zenon_Hfa zenon_H139 zenon_H24 zenon_H173 zenon_H231 zenon_Hbc zenon_H25b zenon_Hf5 zenon_H26a zenon_H1c6 zenon_H55 zenon_H189 zenon_H266 zenon_H1a8 zenon_H156 zenon_H125 zenon_H12e zenon_H1fe zenon_H236 zenon_H1f zenon_H23d zenon_H1d5 zenon_H94 zenon_Hcc. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.32/22.41 apply (zenon_L2_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.32/22.41 apply (zenon_L26_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.32/22.41 apply (zenon_L28_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.32/22.41 apply (zenon_L1765_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.41 apply (zenon_L491_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.41 exact (zenon_H205 zenon_H2a). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.41 apply (zenon_L25_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.41 apply (zenon_L27_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.41 exact (zenon_H6c zenon_H67). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.41 apply (zenon_L214_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.41 apply (zenon_L264_); trivial. % 22.32/22.41 apply (zenon_L1854_); trivial. % 22.32/22.41 exact (zenon_H238 zenon_H38). % 22.32/22.41 apply (zenon_L1858_); trivial. % 22.32/22.41 apply (zenon_L1865_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.32/22.41 apply (zenon_L11_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.32/22.41 apply (zenon_L16_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.32/22.41 apply (zenon_L18_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.32/22.41 apply (zenon_L1870_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.32/22.41 apply (zenon_L1872_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.32/22.41 apply (zenon_L37_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.32/22.41 apply (zenon_L39_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.32/22.41 apply (zenon_L1877_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.32/22.41 apply (zenon_L1878_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.32/22.41 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.32/22.41 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.32/22.41 exact (zenon_H7b zenon_H65). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.41 exact (zenon_H1f zenon_H1e). % 22.32/22.41 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.41 apply (zenon_L25_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.41 apply (zenon_L27_); trivial. % 22.32/22.41 apply (zenon_L1104_); trivial. % 22.32/22.41 apply (zenon_L51_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.32/22.41 apply (zenon_L2_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.32/22.41 apply (zenon_L26_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.32/22.41 apply (zenon_L28_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.32/22.41 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.41 apply (zenon_L1475_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.41 apply (zenon_L180_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.41 apply (zenon_L214_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.41 apply (zenon_L1879_); trivial. % 22.32/22.41 apply (zenon_L165_); trivial. % 22.32/22.41 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.41 apply (zenon_L1880_); trivial. % 22.32/22.42 apply (zenon_L246_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.32/22.42 apply (zenon_L1884_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.32/22.42 apply (zenon_L11_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.32/22.42 apply (zenon_L16_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.32/22.42 apply (zenon_L18_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.32/22.42 apply (zenon_L1888_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.32/22.42 apply (zenon_L35_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.32/22.42 apply (zenon_L37_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.32/22.42 apply (zenon_L39_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.32/22.42 apply (zenon_L1877_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.32/22.42 apply (zenon_L221_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.32/22.42 apply (zenon_L201_); trivial. % 22.32/22.42 apply (zenon_L51_); trivial. % 22.32/22.42 (* end of lemma zenon_L1889_ *) % 22.32/22.42 assert (zenon_L1890_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((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 (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (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) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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) (e1)) = (op (e2) (e3)))) -> (((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 (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 22.32/22.42 do 0 intro. intros zenon_H3a zenon_H111 zenon_Ha4 zenon_H77 zenon_H183 zenon_Ha9 zenon_H38 zenon_H68 zenon_H1c3 zenon_H104 zenon_H24e zenon_He7 zenon_H11a zenon_H3d zenon_H192 zenon_H1b7 zenon_H1c0 zenon_H3c zenon_H48 zenon_H1cd zenon_H1b4 zenon_H20f zenon_H129 zenon_H15d zenon_H2c zenon_H13c zenon_H109 zenon_H117 zenon_H195 zenon_Ha0 zenon_H186 zenon_H190 zenon_H1a2 zenon_Hf0 zenon_H196 zenon_H141 zenon_H33 zenon_H121 zenon_Hb6 zenon_H73 zenon_H1cf zenon_H18a zenon_H1bb zenon_H1ef zenon_He4 zenon_H1f1 zenon_H13f zenon_H4e zenon_H5d zenon_H1cb zenon_H18d zenon_H6f zenon_H201 zenon_H23c zenon_H1d8 zenon_H13a zenon_Hfa zenon_H139 zenon_H24 zenon_H173 zenon_H231 zenon_Hbc zenon_H25b zenon_Hf5 zenon_H26a zenon_H1c6 zenon_H55 zenon_H189 zenon_H266 zenon_H1a8 zenon_H156 zenon_H125 zenon_H12e zenon_H1fe zenon_H236 zenon_H1f zenon_H23d zenon_H1d5 zenon_H94 zenon_Hcc zenon_H16a zenon_Hfe zenon_H67 zenon_H2d zenon_H9d zenon_H7d. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.42 apply (zenon_L46_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.42 apply (zenon_L1845_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.42 apply (zenon_L89_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.32/22.42 apply (zenon_L55_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.32/22.42 apply (zenon_L1845_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.32/22.42 apply (zenon_L217_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.32/22.42 apply (zenon_L113_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.32/22.42 apply (zenon_L446_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.42 apply (zenon_L1889_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.42 apply (zenon_L289_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.32/22.42 apply (zenon_L91_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.32/22.42 apply (zenon_L1444_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.32/22.42 apply (zenon_L231_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_He0 | zenon_intro zenon_H24f ]. % 22.32/22.42 apply (zenon_L1801_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H7f | zenon_intro zenon_H250 ]. % 22.32/22.42 apply (zenon_L146_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H171 | zenon_intro zenon_Hac ]. % 22.32/22.42 apply (zenon_L188_); trivial. % 22.32/22.42 apply (zenon_L44_); trivial. % 22.32/22.42 apply (zenon_L218_); trivial. % 22.32/22.42 apply (zenon_L44_); trivial. % 22.32/22.42 (* end of lemma zenon_L1890_ *) % 22.32/22.42 assert (zenon_L1891_ : (~((e0) = (e2))) -> (((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 (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (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) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (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) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((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 (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((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)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e3)) = (e0))) -> False). % 22.32/22.42 do 0 intro. intros zenon_H68 zenon_H13a zenon_Hf5 zenon_H1a8 zenon_H156 zenon_H201 zenon_H1d8 zenon_H4e zenon_H48 zenon_H12e zenon_H117 zenon_H1cf zenon_H1ef zenon_H1a2 zenon_H1cb zenon_H266 zenon_He7 zenon_Hf0 zenon_H189 zenon_H55 zenon_H3c zenon_H125 zenon_H190 zenon_H5d zenon_H18d zenon_H121 zenon_H33 zenon_H129 zenon_H192 zenon_Hfa zenon_Hb6 zenon_Ha0 zenon_H139 zenon_H6c zenon_H77 zenon_H3d zenon_Ha9 zenon_H236 zenon_H1f zenon_H173 zenon_H164 zenon_H109 zenon_H11a zenon_H177 zenon_H1c0 zenon_H1fe zenon_H18a zenon_H6f zenon_H16a zenon_H1f1 zenon_He4 zenon_H15d zenon_H13e zenon_H13d zenon_H183 zenon_H163 zenon_H13f zenon_H26a zenon_H100 zenon_H141 zenon_H23c zenon_H7d zenon_H1c6 zenon_H1c3 zenon_H13c zenon_H73 zenon_H13b zenon_H20f zenon_Heb zenon_H158 zenon_Hbc zenon_Hcc zenon_H238. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.42 exact (zenon_H1f zenon_H1e). % 22.32/22.42 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.42 apply (zenon_L65_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.42 exact (zenon_H1f zenon_H1e). % 22.32/22.42 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.42 apply (zenon_L25_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.42 apply (zenon_L1837_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.42 exact (zenon_H6c zenon_H67). % 22.32/22.42 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.42 apply (zenon_L214_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.42 apply (zenon_L1869_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.32/22.42 exact (zenon_H6c zenon_H67). % 22.32/22.42 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.32/22.42 apply (zenon_L24_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.32/22.42 apply (zenon_L1854_); trivial. % 22.32/22.42 apply (zenon_L291_); trivial. % 22.32/22.42 exact (zenon_H238 zenon_H38). % 22.32/22.42 (* end of lemma zenon_L1891_ *) % 22.32/22.42 assert (zenon_L1892_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 22.32/22.42 do 0 intro. intros zenon_H236 zenon_H1f zenon_He7 zenon_H173 zenon_H237 zenon_H9e zenon_Ha0. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.42 exact (zenon_H1f zenon_H1e). % 22.32/22.42 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.42 apply (zenon_L272_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.42 exact (zenon_H237 zenon_H31). % 22.32/22.42 apply (zenon_L156_); trivial. % 22.32/22.42 (* end of lemma zenon_L1892_ *) % 22.32/22.42 assert (zenon_L1893_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.32/22.42 do 0 intro. intros zenon_H240 zenon_H4c zenon_H33 zenon_H9d zenon_H23d zenon_H1f zenon_H173 zenon_He7 zenon_Ha0 zenon_H9e zenon_H236. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.42 apply (zenon_L1892_); trivial. % 22.32/22.42 apply (zenon_L611_); trivial. % 22.32/22.42 (* end of lemma zenon_L1893_ *) % 22.32/22.42 assert (zenon_L1894_ : ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((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 (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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) (e1)) = (op (e2) (e3)))) -> (((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 (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.32/22.42 do 0 intro. intros zenon_He7 zenon_H173 zenon_H4c zenon_H3a zenon_H111 zenon_Ha4 zenon_H183 zenon_H1c3 zenon_H104 zenon_H24e zenon_H11a zenon_H192 zenon_H1b7 zenon_H1c0 zenon_H1cd zenon_H1b4 zenon_H20f zenon_H129 zenon_H2c zenon_H13c zenon_H109 zenon_H117 zenon_H195 zenon_H186 zenon_H190 zenon_H1a2 zenon_Hf0 zenon_H196 zenon_H141 zenon_H121 zenon_H73 zenon_H1cf zenon_H18a zenon_H1bb zenon_H1ef zenon_He4 zenon_H1f1 zenon_H13f zenon_H4e zenon_H5d zenon_H1cb zenon_H18d zenon_H6f zenon_H201 zenon_H23c zenon_H1d8 zenon_Hfa zenon_H231 zenon_Hbc zenon_H25b zenon_Hf5 zenon_H26a zenon_H1c6 zenon_H55 zenon_H189 zenon_H266 zenon_H1a8 zenon_H156 zenon_H125 zenon_H12e zenon_H1fe zenon_H94 zenon_Hcc zenon_H16a zenon_H2d zenon_H7d zenon_H3d zenon_H240 zenon_H139 zenon_H236 zenon_H1f zenon_H24 zenon_H3c zenon_H13a zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H77 zenon_H48 zenon_H15d zenon_H23b zenon_H9d zenon_H33 zenon_H23d zenon_H1d5 zenon_H204 zenon_H38 zenon_H68. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.42 exact (zenon_Ha4 zenon_H9f). % 22.32/22.42 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.42 apply (zenon_L55_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.42 apply (zenon_L1890_); trivial. % 22.32/22.42 apply (zenon_L1893_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.42 apply (zenon_L214_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.42 apply (zenon_L1887_); trivial. % 22.32/22.42 apply (zenon_L165_); trivial. % 22.32/22.42 (* end of lemma zenon_L1894_ *) % 22.32/22.42 assert (zenon_L1895_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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)) = (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))))) -> (~((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 22.32/22.42 do 0 intro. intros zenon_Hcc zenon_Hbc zenon_H173 zenon_H158 zenon_H156 zenon_Heb zenon_H20f zenon_H13b zenon_H4e zenon_H236 zenon_H73 zenon_H1ef zenon_H13c zenon_Hf5 zenon_H1c3 zenon_H1c6 zenon_H7d zenon_Hfa zenon_H23c zenon_H129 zenon_H100 zenon_H26a zenon_H13f zenon_H163 zenon_H183 zenon_H125 zenon_Ha9 zenon_H190 zenon_H13e zenon_H15d zenon_H33 zenon_He4 zenon_H1f1 zenon_H77 zenon_H16a zenon_H55 zenon_H6f zenon_H266 zenon_Hb6 zenon_Ha0 zenon_H5d zenon_H18d zenon_H1f zenon_H18a zenon_H1fe zenon_H13a zenon_H48 zenon_H3c zenon_H1c0 zenon_H177 zenon_H31 zenon_H11a zenon_H164 zenon_H141 zenon_H109 zenon_He7 zenon_Hf0 zenon_H13d zenon_H68 zenon_H93. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.42 exact (zenon_H1f zenon_H1e). % 22.32/22.42 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.42 apply (zenon_L25_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.42 apply (zenon_L1837_); trivial. % 22.32/22.42 apply (zenon_L1072_); trivial. % 22.32/22.42 (* end of lemma zenon_L1895_ *) % 22.32/22.42 assert (zenon_L1896_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 22.32/22.42 do 0 intro. intros zenon_H266 zenon_H2d zenon_H55 zenon_H105 zenon_Hf0 zenon_Hef zenon_H110 zenon_H190. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_Hdd | zenon_intro zenon_H267 ]. % 22.32/22.42 apply (zenon_L702_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H53 | zenon_intro zenon_H268 ]. % 22.32/22.42 apply (zenon_L143_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H6d | zenon_intro zenon_H10d ]. % 22.32/22.42 apply (zenon_L61_); trivial. % 22.32/22.42 apply (zenon_L163_); trivial. % 22.32/22.42 (* end of lemma zenon_L1896_ *) % 22.32/22.42 assert (zenon_L1897_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.32/22.42 do 0 intro. intros zenon_H164 zenon_H68 zenon_H13d zenon_Hf0 zenon_He7 zenon_H109 zenon_H141 zenon_Hef zenon_H77 zenon_H93 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_Hbb zenon_Ha0 zenon_H162. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.32/22.42 apply (zenon_L1072_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.32/22.42 apply (zenon_L1685_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.32/22.42 apply (zenon_L80_); trivial. % 22.32/22.42 exact (zenon_H162 zenon_H167). % 22.32/22.42 (* end of lemma zenon_L1897_ *) % 22.32/22.42 assert (zenon_L1898_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (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) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (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) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (((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 (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 22.32/22.42 do 0 intro. intros zenon_H13f zenon_H195 zenon_H163 zenon_H160 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H189 zenon_H24e zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_Hfa zenon_H162 zenon_Ha0 zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H3c zenon_Hef zenon_H141 zenon_H109 zenon_He7 zenon_Hf0 zenon_H13d zenon_H68 zenon_H164 zenon_H266 zenon_H2d zenon_H55 zenon_H190 zenon_Hf3 zenon_H67 zenon_H1a2 zenon_H77 zenon_H93. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.32/22.42 apply (zenon_L217_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.32/22.42 apply (zenon_L1721_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.32/22.42 apply (zenon_L446_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.32/22.42 apply (zenon_L162_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.32/22.42 apply (zenon_L1896_); trivial. % 22.32/22.42 apply (zenon_L1897_); trivial. % 22.32/22.42 apply (zenon_L218_); trivial. % 22.32/22.42 (* end of lemma zenon_L1898_ *) % 22.32/22.42 assert (zenon_L1899_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (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) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((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)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (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 (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 22.32/22.42 do 0 intro. intros zenon_H140 zenon_Hcc zenon_Hbc zenon_H173 zenon_H158 zenon_H156 zenon_Heb zenon_H13b zenon_H4e zenon_H236 zenon_H73 zenon_H1ef zenon_H13c zenon_Hf5 zenon_H1c3 zenon_H1c6 zenon_H7d zenon_H23c zenon_H26a zenon_H183 zenon_H125 zenon_Ha9 zenon_H13e zenon_H15d zenon_H33 zenon_He4 zenon_H1f1 zenon_H16a zenon_H6f zenon_H1f zenon_H18a zenon_H1fe zenon_H13a zenon_H1c0 zenon_H177 zenon_H11a zenon_H164 zenon_H68 zenon_He7 zenon_H109 zenon_H141 zenon_H162 zenon_Hfa zenon_H163 zenon_H13d zenon_H1c7 zenon_H160 zenon_H1cd zenon_H1b7 zenon_H18d zenon_H48 zenon_H38 zenon_H5d zenon_H24e zenon_H189 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H195 zenon_Ha5 zenon_H266 zenon_H2d zenon_H55 zenon_Hf0 zenon_Hef zenon_H190 zenon_H13f zenon_H3c zenon_H100 zenon_Hb6 zenon_Ha0 zenon_H186 zenon_H67 zenon_H1a2 zenon_H117 zenon_H77 zenon_H93. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.32/22.42 apply (zenon_L1837_); trivial. % 22.32/22.42 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.32/22.43 apply (zenon_L1898_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.32/22.43 exact (zenon_H13d zenon_H14c). % 22.32/22.43 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.32/22.43 apply (zenon_L69_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.32/22.43 apply (zenon_L1687_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.32/22.43 apply (zenon_L67_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.32/22.43 apply (zenon_L1728_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.32/22.43 apply (zenon_L1896_); trivial. % 22.32/22.43 apply (zenon_L172_); trivial. % 22.32/22.43 apply (zenon_L218_); trivial. % 22.32/22.43 (* end of lemma zenon_L1899_ *) % 22.32/22.43 assert (zenon_L1900_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.43 do 0 intro. intros zenon_Hfa zenon_H77 zenon_Hfe zenon_H67 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H189 zenon_H24e zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H2d zenon_H13f zenon_H160 zenon_H163 zenon_H93 zenon_H195. % 22.32/22.43 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.32/22.43 apply (zenon_L24_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.32/22.43 apply (zenon_L217_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.32/22.43 apply (zenon_L1687_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.32/22.43 apply (zenon_L446_); trivial. % 22.32/22.43 apply (zenon_L218_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.32/22.43 apply (zenon_L227_); trivial. % 22.32/22.43 apply (zenon_L228_); trivial. % 22.32/22.43 (* end of lemma zenon_L1900_ *) % 22.32/22.43 assert (zenon_L1901_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((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 (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.32/22.43 do 0 intro. intros zenon_He4 zenon_H1d8 zenon_H23c zenon_H195 zenon_H163 zenon_H189 zenon_H3c zenon_H5d zenon_Hfa zenon_H139 zenon_Ha0 zenon_H13f zenon_Hb6 zenon_H117 zenon_H1a2 zenon_H186 zenon_H100 zenon_H190 zenon_Hf0 zenon_H55 zenon_H266 zenon_H13d zenon_H162 zenon_H141 zenon_H109 zenon_He7 zenon_H68 zenon_H164 zenon_H11a zenon_H1c0 zenon_H13a zenon_H1fe zenon_H1f zenon_H6f zenon_H16a zenon_H1f1 zenon_H33 zenon_H15d zenon_H13e zenon_Ha9 zenon_H125 zenon_H183 zenon_H26a zenon_H1c6 zenon_H1c3 zenon_Hf5 zenon_H13c zenon_H1ef zenon_H73 zenon_H236 zenon_H4e zenon_H13b zenon_Heb zenon_H156 zenon_H158 zenon_H173 zenon_Hbc zenon_Hcc zenon_H140 zenon_H1a3 zenon_H121 zenon_H99 zenon_H192 zenon_H104 zenon_H25b zenon_H177 zenon_H196 zenon_H24 zenon_H12e zenon_H77 zenon_H93 zenon_H1b4 zenon_H20f zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H160 zenon_H1c7. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.43 exact (zenon_H1f zenon_H1e). % 22.32/22.43 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.43 apply (zenon_L272_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.43 apply (zenon_L1895_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.43 exact (zenon_H1f zenon_H1e). % 22.32/22.43 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.43 apply (zenon_L25_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.43 apply (zenon_L1475_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.32/22.43 apply (zenon_L24_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.43 apply (zenon_L46_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.43 apply (zenon_L538_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.43 apply (zenon_L1731_); trivial. % 22.32/22.43 apply (zenon_L1899_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.32/22.43 apply (zenon_L227_); trivial. % 22.32/22.43 apply (zenon_L228_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.43 apply (zenon_L55_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.43 apply (zenon_L1900_); trivial. % 22.32/22.43 apply (zenon_L156_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.43 apply (zenon_L214_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.43 apply (zenon_L122_); trivial. % 22.32/22.43 apply (zenon_L167_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.43 apply (zenon_L1722_); trivial. % 22.32/22.43 apply (zenon_L246_); trivial. % 22.32/22.43 apply (zenon_L1510_); trivial. % 22.32/22.43 (* end of lemma zenon_L1901_ *) % 22.32/22.43 assert (zenon_L1902_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((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)) = (op (e2) (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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((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 (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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))))) -> (~((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) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.43 do 0 intro. intros zenon_H11a zenon_H1c0 zenon_H13a zenon_Hb6 zenon_H6f zenon_H16a zenon_H1f1 zenon_H33 zenon_H13e zenon_Ha9 zenon_H125 zenon_H183 zenon_H100 zenon_H7d zenon_H1c6 zenon_H1c3 zenon_H13c zenon_H1ef zenon_H73 zenon_H236 zenon_H4e zenon_H13b zenon_Heb zenon_H156 zenon_H158 zenon_H173 zenon_Hbc zenon_Hcc zenon_H1fe zenon_H1f zenon_H48 zenon_He4 zenon_H1d8 zenon_H23c zenon_H195 zenon_H163 zenon_H160 zenon_H189 zenon_H24e zenon_H3c zenon_H5d zenon_H1cd zenon_H1c7 zenon_Hfa zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H1b7 zenon_H139 zenon_H140 zenon_H26d zenon_H164 zenon_H13f zenon_Ha0 zenon_H266 zenon_H55 zenon_H190 zenon_H12e zenon_H181 zenon_H18a zenon_H162 zenon_H1cb zenon_H26a zenon_H186 zenon_Hf5 zenon_H25b zenon_H1a2 zenon_H177 zenon_H68 zenon_H24 zenon_H15d zenon_H141 zenon_H109 zenon_He7 zenon_Hf0 zenon_H13d zenon_H196. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.43 exact (zenon_H1f zenon_H1e). % 22.32/22.43 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.43 apply (zenon_L272_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.43 apply (zenon_L1895_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.43 exact (zenon_H1f zenon_H1e). % 22.32/22.43 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.43 apply (zenon_L25_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.43 apply (zenon_L1475_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.32/22.43 apply (zenon_L24_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.32/22.43 apply (zenon_L756_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.32/22.43 apply (zenon_L1898_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.32/22.43 exact (zenon_H13d zenon_H14c). % 22.32/22.43 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.32/22.43 apply (zenon_L217_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.32/22.43 apply (zenon_L1721_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.32/22.43 apply (zenon_L446_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.32/22.43 apply (zenon_L1700_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.32/22.43 apply (zenon_L1896_); trivial. % 22.32/22.43 apply (zenon_L80_); trivial. % 22.32/22.43 apply (zenon_L218_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.32/22.43 apply (zenon_L227_); trivial. % 22.32/22.43 apply (zenon_L228_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.43 apply (zenon_L214_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.43 apply (zenon_L122_); trivial. % 22.32/22.43 apply (zenon_L165_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.43 apply (zenon_L1722_); trivial. % 22.32/22.43 apply (zenon_L246_); trivial. % 22.32/22.43 apply (zenon_L1839_); trivial. % 22.32/22.43 (* end of lemma zenon_L1902_ *) % 22.32/22.43 assert (zenon_L1903_ : ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 22.32/22.43 do 0 intro. intros zenon_He7 zenon_H173 zenon_H23d zenon_H236 zenon_Ha0 zenon_H1f zenon_H9b zenon_H24 zenon_H3c zenon_H139 zenon_H33 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H68 zenon_H77 zenon_H48 zenon_H15d. % 22.32/22.43 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.32/22.43 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.32/22.43 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.32/22.43 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.32/22.43 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.32/22.43 apply (zenon_L1875_); trivial. % 22.32/22.43 apply (zenon_L1893_); trivial. % 22.32/22.43 (* end of lemma zenon_L1903_ *) % 22.32/22.43 assert (zenon_L1904_ : (((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 (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((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)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((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) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (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 (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((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 (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (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) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.32/22.43 do 0 intro. intros zenon_H16a zenon_Hcc zenon_H94 zenon_H1d5 zenon_H23d zenon_H1f zenon_H236 zenon_H1fe zenon_H12e zenon_H125 zenon_H156 zenon_H1a8 zenon_H266 zenon_H189 zenon_H55 zenon_H1c6 zenon_H26a zenon_Hf5 zenon_H25b zenon_Hbc zenon_H231 zenon_H173 zenon_H24 zenon_H139 zenon_Hfa zenon_H13a zenon_H1d8 zenon_H23c zenon_H201 zenon_H6f zenon_H1cb zenon_H4e zenon_H13f zenon_H1b7 zenon_H1f1 zenon_He4 zenon_H1ef zenon_H1bb zenon_H18a zenon_H1cf zenon_H73 zenon_Hb6 zenon_H121 zenon_H11a zenon_H33 zenon_H196 zenon_Ha9 zenon_H1a2 zenon_H190 zenon_H186 zenon_H195 zenon_H117 zenon_H13c zenon_H2c zenon_H15d zenon_H104 zenon_H1c3 zenon_H129 zenon_H20f zenon_H1b4 zenon_H192 zenon_H7d zenon_H1cd zenon_H24e zenon_H183 zenon_H1c0 zenon_H1ba zenon_H8b zenon_H164 zenon_H68 zenon_H13d zenon_Hf0 zenon_He7 zenon_H109 zenon_H141 zenon_Hef zenon_H77 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_Hbb zenon_Ha0 zenon_H162. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.43 apply (zenon_L1889_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.43 exact (zenon_H1ba zenon_H6d). % 22.32/22.43 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.43 exact (zenon_H8b zenon_H8a). % 22.32/22.43 apply (zenon_L1897_); trivial. % 22.32/22.43 (* end of lemma zenon_L1904_ *) % 22.32/22.43 assert (zenon_L1905_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 22.32/22.43 do 0 intro. intros zenon_H1fe zenon_H1f zenon_Hbb zenon_H4e zenon_H38 zenon_H26d zenon_H140 zenon_H68 zenon_H65 zenon_H141 zenon_H109 zenon_He7 zenon_Hf0 zenon_H13d zenon_Ha0 zenon_Hb9. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.43 exact (zenon_H1f zenon_H1e). % 22.32/22.43 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.43 apply (zenon_L1385_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.43 apply (zenon_L27_); trivial. % 22.32/22.43 apply (zenon_L1104_); trivial. % 22.32/22.43 (* end of lemma zenon_L1905_ *) % 22.32/22.43 assert (zenon_L1906_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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 (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.43 do 0 intro. intros zenon_H16a zenon_Hb9 zenon_Ha0 zenon_H13d zenon_Hf0 zenon_He7 zenon_H109 zenon_H141 zenon_H68 zenon_H140 zenon_H26d zenon_H38 zenon_H4e zenon_Hbb zenon_H1f zenon_H1fe zenon_H1ba zenon_H8b zenon_Hf7 zenon_H195. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.43 apply (zenon_L1905_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.43 exact (zenon_H1ba zenon_H6d). % 22.32/22.43 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.43 exact (zenon_H8b zenon_H8a). % 22.32/22.43 apply (zenon_L228_); trivial. % 22.32/22.43 (* end of lemma zenon_L1906_ *) % 22.32/22.43 assert (zenon_L1907_ : (~((op (e0) (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 (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (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))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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) (e1)) = (op (e2) (e3)))) -> (((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 (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.43 do 0 intro. intros zenon_H177 zenon_H13e zenon_H163 zenon_H100 zenon_H13b zenon_Heb zenon_H158 zenon_H162 zenon_H18d zenon_H48 zenon_H5d zenon_H3c zenon_H77 zenon_H164 zenon_H1c0 zenon_H183 zenon_H24e zenon_H1cd zenon_H7d zenon_H192 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1c3 zenon_H104 zenon_H15d zenon_H2c zenon_H13c zenon_H117 zenon_H186 zenon_H190 zenon_H1a2 zenon_Ha9 zenon_H196 zenon_H33 zenon_H11a zenon_H121 zenon_Hb6 zenon_H73 zenon_H1cf zenon_H18a zenon_H1bb zenon_H1ef zenon_He4 zenon_H1f1 zenon_H1b7 zenon_H13f zenon_H1cb zenon_H6f zenon_H201 zenon_H23c zenon_H1d8 zenon_H13a zenon_Hfa zenon_H139 zenon_H24 zenon_H173 zenon_H231 zenon_Hbc zenon_H25b zenon_Hf5 zenon_H26a zenon_H1c6 zenon_H55 zenon_H189 zenon_H266 zenon_H1a8 zenon_H156 zenon_H125 zenon_H12e zenon_H236 zenon_H23d zenon_H1d5 zenon_H94 zenon_Hcc zenon_H16a zenon_Hb9 zenon_Ha0 zenon_H13d zenon_Hf0 zenon_He7 zenon_H109 zenon_H141 zenon_H68 zenon_H140 zenon_H26d zenon_H4e zenon_Hbb zenon_H1f zenon_H1fe zenon_H1ba zenon_H8b zenon_H195. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.43 exact (zenon_H1f zenon_H1e). % 22.32/22.43 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.43 apply (zenon_L272_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.43 exact (zenon_H1f zenon_H1e). % 22.32/22.43 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.43 apply (zenon_L25_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.43 apply (zenon_L1837_); trivial. % 22.32/22.43 apply (zenon_L1104_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.32/22.43 apply (zenon_L24_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.32/22.43 apply (zenon_L1904_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.32/22.43 apply (zenon_L756_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.32/22.43 apply (zenon_L62_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.32/22.43 exact (zenon_H13d zenon_H14c). % 22.32/22.43 apply (zenon_L80_); trivial. % 22.32/22.43 apply (zenon_L1906_); trivial. % 22.32/22.43 (* end of lemma zenon_L1907_ *) % 22.32/22.43 assert (zenon_L1908_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (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))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 22.32/22.43 do 0 intro. intros zenon_H141 zenon_H34 zenon_H196 zenon_H9e zenon_H133 zenon_H131 zenon_Ha0 zenon_H9d zenon_H109 zenon_H117 zenon_H13d zenon_H68 zenon_H93. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.32/22.43 apply (zenon_L359_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.32/22.43 apply (zenon_L587_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.32/22.43 exact (zenon_H13d zenon_H14c). % 22.32/22.43 apply (zenon_L158_); trivial. % 22.32/22.43 (* end of lemma zenon_L1908_ *) % 22.32/22.43 assert (zenon_L1909_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.32/22.43 do 0 intro. intros zenon_H13c zenon_H179 zenon_H9d zenon_H173 zenon_Hdb zenon_Hb6 zenon_H4d zenon_H19a zenon_H48 zenon_H155 zenon_Ha0 zenon_H93 zenon_H68 zenon_H162. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.43 apply (zenon_L123_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.43 apply (zenon_L120_); trivial. % 22.32/22.43 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.43 apply (zenon_L124_); trivial. % 22.32/22.43 apply (zenon_L247_); trivial. % 22.32/22.43 (* end of lemma zenon_L1909_ *) % 22.32/22.43 assert (zenon_L1910_ : (((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 (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (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))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H13c zenon_H179 zenon_H173 zenon_H177 zenon_H31 zenon_H7f zenon_H141 zenon_H109 zenon_He7 zenon_Hf0 zenon_H13d zenon_H164 zenon_H131 zenon_H6f zenon_Hdb zenon_H9d zenon_H117 zenon_H19a zenon_H48 zenon_H155 zenon_Ha0 zenon_H93 zenon_H68 zenon_H162. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.44 apply (zenon_L123_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.44 apply (zenon_L120_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.32/22.44 apply (zenon_L73_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.32/22.44 apply (zenon_L205_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.32/22.44 apply (zenon_L259_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.32/22.44 apply (zenon_L1104_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.32/22.44 apply (zenon_L57_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.32/22.44 apply (zenon_L406_); trivial. % 22.32/22.44 exact (zenon_H162 zenon_H167). % 22.32/22.44 apply (zenon_L247_); trivial. % 22.32/22.44 (* end of lemma zenon_L1910_ *) % 22.32/22.44 assert (zenon_L1911_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((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 (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.32/22.44 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_Hdb zenon_H111 zenon_H153 zenon_Hf0 zenon_H2d zenon_H13f zenon_H195 zenon_H163 zenon_H160 zenon_H189 zenon_H24e zenon_H3c zenon_H5d zenon_H1cd zenon_H1c7 zenon_Hfa zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H38 zenon_H1bb zenon_H93 zenon_H77 zenon_H1b7. % 22.32/22.44 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.32/22.44 apply (zenon_L55_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.32/22.44 apply (zenon_L219_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.32/22.44 apply (zenon_L1721_); trivial. % 22.32/22.44 apply (zenon_L1276_); trivial. % 22.32/22.44 (* end of lemma zenon_L1911_ *) % 22.32/22.44 assert (zenon_L1912_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((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 (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H15d zenon_H24 zenon_H68 zenon_Ha9 zenon_H139 zenon_Ha0 zenon_Hb6 zenon_He4 zenon_H111 zenon_Hf0 zenon_H2d zenon_H13f zenon_H195 zenon_H163 zenon_H160 zenon_H189 zenon_H24e zenon_H3c zenon_H5d zenon_H1cd zenon_H1c7 zenon_Hfa zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H1b7 zenon_H9d zenon_H33 zenon_H13a zenon_H38 zenon_H48. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.44 apply (zenon_L1475_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.44 apply (zenon_L245_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.44 apply (zenon_L55_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.44 apply (zenon_L1900_); trivial. % 22.32/22.44 apply (zenon_L156_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.44 apply (zenon_L214_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.44 apply (zenon_L1879_); trivial. % 22.32/22.44 apply (zenon_L165_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.44 apply (zenon_L245_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.44 apply (zenon_L1911_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.44 apply (zenon_L95_); trivial. % 22.32/22.44 apply (zenon_L156_); trivial. % 22.32/22.44 apply (zenon_L246_); trivial. % 22.32/22.44 (* end of lemma zenon_L1912_ *) % 22.32/22.44 assert (zenon_L1913_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (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) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((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)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H236 zenon_H13d zenon_He7 zenon_H109 zenon_H141 zenon_H4e zenon_H1d8 zenon_H196 zenon_Hf5 zenon_H162 zenon_H19a zenon_H117 zenon_H6f zenon_H131 zenon_H164 zenon_H177 zenon_H173 zenon_H179 zenon_H13c zenon_H201 zenon_H190 zenon_H23c zenon_H1fe zenon_H1f zenon_H13a zenon_H33 zenon_H9d zenon_Hfa zenon_H5d zenon_H3c zenon_H189 zenon_H163 zenon_H195 zenon_H13f zenon_Hf0 zenon_H111 zenon_He4 zenon_Hb6 zenon_Ha0 zenon_H139 zenon_Ha9 zenon_H68 zenon_H24 zenon_H15d zenon_H12e zenon_H77 zenon_H93 zenon_H1b4 zenon_H20f zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H160 zenon_H1c7. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.44 exact (zenon_H1f zenon_H1e). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.44 apply (zenon_L272_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.44 exact (zenon_H1f zenon_H1e). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.44 apply (zenon_L25_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.44 apply (zenon_L1475_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.44 apply (zenon_L245_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.44 apply (zenon_L55_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.44 apply (zenon_L68_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.32/22.44 apply (zenon_L24_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.44 apply (zenon_L46_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.44 apply (zenon_L738_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.44 apply (zenon_L14_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.44 apply (zenon_L707_); trivial. % 22.32/22.44 apply (zenon_L367_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.32/22.44 apply (zenon_L1908_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.32/22.44 apply (zenon_L808_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.32/22.44 apply (zenon_L406_); trivial. % 22.32/22.44 exact (zenon_H162 zenon_H167). % 22.32/22.44 apply (zenon_L262_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.32/22.44 apply (zenon_L227_); trivial. % 22.32/22.44 apply (zenon_L228_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.44 apply (zenon_L239_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.44 apply (zenon_L245_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.32/22.44 apply (zenon_L55_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.32/22.44 apply (zenon_L492_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.44 apply (zenon_L239_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.44 apply (zenon_L1909_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.44 apply (zenon_L143_); trivial. % 22.32/22.44 apply (zenon_L367_); trivial. % 22.32/22.44 apply (zenon_L1910_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.44 apply (zenon_L68_); trivial. % 22.32/22.44 apply (zenon_L115_); trivial. % 22.32/22.44 apply (zenon_L1072_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.44 exact (zenon_H1f zenon_H1e). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.44 apply (zenon_L25_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.44 apply (zenon_L1912_); trivial. % 22.32/22.44 apply (zenon_L1510_); trivial. % 22.32/22.44 (* end of lemma zenon_L1913_ *) % 22.32/22.44 assert (zenon_L1914_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (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 (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((e1) = (e2))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H82 zenon_H4c zenon_H23c zenon_H1c6 zenon_Hb6 zenon_H16b zenon_Ha9 zenon_H2d zenon_H16a zenon_H125 zenon_H177 zenon_Ha0 zenon_H48 zenon_H164 zenon_H8b zenon_H4e zenon_H31 zenon_H1cf zenon_H1bf zenon_H3f zenon_H156 zenon_H3d zenon_H1d8 zenon_H201 zenon_H68 zenon_H2f zenon_H77. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.44 exact (zenon_H4c zenon_H47). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.44 apply (zenon_L492_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.44 apply (zenon_L217_); trivial. % 22.32/22.44 apply (zenon_L742_); trivial. % 22.32/22.44 (* end of lemma zenon_L1914_ *) % 22.32/22.44 assert (zenon_L1915_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H15d zenon_H2f zenon_H201 zenon_H1d8 zenon_H156 zenon_H1bf zenon_H1cf zenon_H4e zenon_H8b zenon_H125 zenon_H82 zenon_H4c zenon_H3f zenon_H23c zenon_H2d zenon_H139 zenon_H177 zenon_Ha0 zenon_Hac zenon_H48 zenon_H164 zenon_H6f zenon_H6d zenon_H68 zenon_H31 zenon_H77. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.44 exact (zenon_H4c zenon_H47). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.44 exact (zenon_H4c zenon_H47). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.44 apply (zenon_L492_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.44 apply (zenon_L217_); trivial. % 22.32/22.44 apply (zenon_L741_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.44 apply (zenon_L239_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.44 exact (zenon_H4c zenon_H47). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.44 apply (zenon_L492_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.44 apply (zenon_L217_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.44 apply (zenon_L718_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.44 apply (zenon_L21_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.44 apply (zenon_L264_); trivial. % 22.32/22.44 apply (zenon_L98_); trivial. % 22.32/22.44 (* end of lemma zenon_L1915_ *) % 22.32/22.44 assert (zenon_L1916_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 22.32/22.44 do 0 intro. intros zenon_H201 zenon_H48 zenon_H1cb zenon_H17c zenon_H8b zenon_H77 zenon_H31 zenon_H68 zenon_H1cf zenon_H1bf zenon_Hb6 zenon_Hbb. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.44 apply (zenon_L239_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.44 apply (zenon_L781_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.44 exact (zenon_H1bf zenon_H105). % 22.32/22.44 apply (zenon_L363_); trivial. % 22.32/22.44 (* end of lemma zenon_L1916_ *) % 22.32/22.44 assert (zenon_L1917_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((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 (e2) (e2)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 22.32/22.44 do 0 intro. intros zenon_H121 zenon_H6d zenon_H6f zenon_H164 zenon_Ha0 zenon_H177 zenon_H139 zenon_H2d zenon_H23c zenon_H3f zenon_H4c zenon_H82 zenon_H125 zenon_H4e zenon_H156 zenon_H1d8 zenon_H2f zenon_H15d zenon_Hb6 zenon_H1bf zenon_H1cf zenon_H68 zenon_H31 zenon_H77 zenon_H8b zenon_H1cb zenon_H48 zenon_H201 zenon_Ha9 zenon_H17c. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 22.32/22.44 apply (zenon_L586_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 22.32/22.44 apply (zenon_L1915_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 22.32/22.44 apply (zenon_L1916_); trivial. % 22.32/22.44 apply (zenon_L133_); trivial. % 22.32/22.44 (* end of lemma zenon_L1917_ *) % 22.32/22.44 assert (zenon_L1918_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((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 (e2) (e2)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H1c3 zenon_H155 zenon_H106 zenon_H186 zenon_H16b zenon_H121 zenon_H6d zenon_H6f zenon_H164 zenon_Ha0 zenon_H177 zenon_H139 zenon_H2d zenon_H23c zenon_H3f zenon_H4c zenon_H82 zenon_H125 zenon_H4e zenon_H156 zenon_H1d8 zenon_H2f zenon_H15d zenon_Hb6 zenon_H1bf zenon_H1cf zenon_H68 zenon_H31 zenon_H77 zenon_H8b zenon_H1cb zenon_H48 zenon_H201 zenon_Ha9. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 22.32/22.44 apply (zenon_L98_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 22.32/22.44 apply (zenon_L750_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 22.32/22.44 exact (zenon_H16b zenon_H93). % 22.32/22.44 apply (zenon_L1917_); trivial. % 22.32/22.44 (* end of lemma zenon_L1918_ *) % 22.32/22.44 assert (zenon_L1919_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (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)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (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) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H16a zenon_H2c zenon_H67 zenon_Ha9 zenon_H201 zenon_H48 zenon_H1cb zenon_H77 zenon_H31 zenon_H68 zenon_H1cf zenon_H1bf zenon_Hb6 zenon_H15d zenon_H2f zenon_H1d8 zenon_H156 zenon_H4e zenon_H125 zenon_H82 zenon_H4c zenon_H3f zenon_H23c zenon_H2d zenon_H139 zenon_H177 zenon_Ha0 zenon_H164 zenon_H6f zenon_H121 zenon_H186 zenon_H106 zenon_H155 zenon_H1c3 zenon_H8b zenon_H16b. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.44 apply (zenon_L180_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.44 apply (zenon_L1918_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.44 exact (zenon_H8b zenon_H8a). % 22.32/22.44 exact (zenon_H16b zenon_H93). % 22.32/22.44 (* end of lemma zenon_L1919_ *) % 22.32/22.44 assert (zenon_L1920_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((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) (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))))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H92 zenon_H1ef zenon_H13e zenon_H4c zenon_H82 zenon_Hb6 zenon_H16a zenon_H8b zenon_Ha9 zenon_H68 zenon_H125 zenon_H2f zenon_H1d8 zenon_H156 zenon_H1bf zenon_H1cf zenon_H77 zenon_H4e zenon_H201 zenon_Ha0 zenon_H177 zenon_H31 zenon_H164 zenon_H1c6 zenon_H2d zenon_H48 zenon_H3f zenon_H23c zenon_Hac zenon_H13a zenon_H183 zenon_H139 zenon_H15d. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.44 exact (zenon_H4c zenon_H47). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.44 apply (zenon_L1914_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.44 apply (zenon_L239_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.44 exact (zenon_H4c zenon_H47). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.44 apply (zenon_L492_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.44 apply (zenon_L217_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.44 apply (zenon_L718_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.44 apply (zenon_L239_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.44 apply (zenon_L486_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.44 exact (zenon_H1bf zenon_H105). % 22.32/22.44 apply (zenon_L514_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.44 apply (zenon_L110_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.44 apply (zenon_L68_); trivial. % 22.32/22.44 apply (zenon_L115_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.44 apply (zenon_L264_); trivial. % 22.32/22.44 apply (zenon_L98_); trivial. % 22.32/22.44 apply (zenon_L644_); trivial. % 22.32/22.44 (* end of lemma zenon_L1920_ *) % 22.32/22.44 assert (zenon_L1921_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (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)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H82 zenon_H4c zenon_H23c zenon_H38 zenon_H196 zenon_H117 zenon_Ha9 zenon_H6d zenon_Ha0 zenon_H18d zenon_H234 zenon_H3f zenon_Hb6 zenon_H120 zenon_H68 zenon_H141 zenon_H34 zenon_H48. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.44 exact (zenon_H4c zenon_H47). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.44 apply (zenon_L492_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.44 apply (zenon_L1647_); trivial. % 22.32/22.44 apply (zenon_L456_); trivial. % 22.32/22.44 (* end of lemma zenon_L1921_ *) % 22.32/22.44 assert (zenon_L1922_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (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)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H36 zenon_H82 zenon_H4c zenon_H23c zenon_H196 zenon_H117 zenon_Ha9 zenon_H6d zenon_Ha0 zenon_H18d zenon_H234 zenon_H3f zenon_Hb6 zenon_H120 zenon_H68 zenon_H141 zenon_H48. % 22.32/22.44 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.32/22.44 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.32/22.44 apply (zenon_L1921_); trivial. % 22.32/22.44 (* end of lemma zenon_L1922_ *) % 22.32/22.44 assert (zenon_L1923_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.32/22.44 do 0 intro. intros zenon_H1a8 zenon_H3d zenon_H77 zenon_H48 zenon_H141 zenon_H68 zenon_H120 zenon_Hb6 zenon_H3f zenon_H234 zenon_H18d zenon_Ha0 zenon_H117 zenon_H196 zenon_H23c zenon_H4c zenon_H82 zenon_H36 zenon_Ha9 zenon_Hac. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.32/22.44 apply (zenon_L214_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.32/22.44 apply (zenon_L186_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.32/22.44 apply (zenon_L1922_); trivial. % 22.32/22.44 apply (zenon_L371_); trivial. % 22.32/22.44 (* end of lemma zenon_L1923_ *) % 22.32/22.44 assert (zenon_L1924_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (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) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((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 (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (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))))) -> (~((e2) = (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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (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))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (e0))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H23b zenon_H4c zenon_H66 zenon_H1f zenon_H264 zenon_H230 zenon_H109 zenon_H1d5 zenon_Hf5 zenon_H6f zenon_H1c3 zenon_H189 zenon_H1cf zenon_H16a zenon_H13b zenon_H173 zenon_H25e zenon_H25b zenon_H94 zenon_Hb2 zenon_H19a zenon_H18d zenon_H1b4 zenon_H20f zenon_H1b7 zenon_H179 zenon_H24e zenon_H125 zenon_H1ef zenon_H186 zenon_H1a2 zenon_Hcc zenon_H1cd zenon_H1cb zenon_H19d zenon_H195 zenon_H12e zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H1bb zenon_Hfa zenon_H13c zenon_H55 zenon_H1a8 zenon_H23d zenon_H11a zenon_H1fe zenon_H1c6 zenon_H13e zenon_H111 zenon_H140 zenon_H68 zenon_H13f zenon_H156 zenon_H117 zenon_Hb6 zenon_H4e zenon_H163 zenon_H73 zenon_H131 zenon_H1ec zenon_Ha9 zenon_H201 zenon_H82 zenon_H139 zenon_H13a zenon_H2c zenon_H236 zenon_H15d zenon_H23c zenon_H183 zenon_H196 zenon_H33 zenon_H129 zenon_H121 zenon_H190 zenon_H177 zenon_He4 zenon_H192 zenon_H104 zenon_H164 zenon_H141 zenon_Ha0 zenon_H77 zenon_H234 zenon_Hf0 zenon_H48 zenon_H1fb zenon_H1d8 zenon_H3f zenon_H237. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.44 exact (zenon_H1f zenon_H1e). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.44 apply (zenon_L699_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.44 exact (zenon_H237 zenon_H31). % 22.32/22.44 exact (zenon_H238 zenon_H38). % 22.32/22.44 apply (zenon_L601_); trivial. % 22.32/22.44 (* end of lemma zenon_L1924_ *) % 22.32/22.44 assert (zenon_L1925_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (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))))) -> (~((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 (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (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) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (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 (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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 (e1) (e2)) = (op (e1) (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) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (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)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H240 zenon_H65 zenon_Hac zenon_H1bf zenon_H3f zenon_H1d8 zenon_H1fb zenon_H48 zenon_Hf0 zenon_H234 zenon_H77 zenon_Ha0 zenon_H141 zenon_H164 zenon_H104 zenon_H192 zenon_He4 zenon_H177 zenon_H190 zenon_H121 zenon_H129 zenon_H33 zenon_H196 zenon_H183 zenon_H23c zenon_H15d zenon_H236 zenon_H2c zenon_H13a zenon_H139 zenon_H82 zenon_H201 zenon_Ha9 zenon_H1ec zenon_H131 zenon_H73 zenon_H163 zenon_H4e zenon_Hb6 zenon_H117 zenon_H156 zenon_H13f zenon_H68 zenon_H140 zenon_H111 zenon_H13e zenon_H1c6 zenon_H1fe zenon_H11a zenon_H23d zenon_H1a8 zenon_H55 zenon_H13c zenon_Hfa zenon_H1bb zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H12e zenon_H195 zenon_H19d zenon_H1cb zenon_H1cd zenon_Hcc zenon_H1a2 zenon_H186 zenon_H1ef zenon_H125 zenon_H24e zenon_H179 zenon_H1b7 zenon_H20f zenon_H1b4 zenon_H18d zenon_H19a zenon_Hb2 zenon_H94 zenon_H25b zenon_H25e zenon_H173 zenon_H13b zenon_H16a zenon_H1cf zenon_H189 zenon_H1c3 zenon_H6f zenon_Hf5 zenon_H1d5 zenon_H109 zenon_H230 zenon_H264 zenon_H1f zenon_H66 zenon_H4c zenon_H23b. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.44 apply (zenon_L1924_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.44 exact (zenon_H1f zenon_H1e). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.44 apply (zenon_L520_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.44 apply (zenon_L264_); trivial. % 22.32/22.44 exact (zenon_H238 zenon_H38). % 22.32/22.44 apply (zenon_L1861_); trivial. % 22.32/22.44 (* end of lemma zenon_L1925_ *) % 22.32/22.44 assert (zenon_L1926_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((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 (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)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H13a zenon_Ha0 zenon_Ha9 zenon_H6e zenon_H1bf zenon_Hf0 zenon_H201 zenon_H196 zenon_H177 zenon_He4 zenon_H156 zenon_H55 zenon_H1bb zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H129 zenon_Hc4 zenon_H1e zenon_H68 zenon_H139 zenon_H160 zenon_H13f zenon_H18d zenon_Hb6 zenon_H234 zenon_H3f zenon_H93 zenon_H77 zenon_H120. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.44 apply (zenon_L41_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.44 apply (zenon_L110_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.44 apply (zenon_L95_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.44 apply (zenon_L857_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.44 exact (zenon_H1bf zenon_H105). % 22.32/22.44 apply (zenon_L367_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.32/22.44 apply (zenon_L118_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.32/22.44 exact (zenon_H1bf zenon_H105). % 22.32/22.44 apply (zenon_L218_); trivial. % 22.32/22.44 apply (zenon_L540_); trivial. % 22.32/22.44 (* end of lemma zenon_L1926_ *) % 22.32/22.44 assert (zenon_L1927_ : (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H120 zenon_H77 zenon_H3f zenon_H234 zenon_Hb6 zenon_H18d zenon_H13f zenon_H139 zenon_H68 zenon_H1e zenon_Hc4 zenon_H129 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H55 zenon_H156 zenon_He4 zenon_H201 zenon_Hf0 zenon_H1bf zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.44 apply (zenon_L20_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.44 apply (zenon_L1926_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.44 apply (zenon_L122_); trivial. % 22.32/22.44 apply (zenon_L167_); trivial. % 22.32/22.44 (* end of lemma zenon_L1927_ *) % 22.32/22.44 assert (zenon_L1928_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 22.32/22.44 do 0 intro. intros zenon_H13a zenon_H1e zenon_Ha9 zenon_H6e zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H155. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.44 apply (zenon_L41_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.44 apply (zenon_L110_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.44 apply (zenon_L68_); trivial. % 22.32/22.44 apply (zenon_L115_); trivial. % 22.32/22.44 (* end of lemma zenon_L1928_ *) % 22.32/22.44 assert (zenon_L1929_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H15d zenon_H4c zenon_H177 zenon_H160 zenon_H77 zenon_H48 zenon_H139 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H1e zenon_H13a zenon_H68 zenon_H31 zenon_H93 zenon_H196. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.44 exact (zenon_H4c zenon_H47). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.44 apply (zenon_L215_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.44 apply (zenon_L239_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.44 apply (zenon_L20_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.44 apply (zenon_L1928_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.44 apply (zenon_L264_); trivial. % 22.32/22.44 apply (zenon_L167_); trivial. % 22.32/22.44 (* end of lemma zenon_L1929_ *) % 22.32/22.44 assert (zenon_L1930_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((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 (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (e3))) -> False). % 22.32/22.44 do 0 intro. intros zenon_Hb2 zenon_H120 zenon_H77 zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H67 zenon_H12e zenon_H177 zenon_H31 zenon_H19a zenon_H195 zenon_H163 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_Hfa zenon_H93 zenon_H68 zenon_H1b7 zenon_H179 zenon_H164 zenon_H201 zenon_H1bf zenon_H121 zenon_H33 zenon_H11a zenon_H1a3 zenon_H13c zenon_Ha0 zenon_H25 zenon_Hb6 zenon_H54 zenon_H209. % 22.32/22.44 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.44 apply (zenon_L116_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.44 apply (zenon_L538_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.44 apply (zenon_L239_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.44 apply (zenon_L124_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.44 exact (zenon_H1bf zenon_H105). % 22.32/22.44 apply (zenon_L367_); trivial. % 22.32/22.44 apply (zenon_L862_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.32/22.44 apply (zenon_L116_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.32/22.44 apply (zenon_L151_); trivial. % 22.32/22.44 exact (zenon_H209 zenon_H9d). % 22.32/22.44 (* end of lemma zenon_L1930_ *) % 22.32/22.44 assert (zenon_L1931_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((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)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H139 zenon_H7e zenon_H177 zenon_H121 zenon_H209 zenon_Ha0 zenon_H1a3 zenon_Hc4 zenon_H48 zenon_H164 zenon_H77 zenon_H3d zenon_H68 zenon_H31 zenon_H93 zenon_H196. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.44 apply (zenon_L548_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.44 apply (zenon_L214_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.44 apply (zenon_L264_); trivial. % 22.32/22.44 apply (zenon_L167_); trivial. % 22.32/22.44 (* end of lemma zenon_L1931_ *) % 22.32/22.44 assert (zenon_L1932_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (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 (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((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)) = (e0)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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 (e3) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H82 zenon_H4c zenon_H3f zenon_H23c zenon_H160 zenon_Hb2 zenon_H120 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H12e zenon_H19a zenon_H195 zenon_H163 zenon_H18d zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_Hfa zenon_H1b7 zenon_H179 zenon_H201 zenon_H1bf zenon_H33 zenon_H11a zenon_H13c zenon_H25 zenon_Hb6 zenon_H139 zenon_H177 zenon_H121 zenon_H209 zenon_Ha0 zenon_H1a3 zenon_Hc4 zenon_H48 zenon_H164 zenon_H77 zenon_H3d zenon_H68 zenon_H31 zenon_H93 zenon_H196. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.44 exact (zenon_H4c zenon_H47). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.44 apply (zenon_L492_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.44 apply (zenon_L1930_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.44 apply (zenon_L214_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.44 apply (zenon_L122_); trivial. % 22.32/22.44 apply (zenon_L167_); trivial. % 22.32/22.44 apply (zenon_L1931_); trivial. % 22.32/22.44 (* end of lemma zenon_L1932_ *) % 22.32/22.44 assert (zenon_L1933_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H139 zenon_H209 zenon_H54 zenon_Hb6 zenon_Ha0 zenon_H13c zenon_H1a3 zenon_H11a zenon_H33 zenon_H121 zenon_H1bf zenon_H201 zenon_H164 zenon_H179 zenon_H1b7 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H19a zenon_H177 zenon_H12e zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H120 zenon_Hb2 zenon_H195 zenon_H93 zenon_H163 zenon_H160 zenon_H173 zenon_H25 zenon_Hfa zenon_H68 zenon_H31 zenon_H155 zenon_H77. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.44 apply (zenon_L1930_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.44 apply (zenon_L229_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.44 apply (zenon_L264_); trivial. % 22.32/22.44 apply (zenon_L98_); trivial. % 22.32/22.44 (* end of lemma zenon_L1933_ *) % 22.32/22.44 assert (zenon_L1934_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H125 zenon_H7e zenon_H177 zenon_H31 zenon_Ha0 zenon_Hac zenon_H48 zenon_H164 zenon_H68 zenon_H25 zenon_H94 zenon_H93 zenon_H160 zenon_Hbc. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.32/22.44 apply (zenon_L718_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.32/22.44 apply (zenon_L171_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.32/22.44 apply (zenon_L38_); trivial. % 22.32/22.44 apply (zenon_L104_); trivial. % 22.32/22.44 (* end of lemma zenon_L1934_ *) % 22.32/22.44 assert (zenon_L1935_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (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 (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (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 (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (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) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H236 zenon_He4 zenon_H55 zenon_H186 zenon_H156 zenon_H4e zenon_H1ec zenon_H1d8 zenon_H234 zenon_H73 zenon_H140 zenon_H13e zenon_H104 zenon_H99 zenon_H131 zenon_H19d zenon_H160 zenon_H11a zenon_H3f zenon_H12e zenon_H13f zenon_Hf0 zenon_H1bf zenon_H15d zenon_H196 zenon_H23c zenon_H82 zenon_H4c zenon_Hfa zenon_H173 zenon_H163 zenon_H195 zenon_Hb2 zenon_H212 zenon_H18a zenon_H7d zenon_H19a zenon_H1b7 zenon_H179 zenon_H201 zenon_H121 zenon_H33 zenon_H1a3 zenon_H13c zenon_Hb6 zenon_H209 zenon_H139 zenon_H125 zenon_H177 zenon_Ha0 zenon_Hac zenon_H164 zenon_H68 zenon_H94 zenon_Hbc zenon_Ha9 zenon_H13a zenon_H1fe zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H120. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.44 apply (zenon_L1927_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.44 apply (zenon_L554_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.44 apply (zenon_L1929_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.44 exact (zenon_H4c zenon_H47). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.44 apply (zenon_L1932_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.44 apply (zenon_L239_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.44 exact (zenon_H4c zenon_H47). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.44 apply (zenon_L25_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.44 apply (zenon_L1933_); trivial. % 22.32/22.44 apply (zenon_L1934_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.44 apply (zenon_L526_); trivial. % 22.32/22.44 apply (zenon_L553_); trivial. % 22.32/22.44 apply (zenon_L555_); trivial. % 22.32/22.44 (* end of lemma zenon_L1935_ *) % 22.32/22.44 assert (zenon_L1936_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H19a zenon_H93 zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H20f zenon_H1bb zenon_Hb9 zenon_Ha0 zenon_H12e zenon_H67 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H160 zenon_H77 zenon_H120. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.32/22.44 apply (zenon_L555_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.32/22.44 apply (zenon_L422_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.32/22.44 apply (zenon_L77_); trivial. % 22.32/22.44 apply (zenon_L558_); trivial. % 22.32/22.44 (* end of lemma zenon_L1936_ *) % 22.32/22.44 assert (zenon_L1937_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((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)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H141 zenon_H3f zenon_Hf0 zenon_H93 zenon_H77 zenon_H1bf zenon_H48 zenon_H117 zenon_Hb6 zenon_H131 zenon_H19a zenon_H1b4 zenon_H18d zenon_H20f zenon_Ha0 zenon_H12e zenon_H67 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H160 zenon_H13f zenon_Hef zenon_H133 zenon_H1bb zenon_H129 zenon_H120 zenon_H181 zenon_Hc4. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.32/22.44 apply (zenon_L526_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.32/22.44 apply (zenon_L151_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.32/22.44 apply (zenon_L152_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.32/22.44 apply (zenon_L259_); trivial. % 22.32/22.44 apply (zenon_L1936_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.32/22.44 apply (zenon_L111_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.32/22.44 exact (zenon_H1bf zenon_H105). % 22.32/22.44 apply (zenon_L218_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.32/22.44 apply (zenon_L265_); trivial. % 22.32/22.44 apply (zenon_L415_); trivial. % 22.32/22.44 (* end of lemma zenon_L1937_ *) % 22.32/22.44 assert (zenon_L1938_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((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)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.44 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H186 zenon_H3f zenon_H156 zenon_H4e zenon_H25 zenon_H1ec zenon_H141 zenon_Hf0 zenon_H77 zenon_H1bf zenon_H48 zenon_H117 zenon_Hb6 zenon_H131 zenon_H19a zenon_H1b4 zenon_H18d zenon_H20f zenon_Ha0 zenon_H12e zenon_H67 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H13f zenon_H1bb zenon_H129 zenon_H120 zenon_H181 zenon_Hc4 zenon_Hac zenon_H11a zenon_H13c zenon_H160 zenon_H163 zenon_H93 zenon_H195. % 22.32/22.44 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.32/22.44 apply (zenon_L171_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.44 apply (zenon_L116_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.44 apply (zenon_L79_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.44 apply (zenon_L1937_); trivial. % 22.32/22.44 apply (zenon_L525_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.32/22.44 apply (zenon_L227_); trivial. % 22.32/22.44 apply (zenon_L228_); trivial. % 22.32/22.44 (* end of lemma zenon_L1938_ *) % 22.32/22.44 assert (zenon_L1939_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((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))))) -> (~((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)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (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) (e3)) = (op (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 (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H1fe zenon_H19d zenon_H177 zenon_H2a zenon_H68 zenon_Hfa zenon_H186 zenon_H156 zenon_H4e zenon_H1ec zenon_H141 zenon_H117 zenon_Hb6 zenon_H131 zenon_H19a zenon_H1b4 zenon_H18d zenon_H20f zenon_Ha0 zenon_H181 zenon_Hac zenon_H11a zenon_H13c zenon_H163 zenon_H195 zenon_H139 zenon_H196 zenon_H125 zenon_H94 zenon_H15d zenon_H1bf zenon_H3f zenon_Hf0 zenon_H13f zenon_H12e zenon_H48 zenon_Hc4 zenon_H93 zenon_H129 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H160 zenon_H77 zenon_H120. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.44 apply (zenon_L161_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.44 apply (zenon_L541_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.44 apply (zenon_L65_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.44 apply (zenon_L1938_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.44 apply (zenon_L147_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.44 apply (zenon_L94_); trivial. % 22.32/22.44 apply (zenon_L167_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.44 apply (zenon_L1938_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.44 apply (zenon_L147_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.44 apply (zenon_L122_); trivial. % 22.32/22.44 apply (zenon_L98_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.44 apply (zenon_L526_); trivial. % 22.32/22.44 apply (zenon_L528_); trivial. % 22.32/22.44 (* end of lemma zenon_L1939_ *) % 22.32/22.44 assert (zenon_L1940_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H19a zenon_H26d zenon_H31 zenon_H20f zenon_Hc4 zenon_H181 zenon_H120 zenon_H129 zenon_H1bb zenon_H34 zenon_H18a. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.32/22.44 apply (zenon_L756_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.32/22.44 apply (zenon_L422_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.32/22.44 apply (zenon_L415_); trivial. % 22.32/22.44 apply (zenon_L416_); trivial. % 22.32/22.44 (* end of lemma zenon_L1940_ *) % 22.32/22.44 assert (zenon_L1941_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((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))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (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))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.32/22.44 do 0 intro. intros zenon_H236 zenon_H201 zenon_He4 zenon_H55 zenon_H234 zenon_H19d zenon_H18a zenon_H181 zenon_H26d zenon_H19a zenon_H13f zenon_Hf0 zenon_H3f zenon_H1bf zenon_H82 zenon_H4c zenon_Hfa zenon_H186 zenon_H156 zenon_H4e zenon_H1ec zenon_H141 zenon_H117 zenon_Hb6 zenon_H131 zenon_H12e zenon_H209 zenon_H7d zenon_H212 zenon_H11a zenon_H13c zenon_H163 zenon_H195 zenon_H125 zenon_H177 zenon_Ha0 zenon_Hac zenon_H164 zenon_H68 zenon_H94 zenon_H160 zenon_Hbc zenon_H15d zenon_H139 zenon_Ha9 zenon_H13a zenon_H196 zenon_H1fe zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H120. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.44 apply (zenon_L1927_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.44 apply (zenon_L1939_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.44 apply (zenon_L1929_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.44 exact (zenon_H4c zenon_H47). % 22.32/22.44 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.44 apply (zenon_L25_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.32/22.44 apply (zenon_L1938_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.32/22.44 apply (zenon_L171_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.32/22.44 apply (zenon_L30_); trivial. % 22.32/22.44 apply (zenon_L104_); trivial. % 22.32/22.44 apply (zenon_L1934_); trivial. % 22.32/22.44 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.44 apply (zenon_L526_); trivial. % 22.32/22.44 apply (zenon_L1940_); trivial. % 22.32/22.44 apply (zenon_L555_); trivial. % 22.32/22.44 (* end of lemma zenon_L1941_ *) % 22.32/22.44 assert (zenon_L1942_ : (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((e0) = (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)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (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) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (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))))) -> (~((op (e0) (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.32/22.45 do 0 intro. intros zenon_H1fb zenon_H192 zenon_H190 zenon_H183 zenon_H2c zenon_H111 zenon_H1c6 zenon_H23d zenon_H1a8 zenon_Hcc zenon_H1a2 zenon_H1ef zenon_H24e zenon_H25b zenon_H25e zenon_H13b zenon_H16a zenon_H1cf zenon_H189 zenon_H1c3 zenon_H6f zenon_Hf5 zenon_H1d5 zenon_H109 zenon_H230 zenon_H264 zenon_Ha0 zenon_Ha9 zenon_H13f zenon_Hf0 zenon_Hb6 zenon_H139 zenon_H196 zenon_H177 zenon_H77 zenon_H156 zenon_H55 zenon_H1bb zenon_H129 zenon_H18a zenon_Hbc zenon_H212 zenon_He4 zenon_H1bf zenon_H201 zenon_H18d zenon_H234 zenon_H13a zenon_H68 zenon_H1fe zenon_H12e zenon_H48 zenon_H13c zenon_H4e zenon_H163 zenon_H186 zenon_H1ec zenon_H1d8 zenon_H13e zenon_H131 zenon_H104 zenon_H140 zenon_H33 zenon_H11a zenon_H121 zenon_H195 zenon_Hfa zenon_H82 zenon_H19a zenon_H164 zenon_Hb2 zenon_H73 zenon_H94 zenon_H125 zenon_H15d zenon_H19d zenon_H20f zenon_H1b4 zenon_H1b7 zenon_H179 zenon_H23c zenon_H173 zenon_H4c zenon_H236 zenon_H117 zenon_H141 zenon_H26d zenon_H1cb zenon_H7d zenon_H3f zenon_H1cd zenon_Hac. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.32/22.45 apply (zenon_L2_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.32/22.45 apply (zenon_L482_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.32/22.45 apply (zenon_L1920_); trivial. % 22.32/22.45 apply (zenon_L1920_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.32/22.45 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.32/22.45 exact (zenon_H1c7 zenon_Hac). % 22.32/22.45 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.45 exact (zenon_H4c zenon_H47). % 22.32/22.45 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.45 apply (zenon_L1923_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.45 apply (zenon_L1648_); trivial. % 22.32/22.45 apply (zenon_L246_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.32/22.45 apply (zenon_L513_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.32/22.45 apply (zenon_L11_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.32/22.45 apply (zenon_L483_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.32/22.45 apply (zenon_L485_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.32/22.45 apply (zenon_L1925_); trivial. % 22.32/22.45 apply (zenon_L1925_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.32/22.45 apply (zenon_L522_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.32/22.45 apply (zenon_L37_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.32/22.45 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.32/22.45 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.32/22.45 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.32/22.45 exact (zenon_H1c7 zenon_Hac). % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.32/22.45 apply (zenon_L1935_); trivial. % 22.32/22.45 apply (zenon_L1935_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.32/22.45 apply (zenon_L1941_); trivial. % 22.32/22.45 apply (zenon_L1941_); trivial. % 22.32/22.45 apply (zenon_L530_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.32/22.45 apply (zenon_L387_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.32/22.45 apply (zenon_L531_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.32/22.45 apply (zenon_L388_); trivial. % 22.32/22.45 apply (zenon_L51_); trivial. % 22.32/22.45 (* end of lemma zenon_L1942_ *) % 22.32/22.45 assert (zenon_L1943_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((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)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (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) (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 (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e2))) -> False). % 22.32/22.45 do 0 intro. intros zenon_H2f zenon_H1cd zenon_H3f zenon_H7d zenon_H1cb zenon_H26d zenon_H141 zenon_H117 zenon_H236 zenon_H4c zenon_H173 zenon_H23c zenon_H179 zenon_H1b7 zenon_H1b4 zenon_H20f zenon_H19d zenon_H15d zenon_H125 zenon_H94 zenon_H73 zenon_Hb2 zenon_H164 zenon_H19a zenon_H82 zenon_Hfa zenon_H195 zenon_H121 zenon_H11a zenon_H33 zenon_H140 zenon_H104 zenon_H131 zenon_H13e zenon_H1d8 zenon_H1ec zenon_H186 zenon_H163 zenon_H4e zenon_H13c zenon_H48 zenon_H12e zenon_H1fe zenon_H13a zenon_H234 zenon_H18d zenon_H201 zenon_H1bf zenon_He4 zenon_H212 zenon_Hbc zenon_H18a zenon_H129 zenon_H1bb zenon_H55 zenon_H156 zenon_H177 zenon_H196 zenon_H139 zenon_Hb6 zenon_Hf0 zenon_H13f zenon_Ha9 zenon_Ha0 zenon_H264 zenon_H230 zenon_H109 zenon_H1d5 zenon_Hf5 zenon_H6f zenon_H1c3 zenon_H189 zenon_H1cf zenon_H16a zenon_H13b zenon_H25e zenon_H25b zenon_H24e zenon_H1ef zenon_H1a2 zenon_Hcc zenon_H1a8 zenon_H23d zenon_H1c6 zenon_H111 zenon_H2c zenon_H183 zenon_H190 zenon_H192 zenon_H1fb zenon_H2d zenon_H8b zenon_H16b zenon_H68 zenon_H31 zenon_H77. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.45 exact (zenon_H4c zenon_H47). % 22.32/22.45 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.45 apply (zenon_L1914_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.45 apply (zenon_L239_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.45 apply (zenon_L239_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.45 apply (zenon_L486_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.45 exact (zenon_H1bf zenon_H105). % 22.32/22.45 apply (zenon_L1919_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.32/22.45 apply (zenon_L110_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.32/22.45 apply (zenon_L216_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.32/22.45 apply (zenon_L715_); trivial. % 22.32/22.45 apply (zenon_L1942_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.45 apply (zenon_L264_); trivial. % 22.32/22.45 apply (zenon_L98_); trivial. % 22.32/22.45 (* end of lemma zenon_L1943_ *) % 22.32/22.45 assert (zenon_L1944_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((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 (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (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) (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 (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> False). % 22.32/22.45 do 0 intro. intros zenon_H92 zenon_H4c zenon_H82 zenon_Hb6 zenon_H16a zenon_H8b zenon_Ha9 zenon_H68 zenon_H125 zenon_H2f zenon_H1d8 zenon_H156 zenon_H1bf zenon_H1cf zenon_H77 zenon_H4e zenon_H201 zenon_Ha0 zenon_H177 zenon_H31 zenon_H164 zenon_H1c6 zenon_H2d zenon_H48 zenon_H3f zenon_H23c zenon_H26d zenon_H264 zenon_H230 zenon_H109 zenon_H1d5 zenon_Hf5 zenon_H189 zenon_H13b zenon_H173 zenon_H25e zenon_H25b zenon_H94 zenon_Hb2 zenon_H19a zenon_H1b4 zenon_H20f zenon_H1b7 zenon_H179 zenon_H24e zenon_H1a2 zenon_Hcc zenon_H1cd zenon_H19d zenon_H195 zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H1bb zenon_Hfa zenon_H13c zenon_H55 zenon_H23d zenon_H1fe zenon_H111 zenon_H140 zenon_H13f zenon_H163 zenon_H73 zenon_H131 zenon_H1ec zenon_H236 zenon_H33 zenon_H129 zenon_H190 zenon_He4 zenon_H192 zenon_H104 zenon_H1fb zenon_Hf0 zenon_H1a8 zenon_H117 zenon_H234 zenon_H18d zenon_H196 zenon_H141 zenon_H12e zenon_H11a zenon_H183 zenon_H13a zenon_H13e zenon_H1ef zenon_H186 zenon_H121 zenon_H1cb zenon_H6f zenon_H139 zenon_H15d zenon_H1c3 zenon_H2c. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.32/22.45 apply (zenon_L1943_); trivial. % 22.32/22.45 apply (zenon_L644_); trivial. % 22.32/22.45 (* end of lemma zenon_L1944_ *) % 22.32/22.45 assert (zenon_L1945_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (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 (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.32/22.45 do 0 intro. intros zenon_H13c zenon_H26a zenon_Ha0 zenon_H5d zenon_Hc4 zenon_Hb6 zenon_Hfe zenon_H73 zenon_H18d zenon_H48 zenon_H234 zenon_H3f zenon_H1b7 zenon_H171 zenon_H77 zenon_Ha9 zenon_H38 zenon_H68 zenon_H1c3 zenon_H120. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.45 apply (zenon_L1656_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.45 apply (zenon_L216_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.45 apply (zenon_L89_); trivial. % 22.32/22.45 apply (zenon_L1657_); trivial. % 22.32/22.45 (* end of lemma zenon_L1945_ *) % 22.32/22.45 assert (zenon_L1946_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (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 (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.32/22.45 do 0 intro. intros zenon_H1a8 zenon_H3d zenon_H141 zenon_H117 zenon_H196 zenon_H23c zenon_H4c zenon_H82 zenon_H36 zenon_H13c zenon_H26a zenon_Ha0 zenon_H5d zenon_Hc4 zenon_Hb6 zenon_Hfe zenon_H73 zenon_H18d zenon_H48 zenon_H234 zenon_H3f zenon_H1b7 zenon_H77 zenon_Ha9 zenon_H38 zenon_H68 zenon_H1c3 zenon_H120. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.32/22.45 apply (zenon_L214_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.32/22.45 apply (zenon_L186_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.32/22.45 apply (zenon_L1922_); trivial. % 22.32/22.45 apply (zenon_L1945_); trivial. % 22.32/22.45 (* end of lemma zenon_L1946_ *) % 22.32/22.45 assert (zenon_L1947_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (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). % 22.32/22.45 do 0 intro. intros zenon_H15d zenon_Ha0 zenon_H1a8 zenon_H141 zenon_H117 zenon_H196 zenon_H23c zenon_H4c zenon_H82 zenon_H36 zenon_H13c zenon_H26a zenon_H5d zenon_Hc4 zenon_Hb6 zenon_H73 zenon_H18d zenon_H234 zenon_H1b7 zenon_H77 zenon_Ha9 zenon_H68 zenon_H1c3 zenon_H1a3 zenon_H183 zenon_H20f zenon_H33 zenon_H121 zenon_H1bf zenon_H201 zenon_H13a zenon_H120 zenon_H177 zenon_H11a zenon_H3f zenon_H34 zenon_H12e zenon_H38 zenon_H48. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.45 exact (zenon_H4c zenon_H47). % 22.32/22.45 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.32/22.45 apply (zenon_L214_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.32/22.45 apply (zenon_L186_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.32/22.45 apply (zenon_L1922_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.45 apply (zenon_L1656_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.45 apply (zenon_L538_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.45 apply (zenon_L1648_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.45 apply (zenon_L124_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.45 exact (zenon_H1bf zenon_H105). % 22.32/22.45 apply (zenon_L1652_); trivial. % 22.32/22.45 apply (zenon_L1657_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.45 apply (zenon_L55_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.45 apply (zenon_L1946_); trivial. % 22.32/22.45 apply (zenon_L156_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.45 apply (zenon_L1648_); trivial. % 22.32/22.45 apply (zenon_L246_); trivial. % 22.32/22.45 (* end of lemma zenon_L1947_ *) % 22.32/22.45 assert (zenon_L1948_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 22.32/22.45 do 0 intro. intros zenon_Hc2 zenon_H4c zenon_H13a zenon_H73 zenon_H77 zenon_H3f zenon_H36 zenon_H23c zenon_H141 zenon_H196 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H18d zenon_H120 zenon_H234 zenon_H117 zenon_H68 zenon_H48 zenon_H82 zenon_H13c zenon_H12e zenon_H177 zenon_H34 zenon_H1bf zenon_H20f zenon_H183 zenon_H1b7 zenon_H1c3 zenon_H201 zenon_H33 zenon_H11a zenon_H1a3 zenon_H121 zenon_H38 zenon_H26a zenon_H5d zenon_H1a8 zenon_H15d. % 22.32/22.45 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.32/22.45 apply (zenon_L1947_); trivial. % 22.32/22.45 apply (zenon_L1947_); trivial. % 22.32/22.45 (* end of lemma zenon_L1948_ *) % 22.32/22.45 assert (zenon_L1949_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 22.32/22.45 do 0 intro. intros zenon_H1c6 zenon_H38 zenon_H196 zenon_H201 zenon_H1d8 zenon_H3d zenon_H133 zenon_H1bf zenon_H16a zenon_H2c zenon_H67 zenon_H3f zenon_H234 zenon_Ha0 zenon_H54 zenon_H117 zenon_Hcb zenon_H34 zenon_H183 zenon_H104 zenon_H68 zenon_Hb6 zenon_H120 zenon_H12e zenon_H181 zenon_H209 zenon_H121 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1cb zenon_H109 zenon_H141 zenon_Ha9 zenon_H171. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.32/22.45 apply (zenon_L55_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.32/22.45 apply (zenon_L216_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.32/22.45 apply (zenon_L359_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.32/22.45 apply (zenon_L152_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.45 apply (zenon_L738_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.45 apply (zenon_L124_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.45 exact (zenon_H1bf zenon_H105). % 22.32/22.45 apply (zenon_L1682_); trivial. % 22.32/22.45 apply (zenon_L1162_); trivial. % 22.32/22.45 apply (zenon_L371_); trivial. % 22.32/22.45 (* end of lemma zenon_L1949_ *) % 22.32/22.45 assert (zenon_L1950_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 22.32/22.45 do 0 intro. intros zenon_H92 zenon_H13e zenon_H1ef zenon_H89 zenon_H4c zenon_H82 zenon_Hb6 zenon_H16a zenon_H8b zenon_Ha9 zenon_H68 zenon_H125 zenon_H2f zenon_H1d8 zenon_H156 zenon_H1bf zenon_H1cf zenon_H77 zenon_H4e zenon_H201 zenon_Ha0 zenon_H177 zenon_H31 zenon_H164 zenon_H1c6 zenon_H2d zenon_H48 zenon_H3f zenon_H23c zenon_H186 zenon_H121 zenon_H1cb zenon_H6f zenon_H6d zenon_H139 zenon_H15d zenon_H1c3. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.45 exact (zenon_H4c zenon_H47). % 22.32/22.45 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.45 apply (zenon_L1914_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.45 apply (zenon_L239_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.45 apply (zenon_L239_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.45 apply (zenon_L486_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.45 exact (zenon_H1bf zenon_H105). % 22.32/22.45 apply (zenon_L1918_); trivial. % 22.32/22.45 apply (zenon_L645_); trivial. % 22.32/22.45 (* end of lemma zenon_L1950_ *) % 22.32/22.45 assert (zenon_L1951_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (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 (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 22.32/22.45 do 0 intro. intros zenon_H240 zenon_H1f zenon_H23b zenon_H23d zenon_H1bb zenon_H1b4 zenon_H1cb zenon_Hb2 zenon_H1ef zenon_H173 zenon_H183 zenon_H111 zenon_H13b zenon_H4e zenon_Hfa zenon_H179 zenon_H82 zenon_H1c6 zenon_H1d8 zenon_H1fb zenon_H55 zenon_H189 zenon_Hcc zenon_H131 zenon_H109 zenon_Ha0 zenon_H141 zenon_H9d zenon_H11a zenon_H18d zenon_Ha9 zenon_H1cf zenon_H77 zenon_H120 zenon_H12e zenon_H186 zenon_H1d5 zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H192 zenon_H1c3 zenon_H234 zenon_Hb6 zenon_H196 zenon_H9e zenon_H117 zenon_H48 zenon_Hf5 zenon_H13c zenon_H6d zenon_Hf0 zenon_H68 zenon_H236 zenon_H13a zenon_H33 zenon_H15d zenon_H139 zenon_H3f zenon_H23c zenon_H4c zenon_H140 zenon_Hbc zenon_H6f zenon_H1fe. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.45 exact (zenon_H1f zenon_H1e). % 22.32/22.45 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.45 apply (zenon_L610_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.45 exact (zenon_H237 zenon_H31). % 22.32/22.45 apply (zenon_L156_); trivial. % 22.32/22.45 apply (zenon_L611_); trivial. % 22.32/22.45 (* end of lemma zenon_L1951_ *) % 22.32/22.45 assert (zenon_L1952_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 22.32/22.45 do 0 intro. intros zenon_H201 zenon_H66 zenon_H77 zenon_H156 zenon_H3f zenon_H1bf zenon_Hb6 zenon_Hbb. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.45 apply (zenon_L94_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.45 apply (zenon_L486_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.45 exact (zenon_H1bf zenon_H105). % 22.32/22.45 apply (zenon_L363_); trivial. % 22.32/22.45 (* end of lemma zenon_L1952_ *) % 22.32/22.45 assert (zenon_L1953_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.32/22.45 do 0 intro. intros zenon_H139 zenon_H68 zenon_H1e zenon_H6f zenon_H6d zenon_Hbb zenon_Hb6 zenon_H1bf zenon_H3f zenon_H156 zenon_H201 zenon_H155 zenon_H77. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.45 apply (zenon_L20_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.45 apply (zenon_L21_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.45 apply (zenon_L1952_); trivial. % 22.32/22.45 apply (zenon_L98_); trivial. % 22.32/22.45 (* end of lemma zenon_L1953_ *) % 22.32/22.45 assert (zenon_L1954_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.32/22.45 do 0 intro. intros zenon_H18d zenon_H77 zenon_H201 zenon_H156 zenon_H1bf zenon_Hbb zenon_H6d zenon_H6f zenon_H1e zenon_H68 zenon_H139 zenon_H234 zenon_H3f zenon_Hb9 zenon_Hb6 zenon_H120. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.32/22.45 apply (zenon_L1953_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.32/22.45 apply (zenon_L484_); trivial. % 22.32/22.45 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.32/22.45 apply (zenon_L182_); trivial. % 22.32/22.45 exact (zenon_H120 zenon_H11f). % 22.32/22.45 (* end of lemma zenon_L1954_ *) % 22.32/22.45 assert (zenon_L1955_ : (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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)) = (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)) = (op (e3) (e2)))) -> (~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (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)) = (op (e2) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (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) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e2) (e1)) = (e2)) -> False). % 22.32/22.46 do 0 intro. intros zenon_H4c zenon_H18d zenon_H120 zenon_H234 zenon_H68 zenon_H6f zenon_H201 zenon_Hb6 zenon_H3f zenon_H156 zenon_H77 zenon_H139 zenon_H13a zenon_H196 zenon_H177 zenon_Ha0 zenon_H48 zenon_H1d8 zenon_H4e zenon_H25b zenon_H25e zenon_H19a zenon_H179 zenon_H173 zenon_H13b zenon_H183 zenon_H163 zenon_Hf0 zenon_Hfa zenon_H195 zenon_H16a zenon_H12e zenon_H11a zenon_H1cf zenon_H1c6 zenon_H1cd zenon_Ha9 zenon_H1bb zenon_H129 zenon_H20f zenon_H189 zenon_H1cb zenon_H1c3 zenon_H1a8 zenon_He4 zenon_H121 zenon_H164 zenon_H104 zenon_H73 zenon_H125 zenon_H13f zenon_H2c zenon_H13e zenon_H1fe zenon_Hbc zenon_H140 zenon_H23c zenon_H15d zenon_H33 zenon_H236 zenon_H13c zenon_Hf5 zenon_H117 zenon_H192 zenon_H1b7 zenon_H7d zenon_H24e zenon_H1d5 zenon_H186 zenon_H141 zenon_H109 zenon_H131 zenon_Hcc zenon_H82 zenon_H111 zenon_H1ef zenon_Hb2 zenon_H1b4 zenon_H23d zenon_H55 zenon_H1fb zenon_H230 zenon_H212 zenon_H1a2 zenon_H19d zenon_H6d. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.32/22.46 apply (zenon_L2_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.32/22.46 apply (zenon_L482_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.32/22.46 exact (zenon_H1ba zenon_H6d). % 22.32/22.46 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.32/22.46 apply (zenon_L1950_); trivial. % 22.32/22.46 apply (zenon_L1950_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.32/22.46 apply (zenon_L1922_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.32/22.46 apply (zenon_L513_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.32/22.46 apply (zenon_L11_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.32/22.46 apply (zenon_L483_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.32/22.46 apply (zenon_L485_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.32/22.46 apply (zenon_L435_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.32/22.46 apply (zenon_L522_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.32/22.46 apply (zenon_L37_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.32/22.46 apply (zenon_L458_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.32/22.46 apply (zenon_L1951_); trivial. % 22.32/22.46 apply (zenon_L1951_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.32/22.46 apply (zenon_L531_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.32/22.46 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.32/22.46 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.32/22.46 exact (zenon_H1ba zenon_H6d). % 22.32/22.46 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.46 apply (zenon_L1954_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.46 apply (zenon_L698_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.46 apply (zenon_L1052_); trivial. % 22.32/22.46 apply (zenon_L1645_); trivial. % 22.32/22.46 apply (zenon_L653_); trivial. % 22.32/22.46 apply (zenon_L51_); trivial. % 22.32/22.46 (* end of lemma zenon_L1955_ *) % 22.32/22.46 assert (zenon_L1956_ : ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((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 (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((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)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((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)) = (op (e0) (e2)))) -> (((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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 22.32/22.46 do 0 intro. intros zenon_H3f zenon_H6d zenon_H1c3 zenon_H15d zenon_H139 zenon_H6f zenon_H1cb zenon_H121 zenon_H186 zenon_H23c zenon_H48 zenon_H1c6 zenon_H164 zenon_H177 zenon_Ha0 zenon_H201 zenon_H4e zenon_H77 zenon_H1cf zenon_H156 zenon_H1d8 zenon_H125 zenon_H68 zenon_Ha9 zenon_H16a zenon_Hb6 zenon_H82 zenon_H4c zenon_H1ef zenon_H13e zenon_H141 zenon_H196 zenon_H18d zenon_H234 zenon_H117 zenon_Hf0 zenon_H55 zenon_H189 zenon_H23d zenon_H1bb zenon_H1b4 zenon_Hb2 zenon_H173 zenon_H183 zenon_H111 zenon_H13b zenon_Hfa zenon_H179 zenon_H1fb zenon_Hcc zenon_H131 zenon_H109 zenon_H11a zenon_H12e zenon_H1d5 zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H192 zenon_Hf5 zenon_H13c zenon_H236 zenon_H13a zenon_H33 zenon_H140 zenon_Hbc zenon_H1fe zenon_H25b zenon_H25e zenon_H19a zenon_H163 zenon_H195 zenon_H129 zenon_H20f zenon_H1a8 zenon_He4 zenon_H104 zenon_H73 zenon_H13f zenon_H2c zenon_H230 zenon_H212 zenon_H1a2 zenon_H19d. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 22.32/22.46 apply (zenon_L1955_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.32/22.46 apply (zenon_L2_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.32/22.46 apply (zenon_L482_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.32/22.46 exact (zenon_H1ba zenon_H6d). % 22.32/22.46 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.32/22.46 apply (zenon_L1915_); trivial. % 22.32/22.46 apply (zenon_L1915_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.32/22.46 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.32/22.46 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.32/22.46 exact (zenon_H1c7 zenon_Hac). % 22.32/22.46 apply (zenon_L1921_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.32/22.46 apply (zenon_L513_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.32/22.46 apply (zenon_L11_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.32/22.46 apply (zenon_L319_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.32/22.46 apply (zenon_L485_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.32/22.46 apply (zenon_L435_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.32/22.46 apply (zenon_L522_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.32/22.46 apply (zenon_L37_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.32/22.46 apply (zenon_L458_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.32/22.46 apply (zenon_L387_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.32/22.46 apply (zenon_L531_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.32/22.46 apply (zenon_L388_); trivial. % 22.32/22.46 apply (zenon_L51_); trivial. % 22.32/22.46 (* end of lemma zenon_L1956_ *) % 22.32/22.46 assert (zenon_L1957_ : ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (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))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (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 (e0) (e0)) = (op (e0) (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) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.32/22.46 do 0 intro. intros zenon_H54 zenon_H19d zenon_H1a2 zenon_H212 zenon_H230 zenon_H2c zenon_H13f zenon_H73 zenon_H104 zenon_He4 zenon_H1a8 zenon_H20f zenon_H195 zenon_H163 zenon_H19a zenon_H25e zenon_H25b zenon_H1fe zenon_Hbc zenon_H140 zenon_H33 zenon_H13a zenon_H236 zenon_H13c zenon_Hf5 zenon_H192 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H24e zenon_H1d5 zenon_H12e zenon_H11a zenon_H109 zenon_H131 zenon_Hcc zenon_H1fb zenon_H179 zenon_Hfa zenon_H13b zenon_H173 zenon_Hb2 zenon_H1b4 zenon_H1bb zenon_H23d zenon_H189 zenon_H55 zenon_Hf0 zenon_H117 zenon_H234 zenon_H18d zenon_H196 zenon_H141 zenon_H13e zenon_H1ef zenon_H4c zenon_H82 zenon_Hb6 zenon_H16a zenon_H125 zenon_H1d8 zenon_H156 zenon_H1cf zenon_H77 zenon_H4e zenon_H201 zenon_Ha0 zenon_H164 zenon_H1c6 zenon_H48 zenon_H23c zenon_H186 zenon_H121 zenon_H1cb zenon_H6f zenon_H139 zenon_H15d zenon_H1c3 zenon_H3f zenon_H111 zenon_H183 zenon_H68 zenon_H34 zenon_Hac zenon_Ha9 zenon_H66 zenon_H177 zenon_H129. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.46 apply (zenon_L30_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.46 apply (zenon_L1956_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.46 apply (zenon_L258_); trivial. % 22.32/22.46 apply (zenon_L1596_); trivial. % 22.32/22.46 (* end of lemma zenon_L1957_ *) % 22.32/22.46 assert (zenon_L1958_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (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) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (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))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (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). % 22.32/22.46 do 0 intro. intros zenon_Hcb zenon_H209 zenon_H1c3 zenon_Ha9 zenon_H77 zenon_H1b7 zenon_H234 zenon_H18d zenon_Hc4 zenon_H181 zenon_H1bf zenon_H19d zenon_H1a2 zenon_H212 zenon_H230 zenon_H2c zenon_H13f zenon_H73 zenon_H104 zenon_He4 zenon_H1a8 zenon_H20f zenon_H195 zenon_H163 zenon_H19a zenon_H25e zenon_H25b zenon_H1fe zenon_Hbc zenon_H140 zenon_H33 zenon_H13a zenon_H236 zenon_H13c zenon_Hf5 zenon_H192 zenon_H1cd zenon_H7d zenon_H24e zenon_H1d5 zenon_H109 zenon_H131 zenon_Hcc zenon_H1fb zenon_H179 zenon_Hfa zenon_H13b zenon_H173 zenon_Hb2 zenon_H1b4 zenon_H1bb zenon_H23d zenon_H189 zenon_H55 zenon_Hf0 zenon_H117 zenon_H196 zenon_H141 zenon_H13e zenon_H1ef zenon_H4c zenon_H82 zenon_Hb6 zenon_H16a zenon_H125 zenon_H1d8 zenon_H156 zenon_H1cf zenon_H4e zenon_H201 zenon_Ha0 zenon_H164 zenon_H1c6 zenon_H23c zenon_H186 zenon_H121 zenon_H1cb zenon_H6f zenon_H139 zenon_H15d zenon_H111 zenon_H183 zenon_H129 zenon_H5d zenon_H26a zenon_H68 zenon_H120 zenon_H177 zenon_H11a zenon_H3f zenon_H34 zenon_H12e zenon_H38 zenon_H48. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.46 exact (zenon_H4c zenon_H47). % 22.32/22.46 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.46 exact (zenon_H4c zenon_H47). % 22.32/22.46 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.46 apply (zenon_L492_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.32/22.46 apply (zenon_L214_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.32/22.46 apply (zenon_L186_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.32/22.46 apply (zenon_L1647_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.46 apply (zenon_L1656_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.46 apply (zenon_L216_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.46 apply (zenon_L1949_); trivial. % 22.32/22.46 apply (zenon_L1657_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.46 apply (zenon_L214_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.32/22.46 apply (zenon_L214_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.32/22.46 apply (zenon_L186_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.32/22.46 apply (zenon_L1647_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.46 apply (zenon_L1656_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.46 apply (zenon_L216_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.32/22.46 apply (zenon_L55_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.32/22.46 apply (zenon_L216_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.32/22.46 apply (zenon_L217_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.32/22.46 apply (zenon_L152_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.32/22.46 apply (zenon_L94_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.32/22.46 apply (zenon_L124_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.32/22.46 exact (zenon_H1bf zenon_H105). % 22.32/22.46 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.46 apply (zenon_L516_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.46 apply (zenon_L1646_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.46 apply (zenon_L258_); trivial. % 22.32/22.46 apply (zenon_L1159_); trivial. % 22.32/22.46 apply (zenon_L415_); trivial. % 22.32/22.46 apply (zenon_L1957_); trivial. % 22.32/22.46 apply (zenon_L1657_); trivial. % 22.32/22.46 apply (zenon_L165_); trivial. % 22.32/22.46 apply (zenon_L456_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.46 apply (zenon_L1648_); trivial. % 22.32/22.46 apply (zenon_L246_); trivial. % 22.32/22.46 (* end of lemma zenon_L1958_ *) % 22.32/22.46 assert (zenon_L1959_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (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))))) -> (~((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 (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (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) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (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 (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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 (e1) (e2)) = (op (e1) (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) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (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)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.32/22.46 do 0 intro. intros zenon_H240 zenon_H65 zenon_H1bf zenon_H204 zenon_H3f zenon_H1d8 zenon_H1fb zenon_H48 zenon_Hf0 zenon_H234 zenon_H77 zenon_Ha0 zenon_H141 zenon_H164 zenon_H104 zenon_H192 zenon_He4 zenon_H177 zenon_H190 zenon_H121 zenon_H129 zenon_H33 zenon_H196 zenon_H183 zenon_H23c zenon_H15d zenon_H236 zenon_H2c zenon_H13a zenon_H139 zenon_H82 zenon_H201 zenon_Ha9 zenon_H1ec zenon_H131 zenon_H73 zenon_H163 zenon_H4e zenon_Hb6 zenon_H117 zenon_H156 zenon_H13f zenon_H68 zenon_H140 zenon_H111 zenon_H13e zenon_H1c6 zenon_H1fe zenon_H11a zenon_H23d zenon_H1a8 zenon_H55 zenon_H13c zenon_Hfa zenon_H1bb zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H12e zenon_H195 zenon_H19d zenon_H1cb zenon_H1cd zenon_Hcc zenon_H1a2 zenon_H186 zenon_H1ef zenon_H125 zenon_H24e zenon_H179 zenon_H1b7 zenon_H20f zenon_H1b4 zenon_H18d zenon_H19a zenon_Hb2 zenon_H94 zenon_H25b zenon_H25e zenon_H173 zenon_H13b zenon_H16a zenon_H1cf zenon_H189 zenon_H1c3 zenon_H6f zenon_Hf5 zenon_H1d5 zenon_H109 zenon_H230 zenon_H264 zenon_H1f zenon_H66 zenon_H4c zenon_H23b. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.46 apply (zenon_L1924_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.46 exact (zenon_H1f zenon_H1e). % 22.32/22.46 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.46 apply (zenon_L537_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.46 apply (zenon_L264_); trivial. % 22.32/22.46 exact (zenon_H238 zenon_H38). % 22.32/22.46 apply (zenon_L1861_); trivial. % 22.32/22.46 (* end of lemma zenon_L1959_ *) % 22.32/22.46 assert (zenon_L1960_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (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 (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (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 (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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 (e3) (e0)) = (e3))) -> (~((e0) = (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) (e2)) = (op (e3) (e2)))) -> (~((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))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.32/22.46 do 0 intro. intros zenon_H236 zenon_He4 zenon_H55 zenon_H94 zenon_H125 zenon_H186 zenon_H156 zenon_H4e zenon_H1ec zenon_H1d8 zenon_H234 zenon_H73 zenon_H140 zenon_H13e zenon_H104 zenon_H99 zenon_H131 zenon_H19d zenon_H160 zenon_H11a zenon_H3f zenon_H12e zenon_H13f zenon_Hf0 zenon_H1bf zenon_H15d zenon_H196 zenon_H23c zenon_H82 zenon_H4c zenon_Hb2 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H19a zenon_H1b7 zenon_H179 zenon_H201 zenon_H33 zenon_H13c zenon_Hb6 zenon_H139 zenon_H177 zenon_H121 zenon_H209 zenon_Ha0 zenon_H1a3 zenon_H164 zenon_H195 zenon_H163 zenon_H173 zenon_Hfa zenon_H68 zenon_Ha9 zenon_H13a zenon_H1fe zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H120. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.46 apply (zenon_L1927_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.46 apply (zenon_L554_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.46 apply (zenon_L1929_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.46 exact (zenon_H4c zenon_H47). % 22.32/22.46 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.46 apply (zenon_L1932_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.46 apply (zenon_L239_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.46 exact (zenon_H4c zenon_H47). % 22.32/22.46 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.46 apply (zenon_L25_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.46 apply (zenon_L1933_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.46 apply (zenon_L548_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.46 apply (zenon_L229_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.46 apply (zenon_L264_); trivial. % 22.32/22.46 apply (zenon_L98_); trivial. % 22.32/22.46 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.46 apply (zenon_L526_); trivial. % 22.32/22.46 apply (zenon_L553_); trivial. % 22.32/22.46 apply (zenon_L555_); trivial. % 22.32/22.46 (* end of lemma zenon_L1960_ *) % 22.32/22.47 assert (zenon_L1961_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (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))))) -> (~((op (e3) (e2)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((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 (e0) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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)) = (e2))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H236 zenon_H201 zenon_He4 zenon_H55 zenon_H234 zenon_H140 zenon_H1cb zenon_H104 zenon_H121 zenon_H1cd zenon_H24e zenon_H11a zenon_H4e zenon_H99 zenon_H131 zenon_H13e zenon_H1d8 zenon_H1ec zenon_H186 zenon_H156 zenon_H13c zenon_H19d zenon_Hc2 zenon_H160 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H12e zenon_H13f zenon_Hf0 zenon_H3f zenon_H1bf zenon_H139 zenon_H177 zenon_H19a zenon_H181 zenon_H1b7 zenon_H179 zenon_H164 zenon_H195 zenon_H163 zenon_H173 zenon_Hfa zenon_H68 zenon_H196 zenon_H15d zenon_H4c zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H1fe zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H120. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.47 apply (zenon_L1927_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.47 apply (zenon_L565_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.32/22.47 apply (zenon_L1929_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.47 apply (zenon_L559_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.47 apply (zenon_L229_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.47 apply (zenon_L264_); trivial. % 22.32/22.47 apply (zenon_L167_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.32/22.47 apply (zenon_L526_); trivial. % 22.32/22.47 apply (zenon_L528_); trivial. % 22.32/22.47 apply (zenon_L555_); trivial. % 22.32/22.47 (* end of lemma zenon_L1961_ *) % 22.32/22.47 assert (zenon_L1962_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (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) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H240 zenon_H33 zenon_H23d zenon_H1f zenon_H15d zenon_H9e zenon_Hb6 zenon_H9d zenon_H11a zenon_H3f zenon_H177 zenon_H120 zenon_H12e zenon_H48 zenon_H4c zenon_Ha0 zenon_H236. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.47 exact (zenon_H1f zenon_H1e). % 22.32/22.47 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.47 apply (zenon_L567_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.47 exact (zenon_H237 zenon_H31). % 22.32/22.47 apply (zenon_L156_); trivial. % 22.32/22.47 apply (zenon_L611_); trivial. % 22.32/22.47 (* end of lemma zenon_L1962_ *) % 22.32/22.47 assert (zenon_L1963_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H16a zenon_H7b zenon_H120 zenon_Hb6 zenon_Hb9 zenon_H3f zenon_H234 zenon_H139 zenon_H68 zenon_H1e zenon_H6f zenon_Hbb zenon_H1bf zenon_H156 zenon_H201 zenon_H77 zenon_H18d zenon_H8b zenon_Hf6 zenon_H196. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.47 exact (zenon_H7b zenon_H65). % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.47 apply (zenon_L1954_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.47 exact (zenon_H8b zenon_H8a). % 22.32/22.47 apply (zenon_L167_); trivial. % 22.32/22.47 (* end of lemma zenon_L1963_ *) % 22.32/22.47 assert (zenon_L1964_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((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 (e2) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H177 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H16a zenon_H7b zenon_H120 zenon_Hb6 zenon_Hb9 zenon_H3f zenon_H234 zenon_H139 zenon_H68 zenon_H1e zenon_H6f zenon_Hbb zenon_H1bf zenon_H156 zenon_H201 zenon_H77 zenon_H18d zenon_H8b zenon_H196. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.47 apply (zenon_L20_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.47 apply (zenon_L181_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.47 apply (zenon_L1952_); trivial. % 22.32/22.47 apply (zenon_L1963_); trivial. % 22.32/22.47 (* end of lemma zenon_L1964_ *) % 22.32/22.47 assert (zenon_L1965_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (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) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((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)) = (op (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) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (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)) = (op (e2) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (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) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H92 zenon_H89 zenon_H7b zenon_H18d zenon_H120 zenon_H234 zenon_H6f zenon_H139 zenon_H8b zenon_H16a zenon_H77 zenon_H156 zenon_H3f zenon_H1bf zenon_Hb6 zenon_H201 zenon_Ha0 zenon_Ha9 zenon_H177 zenon_Hbb zenon_H196 zenon_Hb9 zenon_H13a zenon_H68 zenon_H48 zenon_H1d8 zenon_H4e zenon_H25b zenon_H25e zenon_H19a zenon_H179 zenon_H173 zenon_H13b zenon_H183 zenon_H163 zenon_Hf0 zenon_Hfa zenon_H195 zenon_H12e zenon_H11a zenon_H1cf zenon_H1c6 zenon_H1cd zenon_H1bb zenon_H129 zenon_Hc0 zenon_H20f zenon_H189 zenon_H1cb zenon_H1c3 zenon_H1a8 zenon_He4 zenon_H121 zenon_H164 zenon_H104 zenon_H73 zenon_H125 zenon_H13f zenon_H2c zenon_H13e zenon_H1fe zenon_Hbc zenon_H140 zenon_H23c zenon_H15d zenon_H33 zenon_H236 zenon_H13c zenon_Hf5 zenon_H117 zenon_H192 zenon_H1b7 zenon_H7d zenon_H24e zenon_H1d5 zenon_H186 zenon_H141 zenon_H109 zenon_H131 zenon_Hcc zenon_H82 zenon_H111 zenon_H1ef zenon_Hb2 zenon_H1b4 zenon_H23d zenon_H55 zenon_H1fb zenon_H230 zenon_H212 zenon_H1a2 zenon_H19d. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.47 apply (zenon_L1964_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.47 apply (zenon_L694_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.47 apply (zenon_L1052_); trivial. % 22.32/22.47 apply (zenon_L1645_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.32/22.47 apply (zenon_L1964_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.32/22.47 apply (zenon_L696_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.32/22.47 apply (zenon_L1052_); trivial. % 22.32/22.47 apply (zenon_L1645_); trivial. % 22.32/22.47 (* end of lemma zenon_L1965_ *) % 22.32/22.47 assert (zenon_L1966_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> False). % 22.32/22.47 do 0 intro. intros zenon_H28 zenon_Hef zenon_H4d. % 22.32/22.47 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.32/22.47 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.32/22.47 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.32/22.47 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.32/22.47 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.32/22.47 apply (zenon_L984_); trivial. % 22.32/22.47 (* end of lemma zenon_L1966_ *) % 22.32/22.47 assert (zenon_L1967_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_H160 zenon_H177 zenon_H38 zenon_H68. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.47 exact (zenon_H6c zenon_H67). % 22.32/22.47 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.47 apply (zenon_L226_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.47 apply (zenon_L122_); trivial. % 22.32/22.47 apply (zenon_L165_); trivial. % 22.32/22.47 (* end of lemma zenon_L1967_ *) % 22.32/22.47 assert (zenon_L1968_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> False). % 22.32/22.47 do 0 intro. intros zenon_H183 zenon_H34 zenon_H11a zenon_H68 zenon_H38 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H77 zenon_H11f. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.32/22.47 apply (zenon_L291_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.32/22.47 apply (zenon_L119_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.32/22.47 apply (zenon_L1967_); trivial. % 22.32/22.47 apply (zenon_L884_); trivial. % 22.32/22.47 (* end of lemma zenon_L1968_ *) % 22.32/22.47 assert (zenon_L1969_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H12e zenon_H1b7 zenon_H1cb zenon_H93 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H183 zenon_H34 zenon_H11a zenon_H68 zenon_H38 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H77. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.32/22.47 apply (zenon_L456_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.32/22.47 apply (zenon_L1276_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.32/22.47 apply (zenon_L1159_); trivial. % 22.32/22.47 apply (zenon_L1968_); trivial. % 22.32/22.47 (* end of lemma zenon_L1969_ *) % 22.32/22.47 assert (zenon_L1970_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H16a zenon_H54 zenon_Hf0 zenon_H8b zenon_H12e zenon_H1b7 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H183 zenon_H34 zenon_H11a zenon_H68 zenon_H38 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H77. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.47 apply (zenon_L30_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.47 apply (zenon_L61_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.47 exact (zenon_H8b zenon_H8a). % 22.32/22.47 apply (zenon_L1969_); trivial. % 22.32/22.47 (* end of lemma zenon_L1970_ *) % 22.32/22.47 assert (zenon_L1971_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e1)) -> False). % 22.32/22.47 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H65 zenon_Hdb zenon_H6f zenon_H14c zenon_Ha0 zenon_Hb6 zenon_H128. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.32/22.47 apply (zenon_L43_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.32/22.47 apply (zenon_L205_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.32/22.47 apply (zenon_L278_); trivial. % 22.32/22.47 apply (zenon_L182_); trivial. % 22.32/22.47 (* end of lemma zenon_L1971_ *) % 22.32/22.47 assert (zenon_L1972_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H13f zenon_H77 zenon_H7f zenon_H1f1 zenon_H4d zenon_H131 zenon_H117 zenon_Ha9 zenon_H65 zenon_Hdb zenon_H6f zenon_H14c zenon_Ha0 zenon_Hb6. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.32/22.47 apply (zenon_L30_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.32/22.47 apply (zenon_L284_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.32/22.47 apply (zenon_L128_); trivial. % 22.32/22.47 apply (zenon_L1971_); trivial. % 22.32/22.47 (* end of lemma zenon_L1972_ *) % 22.32/22.47 assert (zenon_L1973_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (((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 (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (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 (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H12e zenon_H48 zenon_H6f zenon_Hdb zenon_H65 zenon_H117 zenon_H131 zenon_H4d zenon_H1f1 zenon_H13f zenon_Hb6 zenon_Ha0 zenon_H14c zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H183 zenon_H34 zenon_H11a zenon_H68 zenon_H38 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H77. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.32/22.47 apply (zenon_L456_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.32/22.47 apply (zenon_L1972_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.32/22.47 apply (zenon_L687_); trivial. % 22.32/22.47 apply (zenon_L1968_); trivial. % 22.32/22.47 (* end of lemma zenon_L1973_ *) % 22.32/22.47 assert (zenon_L1974_ : (((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))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((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 (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H16a zenon_H1a2 zenon_Ha9 zenon_H66 zenon_H14c zenon_Ha0 zenon_Hb6 zenon_H13f zenon_H1f1 zenon_H4d zenon_H131 zenon_H117 zenon_Hdb zenon_H6f zenon_H53 zenon_H8b zenon_H12e zenon_H1b7 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H183 zenon_H34 zenon_H11a zenon_H68 zenon_H38 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H77. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.47 apply (zenon_L1973_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.47 apply (zenon_L56_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.47 exact (zenon_H8b zenon_H8a). % 22.32/22.47 apply (zenon_L1969_); trivial. % 22.32/22.47 (* end of lemma zenon_L1974_ *) % 22.32/22.47 assert (zenon_L1975_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> False). % 22.32/22.47 do 0 intro. intros zenon_H16a zenon_Hb6 zenon_Ha0 zenon_H14c zenon_H6f zenon_Hdb zenon_Ha9 zenon_H117 zenon_Hf0 zenon_Hef zenon_H8b zenon_H77 zenon_H128. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.47 apply (zenon_L1971_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.47 apply (zenon_L61_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.47 exact (zenon_H8b zenon_H8a). % 22.32/22.47 apply (zenon_L218_); trivial. % 22.32/22.47 (* end of lemma zenon_L1975_ *) % 22.32/22.47 assert (zenon_L1976_ : (((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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H139 zenon_H6c zenon_H173 zenon_H177 zenon_H38 zenon_H68 zenon_H11a zenon_H34 zenon_H183 zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H1b7 zenon_H12e zenon_H131 zenon_H4d zenon_H1f1 zenon_H13f zenon_H66 zenon_H1a2 zenon_H48 zenon_H16a zenon_Hb6 zenon_Ha0 zenon_H14c zenon_H6f zenon_Hdb zenon_Ha9 zenon_H117 zenon_Hf0 zenon_Hef zenon_H8b zenon_H77. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.32/22.47 apply (zenon_L1970_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.32/22.47 apply (zenon_L1974_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.32/22.47 apply (zenon_L255_); trivial. % 22.32/22.47 apply (zenon_L1975_); trivial. % 22.32/22.47 (* end of lemma zenon_L1976_ *) % 22.32/22.47 assert (zenon_L1977_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (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))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 22.32/22.47 do 0 intro. intros zenon_H140 zenon_H77 zenon_H8b zenon_Hef zenon_Hf0 zenon_H117 zenon_Ha9 zenon_Hdb zenon_H6f zenon_Ha0 zenon_Hb6 zenon_H16a zenon_H48 zenon_H1a2 zenon_H66 zenon_H13f zenon_H1f1 zenon_H4d zenon_H131 zenon_H12e zenon_H1b7 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H183 zenon_H11a zenon_H68 zenon_H38 zenon_H177 zenon_H173 zenon_H6c zenon_H139 zenon_Hbc zenon_H34. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.32/22.47 apply (zenon_L264_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.32/22.47 apply (zenon_L117_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.32/22.47 apply (zenon_L1976_); trivial. % 22.32/22.47 apply (zenon_L328_); trivial. % 22.32/22.47 (* end of lemma zenon_L1977_ *) % 22.32/22.47 assert (zenon_L1978_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((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) (e1)) = (op (e3) (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) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((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 (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H13a zenon_H47 zenon_H34 zenon_Hbc zenon_H139 zenon_H6c zenon_H173 zenon_H177 zenon_H68 zenon_H11a zenon_H183 zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1cb zenon_H1b7 zenon_H12e zenon_H131 zenon_H4d zenon_H1f1 zenon_H13f zenon_H1a2 zenon_H48 zenon_H16a zenon_Hb6 zenon_H6f zenon_H117 zenon_Hf0 zenon_Hef zenon_H8b zenon_H77 zenon_H140 zenon_Ha9 zenon_H66 zenon_H38 zenon_Ha0. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.47 apply (zenon_L253_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.47 apply (zenon_L1977_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.47 apply (zenon_L193_); trivial. % 22.32/22.47 apply (zenon_L156_); trivial. % 22.32/22.47 (* end of lemma zenon_L1978_ *) % 22.32/22.47 assert (zenon_L1979_ : (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (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) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (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) (e1)) = (op (e3) (e1)))) -> ((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 (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.32/22.47 do 0 intro. intros zenon_Ha0 zenon_Ha9 zenon_H140 zenon_H77 zenon_H8b zenon_Hef zenon_Hf0 zenon_H117 zenon_H6f zenon_Hb6 zenon_H16a zenon_H48 zenon_H1a2 zenon_H13f zenon_H1f1 zenon_H4d zenon_H131 zenon_H12e zenon_H1b7 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H183 zenon_H11a zenon_H177 zenon_H173 zenon_H6c zenon_H139 zenon_Hbc zenon_H34 zenon_H47 zenon_H13a zenon_H38 zenon_H68. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.47 exact (zenon_H6c zenon_H67). % 22.32/22.47 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.47 apply (zenon_L226_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.47 apply (zenon_L1978_); trivial. % 22.32/22.47 apply (zenon_L165_); trivial. % 22.32/22.47 (* end of lemma zenon_L1979_ *) % 22.32/22.47 assert (zenon_L1980_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (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))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (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 (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (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). % 22.32/22.47 do 0 intro. intros zenon_H15d zenon_Hbc zenon_H131 zenon_H1f1 zenon_H13f zenon_H1a2 zenon_H6f zenon_H117 zenon_H140 zenon_H34 zenon_H16a zenon_Hf0 zenon_H8b zenon_H12e zenon_H1b7 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H183 zenon_H11a zenon_H68 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H77 zenon_H4e zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H13a zenon_H82 zenon_H73 zenon_H4d zenon_H38 zenon_H48. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.47 apply (zenon_L1979_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.47 apply (zenon_L1149_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.47 apply (zenon_L14_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.47 apply (zenon_L1970_); trivial. % 22.32/22.47 apply (zenon_L456_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.47 apply (zenon_L184_); trivial. % 22.32/22.47 apply (zenon_L246_); trivial. % 22.32/22.47 (* end of lemma zenon_L1980_ *) % 22.32/22.47 assert (zenon_L1981_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_H160 zenon_H177 zenon_H155 zenon_H77. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.47 exact (zenon_H6c zenon_H67). % 22.32/22.47 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.47 apply (zenon_L226_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.47 apply (zenon_L122_); trivial. % 22.32/22.47 apply (zenon_L98_); trivial. % 22.32/22.47 (* end of lemma zenon_L1981_ *) % 22.32/22.47 assert (zenon_L1982_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (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))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H15d zenon_H196 zenon_H93 zenon_H1e zenon_H68 zenon_H73 zenon_H4d zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_H160 zenon_H177 zenon_H77. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.47 apply (zenon_L975_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.47 apply (zenon_L215_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.47 apply (zenon_L184_); trivial. % 22.32/22.47 apply (zenon_L1981_); trivial. % 22.32/22.47 (* end of lemma zenon_L1982_ *) % 22.32/22.47 assert (zenon_L1983_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.32/22.47 do 0 intro. intros zenon_H183 zenon_H7e zenon_H11a zenon_H77 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H4d zenon_H73 zenon_H1e zenon_H93 zenon_H196 zenon_H15d zenon_H68 zenon_H167. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.32/22.47 apply (zenon_L71_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.32/22.47 apply (zenon_L119_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.32/22.47 apply (zenon_L1982_); trivial. % 22.32/22.47 apply (zenon_L295_); trivial. % 22.32/22.47 (* end of lemma zenon_L1983_ *) % 22.32/22.47 assert (zenon_L1984_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (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))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (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 (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 (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H141 zenon_H191 zenon_H10c zenon_H117 zenon_H15d zenon_H196 zenon_H1e zenon_H73 zenon_H4d zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_H177 zenon_H11a zenon_H7e zenon_H183 zenon_H104 zenon_H18d zenon_Hb6 zenon_H1b7 zenon_H48 zenon_H9e zenon_Ha0 zenon_H19a zenon_H189 zenon_H33 zenon_H164 zenon_Hf0 zenon_H16a zenon_H7b zenon_H53 zenon_H77 zenon_H8b zenon_H68. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.32/22.47 apply (zenon_L731_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.32/22.47 apply (zenon_L111_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.47 exact (zenon_H7b zenon_H65). % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.47 apply (zenon_L61_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.47 exact (zenon_H8b zenon_H8a). % 22.32/22.47 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.32/22.47 apply (zenon_L7_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.32/22.47 apply (zenon_L759_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.32/22.47 apply (zenon_L257_); trivial. % 22.32/22.47 apply (zenon_L1983_); trivial. % 22.32/22.47 apply (zenon_L766_); trivial. % 22.32/22.47 (* end of lemma zenon_L1984_ *) % 22.32/22.47 assert (zenon_L1985_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.32/22.47 do 0 intro. intros zenon_H183 zenon_H7e zenon_H11a zenon_H77 zenon_H155 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H181. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.32/22.47 apply (zenon_L71_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.32/22.47 apply (zenon_L119_); trivial. % 22.32/22.47 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.32/22.47 apply (zenon_L1981_); trivial. % 22.32/22.47 exact (zenon_H181 zenon_H17c). % 22.32/22.47 (* end of lemma zenon_L1985_ *) % 22.32/22.47 assert (zenon_L1986_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H82 zenon_H48 zenon_H1e zenon_H4e zenon_H5a zenon_H55 zenon_H53 zenon_H183 zenon_H11a zenon_H77 zenon_H155 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H181. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.48 apply (zenon_L13_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.48 apply (zenon_L16_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.48 apply (zenon_L15_); trivial. % 22.32/22.48 apply (zenon_L1985_); trivial. % 22.32/22.48 (* end of lemma zenon_L1986_ *) % 22.32/22.48 assert (zenon_L1987_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (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) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H196 zenon_H8b zenon_Hf0 zenon_H7b zenon_H16a zenon_H13a zenon_H1c6 zenon_H68 zenon_H164 zenon_H33 zenon_H189 zenon_H19a zenon_Ha0 zenon_H1b7 zenon_H18d zenon_H104 zenon_H15d zenon_H117 zenon_H141 zenon_H1a2 zenon_Ha9 zenon_Hb6 zenon_H191 zenon_H1cd zenon_H73 zenon_H4d zenon_H82 zenon_H48 zenon_H1e zenon_H4e zenon_H5a zenon_H55 zenon_H53 zenon_H183 zenon_H11a zenon_H77 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H181. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.48 apply (zenon_L13_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.48 apply (zenon_L13_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.48 apply (zenon_L16_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.48 apply (zenon_L15_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.48 exact (zenon_H6c zenon_H67). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.48 apply (zenon_L214_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.48 apply (zenon_L41_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.48 apply (zenon_L55_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.48 apply (zenon_L193_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.32/22.48 apply (zenon_L55_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.32/22.48 apply (zenon_L1984_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.32/22.48 apply (zenon_L113_); trivial. % 22.32/22.48 apply (zenon_L379_); trivial. % 22.32/22.48 apply (zenon_L621_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.48 apply (zenon_L184_); trivial. % 22.32/22.48 apply (zenon_L1986_); trivial. % 22.32/22.48 (* end of lemma zenon_L1987_ *) % 22.32/22.48 assert (zenon_L1988_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((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))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H183 zenon_H34 zenon_Hef zenon_H11a zenon_H196 zenon_H93 zenon_H177 zenon_H2a zenon_H68 zenon_H47 zenon_H139 zenon_H16a zenon_H7b zenon_H53 zenon_H77 zenon_H8b zenon_H129. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.32/22.48 apply (zenon_L291_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.32/22.48 apply (zenon_L119_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.32/22.48 apply (zenon_L352_); trivial. % 22.32/22.48 apply (zenon_L127_); trivial. % 22.32/22.48 (* end of lemma zenon_L1988_ *) % 22.32/22.48 assert (zenon_L1989_ : (((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) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 22.32/22.48 do 0 intro. intros zenon_H13f zenon_Hb6 zenon_Ha8 zenon_H7f zenon_H1f1 zenon_H4d zenon_H131 zenon_H77 zenon_H93. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.32/22.48 apply (zenon_L151_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.32/22.48 apply (zenon_L284_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.32/22.48 apply (zenon_L128_); trivial. % 22.32/22.48 apply (zenon_L218_); trivial. % 22.32/22.48 (* end of lemma zenon_L1989_ *) % 22.32/22.48 assert (zenon_L1990_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 22.32/22.48 do 0 intro. intros zenon_H12e zenon_H102 zenon_H93 zenon_H77 zenon_H131 zenon_H4d zenon_H1f1 zenon_Ha8 zenon_H13f zenon_Hb6 zenon_Ha0 zenon_H14c zenon_H66 zenon_Ha9 zenon_H1a2 zenon_Hef zenon_He0. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.32/22.48 apply (zenon_L71_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.32/22.48 apply (zenon_L1989_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.32/22.48 apply (zenon_L687_); trivial. % 22.32/22.48 apply (zenon_L662_); trivial. % 22.32/22.48 (* end of lemma zenon_L1990_ *) % 22.32/22.48 assert (zenon_L1991_ : ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> False). % 22.32/22.48 do 0 intro. intros zenon_H47 zenon_H102 zenon_H167. % 22.32/22.48 apply (zenon_notand_s _ _ ax13); [ zenon_intro zenon_H286 | zenon_intro zenon_H28e ]. % 22.32/22.48 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H24b ]. % 22.32/22.48 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e1) = (op (op (e3) (e3)) (op (e3) (e3))))). % 22.32/22.48 intro zenon_D_pnotp. % 22.32/22.48 apply zenon_H286. % 22.32/22.48 rewrite <- zenon_D_pnotp. % 22.32/22.48 exact zenon_H24a. % 22.32/22.48 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 22.32/22.48 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 22.32/22.48 congruence. % 22.32/22.48 cut (((op (e0) (e0)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 22.32/22.48 intro zenon_D_pnotp. % 22.32/22.48 apply zenon_H287. % 22.32/22.48 rewrite <- zenon_D_pnotp. % 22.32/22.48 exact zenon_H47. % 22.32/22.48 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 22.32/22.48 cut (((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24d]. % 22.32/22.48 congruence. % 22.32/22.48 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H24a | zenon_intro zenon_H24b ]. % 22.32/22.48 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))))). % 22.32/22.48 intro zenon_D_pnotp. % 22.32/22.48 apply zenon_H24d. % 22.32/22.48 rewrite <- zenon_D_pnotp. % 22.32/22.48 exact zenon_H24a. % 22.32/22.48 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 22.32/22.48 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 22.32/22.48 congruence. % 22.32/22.48 apply (zenon_L544_); trivial. % 22.32/22.48 apply zenon_H24b. apply refl_equal. % 22.32/22.48 apply zenon_H24b. apply refl_equal. % 22.32/22.48 apply zenon_H4a. apply refl_equal. % 22.32/22.48 apply zenon_H24b. apply refl_equal. % 22.32/22.48 apply zenon_H24b. apply refl_equal. % 22.32/22.48 apply (zenon_notand_s _ _ zenon_H28e); [ zenon_intro zenon_H20e | zenon_intro zenon_H275 ]. % 22.32/22.48 apply zenon_H20e. apply sym_equal. exact zenon_H167. % 22.32/22.48 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H244 | zenon_intro zenon_H245 ]. % 22.32/22.48 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((e2) = (op (e3) (op (e3) (e3))))). % 22.32/22.48 intro zenon_D_pnotp. % 22.32/22.48 apply zenon_H275. % 22.32/22.48 rewrite <- zenon_D_pnotp. % 22.32/22.48 exact zenon_H244. % 22.32/22.48 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 22.32/22.48 cut (((op (e3) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H276]. % 22.32/22.48 congruence. % 22.32/22.48 cut (((op (e3) (e0)) = (e2)) = ((op (e3) (op (e3) (e3))) = (e2))). % 22.32/22.48 intro zenon_D_pnotp. % 22.32/22.48 apply zenon_H276. % 22.32/22.48 rewrite <- zenon_D_pnotp. % 22.32/22.48 exact zenon_H102. % 22.32/22.48 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 22.32/22.48 cut (((op (e3) (e0)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H247]. % 22.32/22.48 congruence. % 22.32/22.48 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H244 | zenon_intro zenon_H245 ]. % 22.32/22.48 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e0)) = (op (e3) (op (e3) (e3))))). % 22.32/22.48 intro zenon_D_pnotp. % 22.32/22.48 apply zenon_H247. % 22.32/22.48 rewrite <- zenon_D_pnotp. % 22.32/22.48 exact zenon_H244. % 22.32/22.48 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 22.32/22.48 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H242]. % 22.32/22.48 congruence. % 22.32/22.48 apply (zenon_L545_); trivial. % 22.32/22.48 apply zenon_H245. apply refl_equal. % 22.32/22.48 apply zenon_H245. apply refl_equal. % 22.32/22.48 apply zenon_H6a. apply refl_equal. % 22.32/22.48 apply zenon_H245. apply refl_equal. % 22.32/22.48 apply zenon_H245. apply refl_equal. % 22.32/22.48 (* end of lemma zenon_L1991_ *) % 22.32/22.48 assert (zenon_L1992_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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)) = (e0)) -> (~((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)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((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)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((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)) = (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 (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) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H173 zenon_Ha9 zenon_H13c zenon_H25 zenon_H68 zenon_H77 zenon_H53 zenon_H164 zenon_H129 zenon_H139 zenon_H2a zenon_H177 zenon_H11a zenon_H183 zenon_H1a2 zenon_Ha0 zenon_H13f zenon_H1f1 zenon_H131 zenon_H12e zenon_H104 zenon_H47 zenon_H48 zenon_H117 zenon_H191 zenon_H141 zenon_Hb6 zenon_H4d zenon_Hf5 zenon_Hb2 zenon_H13a zenon_H6c zenon_H125 zenon_H16a zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_H196. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.48 exact (zenon_H6c zenon_H67). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.48 apply (zenon_L226_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.32/22.48 exact (zenon_H6c zenon_H67). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.32/22.48 apply (zenon_L171_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.32/22.48 exact (zenon_H7b zenon_H65). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.48 apply (zenon_L253_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.48 apply (zenon_L53_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.48 apply (zenon_L193_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.32/22.48 apply (zenon_L253_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.32/22.48 apply (zenon_L116_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.32/22.48 apply (zenon_L116_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.32/22.48 apply (zenon_L731_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.32/22.48 apply (zenon_L111_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.48 exact (zenon_H7b zenon_H65). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.48 apply (zenon_L61_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.48 exact (zenon_H8b zenon_H8a). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.32/22.48 apply (zenon_L1988_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.32/22.48 apply (zenon_L1990_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.32/22.48 apply (zenon_L257_); trivial. % 22.32/22.48 apply (zenon_L1991_); trivial. % 22.32/22.48 apply (zenon_L766_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.32/22.48 apply (zenon_L124_); trivial. % 22.32/22.48 apply (zenon_L262_); trivial. % 22.32/22.48 apply (zenon_L91_); trivial. % 22.32/22.48 apply (zenon_L621_); trivial. % 22.32/22.48 (* end of lemma zenon_L1992_ *) % 22.32/22.48 assert (zenon_L1993_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H139 zenon_H6c zenon_H68 zenon_Hb6 zenon_Ha9 zenon_H2a zenon_Ha0 zenon_H47 zenon_H13a zenon_H155 zenon_H77. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.48 exact (zenon_H6c zenon_H67). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.48 apply (zenon_L147_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.48 apply (zenon_L253_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.48 apply (zenon_L53_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.48 apply (zenon_L193_); trivial. % 22.32/22.48 apply (zenon_L115_); trivial. % 22.32/22.48 apply (zenon_L98_); trivial. % 22.32/22.48 (* end of lemma zenon_L1993_ *) % 22.32/22.48 assert (zenon_L1994_ : (((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))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H82 zenon_H13a zenon_Ha0 zenon_H2a zenon_Ha9 zenon_Hb6 zenon_H68 zenon_H48 zenon_H25 zenon_H55 zenon_H53 zenon_H183 zenon_H11a zenon_H77 zenon_H155 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H181. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.48 apply (zenon_L1993_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.48 apply (zenon_L25_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.48 apply (zenon_L15_); trivial. % 22.32/22.48 apply (zenon_L1985_); trivial. % 22.32/22.48 (* end of lemma zenon_L1994_ *) % 22.32/22.48 assert (zenon_L1995_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (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) (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) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (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))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H15d zenon_H196 zenon_H8b zenon_Hf0 zenon_H7b zenon_H16a zenon_H125 zenon_Hb2 zenon_Hf5 zenon_H141 zenon_H191 zenon_H117 zenon_H104 zenon_H12e zenon_H131 zenon_H1f1 zenon_H13f zenon_H1a2 zenon_H129 zenon_H164 zenon_H13c zenon_H73 zenon_H4d zenon_H82 zenon_H13a zenon_Ha0 zenon_H2a zenon_Ha9 zenon_Hb6 zenon_H68 zenon_H48 zenon_H25 zenon_H55 zenon_H53 zenon_H183 zenon_H11a zenon_H77 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H181. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.48 apply (zenon_L1992_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.48 apply (zenon_L65_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.48 apply (zenon_L184_); trivial. % 22.32/22.48 apply (zenon_L1994_); trivial. % 22.32/22.48 (* end of lemma zenon_L1995_ *) % 22.32/22.48 assert (zenon_L1996_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((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))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H5a zenon_H183 zenon_H34 zenon_Hef zenon_H11a zenon_H196 zenon_H177 zenon_H2a zenon_H68 zenon_H47 zenon_H139 zenon_H16a zenon_H7b zenon_H53 zenon_H77 zenon_H8b zenon_H129. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.48 exact (zenon_H7b zenon_H65). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.48 apply (zenon_L319_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.48 exact (zenon_H8b zenon_H8a). % 22.32/22.48 apply (zenon_L1988_); trivial. % 22.32/22.48 (* end of lemma zenon_L1996_ *) % 22.32/22.48 assert (zenon_L1997_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (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)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_Hb6 zenon_Ha9 zenon_H2a zenon_Ha0 zenon_He4 zenon_H48 zenon_H156 zenon_H4d zenon_H55 zenon_H54 zenon_H183 zenon_H68 zenon_H34 zenon_H177 zenon_H13a zenon_H155 zenon_H77. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.48 exact (zenon_H6c zenon_H67). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.48 apply (zenon_L226_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.48 apply (zenon_L636_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.48 apply (zenon_L53_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.48 apply (zenon_L193_); trivial. % 22.32/22.48 apply (zenon_L115_); trivial. % 22.32/22.48 apply (zenon_L98_); trivial. % 22.32/22.48 (* end of lemma zenon_L1997_ *) % 22.32/22.48 assert (zenon_L1998_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e1)) = (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 (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (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 (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H15d zenon_H129 zenon_H8b zenon_H53 zenon_H7b zenon_H16a zenon_H196 zenon_H5a zenon_H73 zenon_H82 zenon_H4e zenon_H13a zenon_H34 zenon_H68 zenon_H55 zenon_H4d zenon_H156 zenon_H48 zenon_He4 zenon_Ha0 zenon_H2a zenon_Ha9 zenon_Hb6 zenon_H183 zenon_H11a zenon_H77 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H181. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.48 apply (zenon_L1996_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.48 apply (zenon_L65_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.48 apply (zenon_L184_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.48 apply (zenon_L1993_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.48 apply (zenon_L14_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.48 apply (zenon_L1997_); trivial. % 22.32/22.48 apply (zenon_L1985_); trivial. % 22.32/22.48 (* end of lemma zenon_L1998_ *) % 22.32/22.48 assert (zenon_L1999_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (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) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H15d zenon_H196 zenon_H8b zenon_Hef zenon_Hf0 zenon_H7b zenon_H16a zenon_H13a zenon_H1e zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H77 zenon_H6c zenon_H139 zenon_H73 zenon_H4d zenon_H38 zenon_H48. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.48 apply (zenon_L13_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.48 exact (zenon_H6c zenon_H67). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.48 apply (zenon_L214_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.48 apply (zenon_L41_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.48 apply (zenon_L55_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.48 apply (zenon_L193_); trivial. % 22.32/22.48 apply (zenon_L156_); trivial. % 22.32/22.48 apply (zenon_L621_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.48 apply (zenon_L184_); trivial. % 22.32/22.48 apply (zenon_L246_); trivial. % 22.32/22.48 (* end of lemma zenon_L1999_ *) % 22.32/22.48 assert (zenon_L2000_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (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 (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H12e zenon_H48 zenon_H93 zenon_H131 zenon_H4d zenon_H1f1 zenon_Ha8 zenon_H13f zenon_Hb6 zenon_Ha0 zenon_H14c zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H183 zenon_H34 zenon_H11a zenon_H68 zenon_H38 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H77. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.32/22.48 apply (zenon_L456_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.32/22.48 apply (zenon_L1989_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.32/22.48 apply (zenon_L687_); trivial. % 22.32/22.48 apply (zenon_L1968_); trivial. % 22.32/22.48 (* end of lemma zenon_L2000_ *) % 22.32/22.48 assert (zenon_L2001_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 22.32/22.48 do 0 intro. intros zenon_H16a zenon_H7b zenon_H5a zenon_H8b zenon_H12e zenon_H102 zenon_H77 zenon_H131 zenon_H4d zenon_H1f1 zenon_Ha8 zenon_H13f zenon_Hb6 zenon_Ha0 zenon_H14c zenon_H66 zenon_Ha9 zenon_H1a2 zenon_Hef zenon_He0. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.48 exact (zenon_H7b zenon_H65). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.48 apply (zenon_L319_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.48 exact (zenon_H8b zenon_H8a). % 22.32/22.48 apply (zenon_L1990_); trivial. % 22.32/22.48 (* end of lemma zenon_L2001_ *) % 22.32/22.48 assert (zenon_L2002_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (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 (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> False). % 22.32/22.48 do 0 intro. intros zenon_H164 zenon_H139 zenon_H6c zenon_H173 zenon_H177 zenon_H38 zenon_H68 zenon_H11a zenon_H183 zenon_H93 zenon_H48 zenon_Hef zenon_H1a2 zenon_Ha9 zenon_H66 zenon_H14c zenon_Hb6 zenon_H13f zenon_Ha8 zenon_H1f1 zenon_H4d zenon_H131 zenon_H77 zenon_H12e zenon_H8b zenon_H5a zenon_H7b zenon_H16a zenon_Hbb zenon_Ha0 zenon_H47 zenon_H102. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.32/22.48 apply (zenon_L2000_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.32/22.48 apply (zenon_L2001_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.32/22.48 apply (zenon_L80_); trivial. % 22.32/22.48 apply (zenon_L1991_); trivial. % 22.32/22.48 (* end of lemma zenon_L2002_ *) % 22.32/22.48 assert (zenon_L2003_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((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). % 22.32/22.48 do 0 intro. intros zenon_H139 zenon_H6c zenon_H3d zenon_H77 zenon_H7e zenon_H7b zenon_H25 zenon_H1d5 zenon_H125 zenon_H38 zenon_H68. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.48 exact (zenon_H6c zenon_H67). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.48 apply (zenon_L214_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.48 apply (zenon_L651_); trivial. % 22.32/22.48 apply (zenon_L165_); trivial. % 22.32/22.48 (* end of lemma zenon_L2003_ *) % 22.32/22.48 assert (zenon_L2004_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((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 (e1) (e1)) = (e2)) -> (((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) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (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). % 22.32/22.48 do 0 intro. intros zenon_H15d zenon_H196 zenon_H8b zenon_H16a zenon_Hb2 zenon_H191 zenon_H164 zenon_H173 zenon_H177 zenon_H11a zenon_H183 zenon_Hef zenon_H1a2 zenon_H13f zenon_H1f1 zenon_H131 zenon_H12e zenon_H5a zenon_H141 zenon_H68 zenon_H125 zenon_H1d5 zenon_H25 zenon_H7b zenon_H77 zenon_H6c zenon_H139 zenon_H53 zenon_H55 zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H13a zenon_H82 zenon_H73 zenon_H4d zenon_H38 zenon_H48. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.48 exact (zenon_H6c zenon_H67). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.48 apply (zenon_L226_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.32/22.48 exact (zenon_H6c zenon_H67). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.32/22.48 apply (zenon_L171_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.32/22.48 exact (zenon_H7b zenon_H65). % 22.32/22.48 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.32/22.48 apply (zenon_L253_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.32/22.48 apply (zenon_L116_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.32/22.48 apply (zenon_L67_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.32/22.48 apply (zenon_L111_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.48 exact (zenon_H7b zenon_H65). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.48 apply (zenon_L319_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.48 exact (zenon_H8b zenon_H8a). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.32/22.48 apply (zenon_L193_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.32/22.48 apply (zenon_L265_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.32/22.48 exact (zenon_H191 zenon_H110). % 22.32/22.48 apply (zenon_L2002_); trivial. % 22.32/22.48 apply (zenon_L1162_); trivial. % 22.32/22.48 apply (zenon_L91_); trivial. % 22.32/22.48 apply (zenon_L321_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.32/22.48 apply (zenon_L1149_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.32/22.48 apply (zenon_L25_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.32/22.48 apply (zenon_L15_); trivial. % 22.32/22.48 apply (zenon_L2003_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.48 apply (zenon_L184_); trivial. % 22.32/22.48 apply (zenon_L246_); trivial. % 22.32/22.48 (* end of lemma zenon_L2004_ *) % 22.32/22.48 assert (zenon_L2005_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H18d zenon_H7f zenon_H1cd zenon_H14c zenon_H48 zenon_H186 zenon_H139 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H47 zenon_H13a zenon_H68 zenon_H201 zenon_H77 zenon_H25b zenon_H38 zenon_Hf5 zenon_H20f zenon_H93 zenon_Hb9 zenon_H195. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.32/22.48 apply (zenon_L246_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.32/22.48 apply (zenon_L1285_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.32/22.48 apply (zenon_L218_); trivial. % 22.32/22.48 apply (zenon_L671_); trivial. % 22.32/22.48 (* end of lemma zenon_L2005_ *) % 22.32/22.48 assert (zenon_L2006_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H12e zenon_H34 zenon_H77 zenon_H201 zenon_H68 zenon_H13a zenon_H47 zenon_H139 zenon_H186 zenon_H48 zenon_H1cd zenon_H18d zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Hef zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H25b zenon_H38 zenon_Hf5 zenon_H20f zenon_H93 zenon_Hb9 zenon_H195. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.32/22.48 apply (zenon_L456_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.32/22.48 apply (zenon_L2005_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.32/22.48 apply (zenon_L687_); trivial. % 22.32/22.48 apply (zenon_L671_); trivial. % 22.32/22.48 (* end of lemma zenon_L2006_ *) % 22.32/22.48 assert (zenon_L2007_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (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) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (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)))) -> (~((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)) = (e0)) -> False). % 22.32/22.48 do 0 intro. intros zenon_H141 zenon_H13e zenon_H1ef zenon_H92 zenon_H53 zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hef zenon_Ha0 zenon_Hb6 zenon_H18d zenon_H1cd zenon_H48 zenon_H186 zenon_H139 zenon_H47 zenon_H13a zenon_H68 zenon_H201 zenon_H77 zenon_H34 zenon_H12e zenon_H191 zenon_H6f zenon_Hdb zenon_H131 zenon_H4d zenon_H1f1 zenon_H13f zenon_H183 zenon_H11a zenon_H177 zenon_H173 zenon_H6c zenon_H117 zenon_H8b zenon_Hf0 zenon_H7b zenon_H16a zenon_H196 zenon_H38. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.32/22.48 apply (zenon_L973_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.32/22.48 apply (zenon_L111_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.32/22.48 exact (zenon_H7b zenon_H65). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.32/22.48 apply (zenon_L61_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.32/22.48 exact (zenon_H8b zenon_H8a). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.32/22.48 apply (zenon_L2000_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.32/22.48 apply (zenon_L205_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.32/22.48 exact (zenon_H191 zenon_H110). % 22.32/22.48 apply (zenon_L2006_); trivial. % 22.32/22.48 apply (zenon_L1162_); trivial. % 22.32/22.48 (* end of lemma zenon_L2007_ *) % 22.32/22.48 assert (zenon_L2008_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (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)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((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). % 22.32/22.48 do 0 intro. intros zenon_H15d zenon_H196 zenon_H16a zenon_H7b zenon_Hf0 zenon_H8b zenon_H117 zenon_H6c zenon_H173 zenon_H177 zenon_H11a zenon_H183 zenon_H13f zenon_H1f1 zenon_H131 zenon_H6f zenon_H191 zenon_H12e zenon_H201 zenon_H186 zenon_H1cd zenon_H18d zenon_Hef zenon_H1a2 zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H92 zenon_H1ef zenon_H13e zenon_H141 zenon_H34 zenon_H53 zenon_H55 zenon_H5a zenon_H4e zenon_H139 zenon_H77 zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H13a zenon_H68 zenon_H82 zenon_H73 zenon_H4d zenon_H38 zenon_H48. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.32/22.48 exact (zenon_H6c zenon_H67). % 22.32/22.48 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.32/22.48 apply (zenon_L226_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.48 apply (zenon_L253_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.48 apply (zenon_L2007_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.48 apply (zenon_L193_); trivial. % 22.32/22.48 apply (zenon_L156_); trivial. % 22.32/22.48 apply (zenon_L165_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.32/22.48 apply (zenon_L1714_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.32/22.48 apply (zenon_L184_); trivial. % 22.32/22.48 apply (zenon_L246_); trivial. % 22.32/22.48 (* end of lemma zenon_L2008_ *) % 22.32/22.48 assert (zenon_L2009_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H92 zenon_H13e zenon_H1bf zenon_H1ef zenon_H89 zenon_H68 zenon_H2d zenon_Hf0 zenon_Hef zenon_H8b zenon_H16a. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.32/22.48 apply (zenon_L717_); trivial. % 22.32/22.48 apply (zenon_L645_); trivial. % 22.32/22.48 (* end of lemma zenon_L2009_ *) % 22.32/22.48 assert (zenon_L2010_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((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 (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H18d zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_H177 zenon_H11a zenon_H183 zenon_H55 zenon_H5a zenon_H4e zenon_H1e zenon_H48 zenon_H82 zenon_H181 zenon_H68 zenon_H115 zenon_H77 zenon_Ha9 zenon_H9e zenon_H1c3 zenon_H53 zenon_H189 zenon_H7e zenon_H18a. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.32/22.48 apply (zenon_L1986_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.32/22.48 apply (zenon_L209_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.32/22.48 apply (zenon_L139_); trivial. % 22.32/22.48 apply (zenon_L140_); trivial. % 22.32/22.48 (* end of lemma zenon_L2010_ *) % 22.32/22.48 assert (zenon_L2011_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (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 (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 22.32/22.48 do 0 intro. intros zenon_H13a zenon_H3d zenon_Ha0 zenon_H111 zenon_H53 zenon_Hb6 zenon_H16a zenon_H77 zenon_H8b zenon_H16b zenon_H117 zenon_H13d zenon_H48 zenon_H2c zenon_H1e zenon_H141 zenon_Ha9 zenon_Hf6. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.32/22.48 apply (zenon_L41_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.32/22.48 apply (zenon_L55_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.32/22.48 apply (zenon_L114_); trivial. % 22.32/22.48 apply (zenon_L92_); trivial. % 22.32/22.48 (* end of lemma zenon_L2011_ *) % 22.32/22.48 assert (zenon_L2012_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.32/22.48 do 0 intro. intros zenon_H183 zenon_H9d zenon_Ha9 zenon_Hef zenon_H11a zenon_H66 zenon_H177 zenon_H181. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.32/22.48 apply (zenon_L91_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.32/22.48 apply (zenon_L119_); trivial. % 22.32/22.48 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.32/22.48 apply (zenon_L122_); trivial. % 22.32/22.48 exact (zenon_H181 zenon_H17c). % 22.32/22.48 (* end of lemma zenon_L2012_ *) % 22.32/22.48 assert (zenon_L2013_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((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)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (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) (e1)) = (op (e3) (e2)))) -> (((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 (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.42/22.48 do 0 intro. intros zenon_H236 zenon_H1c3 zenon_Hbc zenon_H1d8 zenon_H140 zenon_H109 zenon_H111 zenon_H1c6 zenon_H183 zenon_H11a zenon_H6c zenon_H181 zenon_H19d zenon_H55 zenon_H5a zenon_H4e zenon_H139 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H77 zenon_H82 zenon_H173 zenon_H117 zenon_H104 zenon_H26a zenon_H7d zenon_H5d zenon_Hb2 zenon_H12e zenon_H1f1 zenon_H163 zenon_H24e zenon_H1b7 zenon_H1cd zenon_H121 zenon_H1cf zenon_H16b zenon_H15d zenon_H156 zenon_H164 zenon_H177 zenon_H129 zenon_H125 zenon_H18a zenon_H189 zenon_H186 zenon_H18d zenon_H73 zenon_H2c zenon_H1fe zenon_H141 zenon_H16a zenon_H8b zenon_Hef zenon_Hf0 zenon_H68 zenon_H13e zenon_H4d zenon_H131 zenon_H1ef zenon_H92 zenon_H53 zenon_H48 zenon_H13d zenon_H196. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.48 apply (zenon_L13_); trivial. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.48 apply (zenon_L13_); trivial. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.48 apply (zenon_L14_); trivial. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.48 apply (zenon_L15_); trivial. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.48 exact (zenon_H6c zenon_H67). % 22.42/22.48 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.48 apply (zenon_L214_); trivial. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.48 apply (zenon_L41_); trivial. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.48 apply (zenon_L55_); trivial. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.48 apply (zenon_L193_); trivial. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.48 apply (zenon_L5_); trivial. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.48 apply (zenon_L111_); trivial. % 22.42/22.48 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.49 exact (zenon_H13d zenon_H14c). % 22.42/22.49 apply (zenon_L2010_); trivial. % 22.42/22.49 apply (zenon_L2011_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L184_); trivial. % 22.42/22.49 apply (zenon_L1986_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.42/22.49 apply (zenon_L161_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L226_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.42/22.49 apply (zenon_L171_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.42/22.49 apply (zenon_L253_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.42/22.49 apply (zenon_L116_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.42/22.49 apply (zenon_L43_); trivial. % 22.42/22.49 apply (zenon_L2012_); trivial. % 22.42/22.49 apply (zenon_L325_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.42/22.49 apply (zenon_L171_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.42/22.49 apply (zenon_L326_); trivial. % 22.42/22.49 apply (zenon_L325_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_L65_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L184_); trivial. % 22.42/22.49 apply (zenon_L1994_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.42/22.49 apply (zenon_L717_); trivial. % 22.42/22.49 apply (zenon_L329_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.42/22.49 apply (zenon_L809_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.49 apply (zenon_L973_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.49 apply (zenon_L111_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.49 exact (zenon_H13d zenon_H14c). % 22.42/22.49 apply (zenon_L1162_); trivial. % 22.42/22.49 (* end of lemma zenon_L2013_ *) % 22.42/22.49 assert (zenon_L2014_ : (((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)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H117 zenon_H109 zenon_H9d zenon_Hb6 zenon_H53 zenon_H14c zenon_Ha0 zenon_Ha5 zenon_H195. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.42/22.49 apply (zenon_L73_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.42/22.49 apply (zenon_L113_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.42/22.49 apply (zenon_L278_); trivial. % 22.42/22.49 apply (zenon_L172_); trivial. % 22.42/22.49 (* end of lemma zenon_L2014_ *) % 22.42/22.49 assert (zenon_L2015_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.42/22.49 do 0 intro. intros zenon_H141 zenon_H68 zenon_H65 zenon_H48 zenon_H195 zenon_Ha5 zenon_Ha0 zenon_H53 zenon_Hb6 zenon_H9d zenon_H109 zenon_H117 zenon_H196 zenon_H38. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.49 apply (zenon_L27_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.49 apply (zenon_L111_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.49 apply (zenon_L2014_); trivial. % 22.42/22.49 apply (zenon_L1162_); trivial. % 22.42/22.49 (* end of lemma zenon_L2015_ *) % 22.42/22.49 assert (zenon_L2016_ : (((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 (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.42/22.49 do 0 intro. intros zenon_H13c zenon_H179 zenon_H173 zenon_Hdb zenon_H4d zenon_H141 zenon_H68 zenon_H65 zenon_H48 zenon_H195 zenon_Ha0 zenon_H53 zenon_Hb6 zenon_H9d zenon_H109 zenon_H117 zenon_H196 zenon_H38. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.42/22.49 apply (zenon_L123_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.42/22.49 apply (zenon_L120_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.42/22.49 apply (zenon_L124_); trivial. % 22.42/22.49 apply (zenon_L2015_); trivial. % 22.42/22.49 (* end of lemma zenon_L2016_ *) % 22.42/22.49 assert (zenon_L2017_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha9 zenon_H6e zenon_H111 zenon_H110 zenon_H38 zenon_Ha0. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 apply (zenon_L253_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.49 apply (zenon_L110_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.49 apply (zenon_L75_); trivial. % 22.42/22.49 apply (zenon_L156_); trivial. % 22.42/22.49 (* end of lemma zenon_L2017_ *) % 22.42/22.49 assert (zenon_L2018_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H139 zenon_H77 zenon_Ha0 zenon_H110 zenon_H111 zenon_Ha9 zenon_H47 zenon_Hb6 zenon_H13a zenon_H160 zenon_H177 zenon_H38 zenon_H68. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 apply (zenon_L251_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L2017_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_L122_); trivial. % 22.42/22.49 apply (zenon_L165_); trivial. % 22.42/22.49 (* end of lemma zenon_L2018_ *) % 22.42/22.49 assert (zenon_L2019_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (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)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H13f zenon_H196 zenon_Ha5 zenon_H195 zenon_H48 zenon_H65 zenon_H141 zenon_H4d zenon_H131 zenon_H117 zenon_H109 zenon_Hdd zenon_H181 zenon_H139 zenon_H77 zenon_Ha0 zenon_H111 zenon_Ha9 zenon_H47 zenon_H13a zenon_H177 zenon_H38 zenon_H68 zenon_H7f zenon_H9d zenon_H183 zenon_Hb6. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.42/22.49 apply (zenon_L30_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.42/22.49 apply (zenon_L2015_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.42/22.49 apply (zenon_L128_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.42/22.49 apply (zenon_L73_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.42/22.49 apply (zenon_L152_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.42/22.49 apply (zenon_L91_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.42/22.49 apply (zenon_L169_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.42/22.49 apply (zenon_L2018_); trivial. % 22.42/22.49 exact (zenon_H181 zenon_H17c). % 22.42/22.49 apply (zenon_L182_); trivial. % 22.42/22.49 (* end of lemma zenon_L2019_ *) % 22.42/22.49 assert (zenon_L2020_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H236 zenon_H1f zenon_H205 zenon_Ha9 zenon_H68 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H9e zenon_Ha0. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.42/22.49 exact (zenon_H1f zenon_H1e). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.42/22.49 exact (zenon_H205 zenon_H2a). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.42/22.49 apply (zenon_L983_); trivial. % 22.42/22.49 apply (zenon_L156_); trivial. % 22.42/22.49 (* end of lemma zenon_L2020_ *) % 22.42/22.49 assert (zenon_L2021_ : (((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 (e1) (e2)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H82 zenon_H4c zenon_H4e zenon_H4d zenon_H65 zenon_H77 zenon_H34 zenon_H48. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.49 exact (zenon_H4c zenon_H47). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.49 apply (zenon_L14_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.49 apply (zenon_L30_); trivial. % 22.42/22.49 apply (zenon_L456_); trivial. % 22.42/22.49 (* end of lemma zenon_L2021_ *) % 22.42/22.49 assert (zenon_L2022_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((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 (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (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) (e0)) = (op (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (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)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H204 zenon_H82 zenon_H4e zenon_H23d zenon_H236 zenon_H66 zenon_H68 zenon_H1f zenon_H15d zenon_Hb2 zenon_H240 zenon_H33 zenon_H48 zenon_H2c zenon_H77 zenon_H13a zenon_Hb6 zenon_H139 zenon_H23b zenon_H156 zenon_H4d zenon_H13c zenon_H117 zenon_H195 zenon_H109 zenon_H196 zenon_H141 zenon_H173 zenon_H179 zenon_H13f zenon_H183 zenon_H181 zenon_H111 zenon_H177 zenon_H131 zenon_H6f zenon_H1f1 zenon_He4 zenon_H65 zenon_Ha9 zenon_Ha0 zenon_H6c zenon_Hef zenon_H63 zenon_H12e zenon_H11a zenon_H1a2 zenon_Hbc zenon_H140 zenon_H1fe. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.42/22.49 apply (zenon_L1866_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.42/22.49 exact (zenon_H1f zenon_H1e). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.42/22.49 exact (zenon_H205 zenon_H2a). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.42/22.49 apply (zenon_L264_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.42/22.49 exact (zenon_H1f zenon_H1e). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 exact (zenon_Ha4 zenon_H9f). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.42/22.49 exact (zenon_Ha4 zenon_H9f). % 22.42/22.49 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.42/22.49 apply (zenon_L116_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.42/22.49 apply (zenon_L43_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.42/22.49 apply (zenon_L1882_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.42/22.49 apply (zenon_L486_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.42/22.49 apply (zenon_L2016_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.42/22.49 apply (zenon_L123_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.42/22.49 apply (zenon_L120_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.42/22.49 apply (zenon_L124_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.49 apply (zenon_L27_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.49 apply (zenon_L2019_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.49 apply (zenon_L1972_); trivial. % 22.42/22.49 apply (zenon_L1162_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.49 apply (zenon_L193_); trivial. % 22.42/22.49 apply (zenon_L2020_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_L489_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L94_); trivial. % 22.42/22.49 apply (zenon_L246_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.42/22.49 apply (zenon_L27_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 exact (zenon_Ha4 zenon_H9f). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.42/22.49 apply (zenon_L814_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.42/22.49 apply (zenon_L117_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.42/22.49 apply (zenon_L1973_); trivial. % 22.42/22.49 apply (zenon_L328_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.49 apply (zenon_L193_); trivial. % 22.42/22.49 apply (zenon_L156_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.42/22.49 exact (zenon_H1f zenon_H1e). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.42/22.49 exact (zenon_H1f zenon_H1e). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 exact (zenon_H4c zenon_H47). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_L65_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L94_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.49 exact (zenon_H4c zenon_H47). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.49 apply (zenon_L25_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.49 apply (zenon_L30_); trivial. % 22.42/22.49 apply (zenon_L1985_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.42/22.49 apply (zenon_L27_); trivial. % 22.42/22.49 apply (zenon_L2021_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.42/22.49 apply (zenon_L264_); trivial. % 22.42/22.49 exact (zenon_H238 zenon_H38). % 22.42/22.49 apply (zenon_L1861_); trivial. % 22.42/22.49 (* end of lemma zenon_L2022_ *) % 22.42/22.49 assert (zenon_L2023_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (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))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H15d zenon_H196 zenon_H93 zenon_H68 zenon_H48 zenon_H2a zenon_H73 zenon_H4d zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_H160 zenon_H177 zenon_H77. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_L352_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_L65_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L184_); trivial. % 22.42/22.49 apply (zenon_L1981_); trivial. % 22.42/22.49 (* end of lemma zenon_L2023_ *) % 22.42/22.49 assert (zenon_L2024_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (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 (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((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) (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (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 (e3) (e3)) = (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H236 zenon_Hca zenon_H2c zenon_H1a2 zenon_H4e zenon_H186 zenon_H189 zenon_H1a8 zenon_Hc2 zenon_H15d zenon_H24e zenon_H1cd zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1b7 zenon_H1b4 zenon_H1bb zenon_H77 zenon_H196 zenon_H93 zenon_H48 zenon_H13a zenon_Hb2 zenon_H156 zenon_H55 zenon_He4 zenon_Ha0 zenon_H117 zenon_H12e zenon_H25b zenon_H195 zenon_H20f zenon_Hf5 zenon_H25e zenon_H192 zenon_H18d zenon_H26d zenon_H19a zenon_H11a zenon_H164 zenon_H33 zenon_H104 zenon_H121 zenon_Hf0 zenon_Hb6 zenon_H4d zenon_H1c6 zenon_H13f zenon_H131 zenon_Hfa zenon_H163 zenon_H129 zenon_H179 zenon_H141 zenon_H13c zenon_H82 zenon_H94 zenon_H125 zenon_H73 zenon_H1f1 zenon_Ha9 zenon_H1cb zenon_H1fe zenon_Hcb zenon_H1c3 zenon_H109 zenon_Hc8 zenon_H209 zenon_H1c7 zenon_Hc4 zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_H160 zenon_H177 zenon_H68. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.42/22.49 apply (zenon_L1982_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.42/22.49 apply (zenon_L2023_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.42/22.49 apply (zenon_L898_); trivial. % 22.42/22.49 apply (zenon_L1967_); trivial. % 22.42/22.49 (* end of lemma zenon_L2024_ *) % 22.42/22.49 assert (zenon_L2025_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (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))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (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 (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H236 zenon_H6c zenon_H1fe zenon_H1a8 zenon_H189 zenon_H13a zenon_Ha9 zenon_Hef zenon_H173 zenon_H179 zenon_H19a zenon_H12e zenon_H164 zenon_H73 zenon_H195 zenon_Hfa zenon_H4e zenon_H4d zenon_H139 zenon_H196 zenon_H177 zenon_H156 zenon_H55 zenon_H18a zenon_H7d zenon_Hbc zenon_H160 zenon_H209 zenon_H212 zenon_He4 zenon_H68 zenon_H1a2 zenon_H181 zenon_H1b7 zenon_H1cd zenon_H24e zenon_H15d zenon_H2c zenon_H141 zenon_Hb6 zenon_Ha0 zenon_H82 zenon_Hc2 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H120. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.42/22.49 apply (zenon_L1982_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.42/22.49 apply (zenon_L2023_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.42/22.49 apply (zenon_L979_); trivial. % 22.42/22.49 apply (zenon_L555_); trivial. % 22.42/22.49 (* end of lemma zenon_L2025_ *) % 22.42/22.49 assert (zenon_L2026_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H15d zenon_Hbc zenon_H94 zenon_H125 zenon_H48 zenon_H2a zenon_H73 zenon_H139 zenon_H6c zenon_H195 zenon_H93 zenon_H4d zenon_H173 zenon_H25 zenon_H68 zenon_Hfa zenon_H160 zenon_H177 zenon_H77. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_L541_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_L65_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L184_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L976_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_L122_); trivial. % 22.42/22.49 apply (zenon_L98_); trivial. % 22.42/22.49 (* end of lemma zenon_L2026_ *) % 22.42/22.49 assert (zenon_L2027_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((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) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (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 (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) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (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 (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H236 zenon_Hc4 zenon_H1fe zenon_H125 zenon_H94 zenon_H13c zenon_H1c3 zenon_H19a zenon_H18d zenon_H129 zenon_H1c6 zenon_H117 zenon_H12e zenon_H25b zenon_H195 zenon_H20f zenon_Hf5 zenon_H1b4 zenon_H25e zenon_H192 zenon_Hfa zenon_H163 zenon_H104 zenon_H121 zenon_H131 zenon_H13f zenon_Hf0 zenon_H141 zenon_Hb2 zenon_H73 zenon_H179 zenon_H1a2 zenon_H48 zenon_H93 zenon_H196 zenon_H77 zenon_H82 zenon_H18a zenon_He4 zenon_H1bb zenon_H181 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H24e zenon_H162 zenon_H212 zenon_H33 zenon_Hbc zenon_H164 zenon_H55 zenon_H156 zenon_H4d zenon_H4e zenon_H13a zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H15d zenon_Hc2 zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_H160 zenon_H177 zenon_H68. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.42/22.49 apply (zenon_L1982_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.42/22.49 apply (zenon_L1982_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.42/22.49 apply (zenon_L2026_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_L352_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_L892_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L184_); trivial. % 22.42/22.49 apply (zenon_L1981_); trivial. % 22.42/22.49 apply (zenon_L870_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.42/22.49 apply (zenon_L981_); trivial. % 22.42/22.49 apply (zenon_L1967_); trivial. % 22.42/22.49 (* end of lemma zenon_L2027_ *) % 22.42/22.49 assert (zenon_L2028_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H204 zenon_H33 zenon_H9d zenon_H23d zenon_H1f zenon_H139 zenon_H9e zenon_Ha9 zenon_H68 zenon_Hef zenon_H173 zenon_H6c zenon_Ha0 zenon_H236. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.42/22.49 apply (zenon_L2020_); trivial. % 22.42/22.49 apply (zenon_L611_); trivial. % 22.42/22.49 (* end of lemma zenon_L2028_ *) % 22.42/22.49 assert (zenon_L2029_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H13a zenon_Ha0 zenon_H1e zenon_Hb6 zenon_H3d zenon_Ha9 zenon_H66 zenon_Hb9 zenon_H196. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 apply (zenon_L41_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.49 apply (zenon_L55_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.49 apply (zenon_L193_); trivial. % 22.42/22.49 apply (zenon_L154_); trivial. % 22.42/22.49 (* end of lemma zenon_L2029_ *) % 22.42/22.49 assert (zenon_L2030_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H139 zenon_H6c zenon_H77 zenon_Hb9 zenon_Ha9 zenon_H3d zenon_Hb6 zenon_H1e zenon_Ha0 zenon_H13a zenon_H16a zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_H196. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L214_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_L2029_); trivial. % 22.42/22.49 apply (zenon_L621_); trivial. % 22.42/22.49 (* end of lemma zenon_L2030_ *) % 22.42/22.49 assert (zenon_L2031_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 22.42/22.49 do 0 intro. intros zenon_H140 zenon_H68 zenon_H66 zenon_H4d zenon_H20f zenon_H136 zenon_H104 zenon_H48 zenon_H7f zenon_H33 zenon_H1e zenon_H164 zenon_Ha0 zenon_Hbb. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.42/22.49 apply (zenon_L264_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.42/22.49 apply (zenon_L117_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.42/22.49 apply (zenon_L7_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.42/22.49 apply (zenon_L57_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.42/22.49 apply (zenon_L257_); trivial. % 22.42/22.49 apply (zenon_L421_); trivial. % 22.42/22.49 apply (zenon_L80_); trivial. % 22.42/22.49 (* end of lemma zenon_L2031_ *) % 22.42/22.49 assert (zenon_L2032_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 22.42/22.49 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_Hdb zenon_H156 zenon_H55 zenon_H54 zenon_H140 zenon_H68 zenon_H66 zenon_H4d zenon_H20f zenon_H136 zenon_H104 zenon_H48 zenon_H33 zenon_H1e zenon_H164 zenon_Ha0 zenon_Hbb. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.42/22.49 apply (zenon_L55_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.42/22.49 apply (zenon_L486_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.42/22.49 apply (zenon_L15_); trivial. % 22.42/22.49 apply (zenon_L2031_); trivial. % 22.42/22.49 (* end of lemma zenon_L2032_ *) % 22.42/22.49 assert (zenon_L2033_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((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)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H22d zenon_H2c zenon_Hbb zenon_Ha0 zenon_H164 zenon_H1e zenon_H33 zenon_H48 zenon_H104 zenon_H136 zenon_H20f zenon_H4d zenon_H66 zenon_H68 zenon_H140 zenon_H55 zenon_H156 zenon_Hdb zenon_Hb6 zenon_He4 zenon_H7b zenon_Hb9 zenon_H94. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H2d | zenon_intro zenon_H22e ]. % 22.42/22.49 apply (zenon_L5_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H54 | zenon_intro zenon_H22f ]. % 22.42/22.49 apply (zenon_L2032_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H65 | zenon_intro zenon_Ha8 ]. % 22.42/22.49 exact (zenon_H7b zenon_H65). % 22.42/22.49 apply (zenon_L47_); trivial. % 22.42/22.49 (* end of lemma zenon_L2033_ *) % 22.42/22.49 assert (zenon_L2034_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H25b zenon_H20f zenon_H167 zenon_H186 zenon_H4d zenon_H195 zenon_H93 zenon_Ha6 zenon_H5d. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H136 | zenon_intro zenon_H25c ]. % 22.42/22.49 apply (zenon_L421_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H5c | zenon_intro zenon_H25d ]. % 22.42/22.49 apply (zenon_L138_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Ha5 ]. % 22.42/22.49 apply (zenon_L228_); trivial. % 22.42/22.49 apply (zenon_L42_); trivial. % 22.42/22.49 (* end of lemma zenon_L2034_ *) % 22.42/22.49 assert (zenon_L2035_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (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) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H19a zenon_H155 zenon_H94 zenon_Hb9 zenon_H7b zenon_He4 zenon_Hb6 zenon_Hdb zenon_H156 zenon_H55 zenon_H140 zenon_H66 zenon_H104 zenon_H48 zenon_H33 zenon_H1e zenon_H164 zenon_Ha0 zenon_Hbb zenon_H2c zenon_H22d zenon_H68 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H195 zenon_H93 zenon_Ha6 zenon_H5d. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.42/22.49 apply (zenon_L246_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.42/22.49 apply (zenon_L2033_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.42/22.49 apply (zenon_L158_); trivial. % 22.42/22.49 apply (zenon_L2034_); trivial. % 22.42/22.49 (* end of lemma zenon_L2035_ *) % 22.42/22.49 assert (zenon_L2036_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (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) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H16a zenon_H1ba zenon_H8b zenon_H19a zenon_H155 zenon_H94 zenon_Hb9 zenon_H7b zenon_He4 zenon_Hb6 zenon_Hdb zenon_H156 zenon_H55 zenon_H140 zenon_H66 zenon_H104 zenon_H48 zenon_H33 zenon_H1e zenon_H164 zenon_Ha0 zenon_Hbb zenon_H2c zenon_H22d zenon_H68 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H195 zenon_Ha6 zenon_H5d. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.42/22.49 exact (zenon_H7b zenon_H65). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.42/22.49 exact (zenon_H1ba zenon_H6d). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.42/22.49 exact (zenon_H8b zenon_H8a). % 22.42/22.49 apply (zenon_L2035_); trivial. % 22.42/22.49 (* end of lemma zenon_L2036_ *) % 22.42/22.49 assert (zenon_L2037_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (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)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H139 zenon_H6c zenon_H2a zenon_H7e zenon_H7b zenon_H25 zenon_H68 zenon_H1d5 zenon_H125 zenon_H155 zenon_H77. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L147_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_L651_); trivial. % 22.42/22.49 apply (zenon_L98_); trivial. % 22.42/22.49 (* end of lemma zenon_L2037_ *) % 22.42/22.49 assert (zenon_L2038_ : (((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)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H15d zenon_H73 zenon_H82 zenon_H196 zenon_Hb9 zenon_Hbb zenon_H4e zenon_H77 zenon_H13a zenon_H177 zenon_H68 zenon_H183 zenon_H55 zenon_H4d zenon_H156 zenon_He4 zenon_Ha0 zenon_H2a zenon_Ha9 zenon_Hb6 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H34 zenon_H48. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_L376_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_L65_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L184_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.49 apply (zenon_L376_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.49 apply (zenon_L14_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.49 apply (zenon_L1997_); trivial. % 22.42/22.49 apply (zenon_L456_); trivial. % 22.42/22.49 (* end of lemma zenon_L2038_ *) % 22.42/22.49 assert (zenon_L2039_ : (((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)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Hef zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H25b zenon_H38 zenon_Hf5 zenon_H20f zenon_H93 zenon_Hb9 zenon_H195. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.42/22.49 apply (zenon_L456_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.42/22.49 apply (zenon_L146_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.42/22.49 apply (zenon_L687_); trivial. % 22.42/22.49 apply (zenon_L671_); trivial. % 22.42/22.49 (* end of lemma zenon_L2039_ *) % 22.42/22.49 assert (zenon_L2040_ : (((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)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H12e zenon_H77 zenon_H102 zenon_He0 zenon_H48 zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Hef zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H25b zenon_H38 zenon_Hf5 zenon_H20f zenon_H93 zenon_Hb9 zenon_H195. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.42/22.49 apply (zenon_L71_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.42/22.49 apply (zenon_L57_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.42/22.49 apply (zenon_L687_); trivial. % 22.42/22.49 apply (zenon_L671_); trivial. % 22.42/22.49 (* end of lemma zenon_L2040_ *) % 22.42/22.49 assert (zenon_L2041_ : (((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)) = (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) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (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)) = (e0)) -> (~((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) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hf0 zenon_H8b zenon_H164 zenon_H192 zenon_H3d zenon_Hf5 zenon_H38 zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hef zenon_Ha0 zenon_Hb6 zenon_H48 zenon_H102 zenon_H77 zenon_H12e zenon_H14c zenon_H104 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H10c zenon_Hb9 zenon_H195. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.42/22.49 exact (zenon_H7b zenon_H65). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.42/22.49 apply (zenon_L61_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.42/22.49 exact (zenon_H8b zenon_H8a). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.42/22.49 apply (zenon_L2039_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.42/22.49 apply (zenon_L2040_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.42/22.49 apply (zenon_L257_); trivial. % 22.42/22.49 apply (zenon_L684_); trivial. % 22.42/22.49 (* end of lemma zenon_L2041_ *) % 22.42/22.49 assert (zenon_L2042_ : (((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) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hf0 zenon_Hef zenon_H8b zenon_H18d zenon_H7f zenon_H1cd zenon_H14c zenon_H48 zenon_H186 zenon_H139 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H47 zenon_H13a zenon_H68 zenon_H201 zenon_H77 zenon_H25b zenon_H38 zenon_Hf5 zenon_H20f zenon_Hb9 zenon_H195. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.42/22.49 exact (zenon_H7b zenon_H65). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.42/22.49 apply (zenon_L61_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.42/22.49 exact (zenon_H8b zenon_H8a). % 22.42/22.49 apply (zenon_L2005_); trivial. % 22.42/22.49 (* end of lemma zenon_L2042_ *) % 22.42/22.49 assert (zenon_L2043_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (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 (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (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))))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 22.42/22.49 do 0 intro. intros zenon_H141 zenon_H131 zenon_H1ef zenon_H13e zenon_H34 zenon_Hbc zenon_H4d zenon_He4 zenon_Hdb zenon_H156 zenon_H1bb zenon_H18a zenon_H1b7 zenon_H1cf zenon_H271 zenon_H1d8 zenon_H1b4 zenon_H111 zenon_Hcc zenon_H270 zenon_H1a2 zenon_H191 zenon_H1cb zenon_H140 zenon_H195 zenon_H20f zenon_Hf5 zenon_H38 zenon_H25b zenon_H77 zenon_H201 zenon_H68 zenon_H13a zenon_H47 zenon_Ha9 zenon_Hb6 zenon_H139 zenon_H186 zenon_H48 zenon_H1cd zenon_H7f zenon_H18d zenon_H8b zenon_Hef zenon_Hf0 zenon_H7b zenon_H16a zenon_Ha0 zenon_Hb9. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.49 apply (zenon_L755_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.42/22.49 apply (zenon_L1107_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.42/22.49 apply (zenon_L117_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.42/22.49 apply (zenon_L2042_); trivial. % 22.42/22.49 apply (zenon_L328_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.49 apply (zenon_L2042_); trivial. % 22.42/22.49 apply (zenon_L77_); trivial. % 22.42/22.49 (* end of lemma zenon_L2043_ *) % 22.42/22.49 assert (zenon_L2044_ : (((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)) = (e2))) -> (((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)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H16a zenon_H7b zenon_Hf0 zenon_H8b zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Hef zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H25b zenon_H38 zenon_Hf5 zenon_H20f zenon_Hb9 zenon_H195. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.42/22.49 exact (zenon_H7b zenon_H65). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.42/22.49 apply (zenon_L61_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.42/22.49 exact (zenon_H8b zenon_H8a). % 22.42/22.49 apply (zenon_L2039_); trivial. % 22.42/22.49 (* end of lemma zenon_L2044_ *) % 22.42/22.49 assert (zenon_L2045_ : (((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)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((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 (e2) (e1)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (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))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 22.42/22.49 do 0 intro. intros zenon_H140 zenon_H196 zenon_H9f zenon_H1b4 zenon_H25e zenon_H77 zenon_H156 zenon_H68 zenon_H1cf zenon_Hdd zenon_H4d zenon_H195 zenon_Hb9 zenon_H20f zenon_Hf5 zenon_H38 zenon_H25b zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hef zenon_Hb6 zenon_H192 zenon_H3d zenon_H34 zenon_H48 zenon_H12e zenon_H8b zenon_Hf0 zenon_H7b zenon_H16a zenon_Ha0 zenon_Hbb. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.42/22.49 apply (zenon_L991_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.42/22.49 apply (zenon_L117_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.42/22.49 apply (zenon_L2044_); trivial. % 22.42/22.49 apply (zenon_L80_); trivial. % 22.42/22.49 (* end of lemma zenon_L2045_ *) % 22.42/22.49 assert (zenon_L2046_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((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) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (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) (e1)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H82 zenon_H4e zenon_H68 zenon_H38 zenon_H13a zenon_H196 zenon_H16a zenon_H7b zenon_Hf0 zenon_H8b zenon_H12e zenon_H192 zenon_Hef zenon_H1a2 zenon_H25b zenon_Hf5 zenon_H20f zenon_Hb9 zenon_H195 zenon_H140 zenon_H1b4 zenon_H25e zenon_H77 zenon_H156 zenon_H1cf zenon_H4d zenon_Hbb zenon_H141 zenon_Hb6 zenon_H3d zenon_Ha9 zenon_Ha0 zenon_H173 zenon_H6c zenon_H139 zenon_H34 zenon_H48. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.49 apply (zenon_L1149_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.49 apply (zenon_L14_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L226_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.49 apply (zenon_L217_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.49 apply (zenon_L2045_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.49 apply (zenon_L2044_); trivial. % 22.42/22.49 apply (zenon_L1162_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.49 apply (zenon_L55_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.49 apply (zenon_L193_); trivial. % 22.42/22.49 apply (zenon_L156_); trivial. % 22.42/22.49 apply (zenon_L165_); trivial. % 22.42/22.49 apply (zenon_L456_); trivial. % 22.42/22.49 (* end of lemma zenon_L2046_ *) % 22.42/22.49 assert (zenon_L2047_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e0)) -> False). % 22.42/22.49 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_Hdb zenon_H156 zenon_H4d zenon_H94 zenon_Hb9 zenon_H7b zenon_H55 zenon_H92 zenon_H13e zenon_H1bf zenon_H1ef zenon_H89 zenon_H22d zenon_H8b zenon_H77 zenon_H16a zenon_H48 zenon_He0. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.42/22.49 apply (zenon_L55_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.42/22.49 apply (zenon_L486_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.42/22.49 apply (zenon_L998_); trivial. % 22.42/22.49 apply (zenon_L57_); trivial. % 22.42/22.49 (* end of lemma zenon_L2047_ *) % 22.42/22.49 assert (zenon_L2048_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H25b zenon_H20f zenon_H167 zenon_Hf5 zenon_H155 zenon_H93 zenon_H117 zenon_Hb6 zenon_H54 zenon_Hdb zenon_H6f zenon_H14c zenon_Ha0 zenon_H195. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H136 | zenon_intro zenon_H25c ]. % 22.42/22.49 apply (zenon_L421_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H5c | zenon_intro zenon_H25d ]. % 22.42/22.49 apply (zenon_L192_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Ha5 ]. % 22.42/22.49 apply (zenon_L228_); trivial. % 22.42/22.49 apply (zenon_L1466_); trivial. % 22.42/22.49 (* end of lemma zenon_L2048_ *) % 22.42/22.49 assert (zenon_L2049_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (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 (e3) (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 (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_Hf0 zenon_Hef zenon_H164 zenon_H1e zenon_H33 zenon_H48 zenon_H16a zenon_H77 zenon_H8b zenon_H22d zenon_H89 zenon_H1ef zenon_H1bf zenon_H13e zenon_H92 zenon_H55 zenon_H7b zenon_Hb9 zenon_H94 zenon_H4d zenon_H156 zenon_He4 zenon_Hbb zenon_H25b zenon_H20f zenon_Hf5 zenon_H155 zenon_H117 zenon_Hb6 zenon_H54 zenon_Hdb zenon_H6f zenon_H14c zenon_Ha0 zenon_H195. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.42/22.49 exact (zenon_H7b zenon_H65). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.42/22.49 apply (zenon_L61_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.42/22.49 exact (zenon_H8b zenon_H8a). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.42/22.49 apply (zenon_L7_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.42/22.49 apply (zenon_L2047_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.42/22.49 apply (zenon_L80_); trivial. % 22.42/22.49 apply (zenon_L2048_); trivial. % 22.42/22.49 (* end of lemma zenon_L2049_ *) % 22.42/22.49 assert (zenon_L2050_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H13a zenon_Ha0 zenon_H1e zenon_H7e zenon_H7d zenon_H16a zenon_H77 zenon_H8b zenon_H22d zenon_H89 zenon_H1ef zenon_H1bf zenon_H13e zenon_H92 zenon_H55 zenon_H7b zenon_H94 zenon_H4d zenon_H156 zenon_Hb6 zenon_He4 zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 apply (zenon_L41_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.49 apply (zenon_L1049_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.49 apply (zenon_L178_); trivial. % 22.42/22.49 apply (zenon_L154_); trivial. % 22.42/22.49 (* end of lemma zenon_L2050_ *) % 22.42/22.49 assert (zenon_L2051_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((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) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (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) (e2)) = (op (e1) (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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((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))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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 (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 22.42/22.49 do 0 intro. intros zenon_H173 zenon_H212 zenon_H179 zenon_H7d zenon_Hbc zenon_H141 zenon_H104 zenon_H1bb zenon_He4 zenon_H19a zenon_H13a zenon_Hc0 zenon_H129 zenon_H1cb zenon_H191 zenon_H270 zenon_Hcc zenon_H1cd zenon_H111 zenon_H139 zenon_H1d8 zenon_H271 zenon_H1b7 zenon_H18a zenon_H201 zenon_H1d5 zenon_H94 zenon_H55 zenon_H92 zenon_H13e zenon_H1bf zenon_H1ef zenon_H89 zenon_H22d zenon_H13c zenon_H177 zenon_H73 zenon_H125 zenon_H15d zenon_H25 zenon_H4e zenon_H195 zenon_Hb9 zenon_H10c zenon_H4d zenon_H186 zenon_H20f zenon_H25b zenon_H12e zenon_H77 zenon_H102 zenon_H48 zenon_Hb6 zenon_Hef zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H38 zenon_Hf5 zenon_H140 zenon_H196 zenon_H9f zenon_H1b4 zenon_H25e zenon_H156 zenon_H68 zenon_H1cf zenon_Hdd zenon_H192 zenon_H3d zenon_H8b zenon_Hf0 zenon_H7b zenon_H16a zenon_H164 zenon_Ha0 zenon_Hbb. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.42/22.49 apply (zenon_L1002_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.42/22.49 apply (zenon_L274_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.42/22.49 exact (zenon_H7b zenon_H65). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.42/22.49 apply (zenon_L61_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.42/22.49 exact (zenon_H8b zenon_H8a). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.42/22.49 apply (zenon_L2045_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.42/22.49 apply (zenon_L2040_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.42/22.49 apply (zenon_L80_); trivial. % 22.42/22.49 apply (zenon_L684_); trivial. % 22.42/22.49 apply (zenon_L80_); trivial. % 22.42/22.49 (* end of lemma zenon_L2051_ *) % 22.42/22.49 assert (zenon_L2052_ : ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((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 (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> False). % 22.42/22.49 do 0 intro. intros zenon_H8f zenon_H15d zenon_H4e zenon_Hb2 zenon_Hbc zenon_H19a zenon_H186 zenon_H195 zenon_H5d zenon_H25b zenon_H2c zenon_He4 zenon_H68 zenon_H164 zenon_H20f zenon_H104 zenon_H33 zenon_Hbb zenon_H140 zenon_H55 zenon_H156 zenon_H94 zenon_H22d zenon_H177 zenon_H173 zenon_H82 zenon_H4d zenon_H73 zenon_H6c zenon_H77 zenon_H13a zenon_Hb9 zenon_H196 zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H139 zenon_H48 zenon_H1fe zenon_H1ef zenon_H131 zenon_H13e zenon_H125 zenon_H1d5 zenon_H163 zenon_H183 zenon_H13c zenon_H19d zenon_H190 zenon_H6f zenon_H266 zenon_H13f zenon_H1c6 zenon_H129 zenon_H7d zenon_Hc0 zenon_H1bb zenon_H12e zenon_Hf5 zenon_H1b4 zenon_H25e zenon_H192 zenon_H1cf zenon_H212 zenon_H179 zenon_H18a zenon_H1b7 zenon_H270 zenon_Hcc zenon_H1cd zenon_H111 zenon_H1d8 zenon_H271 zenon_H1cb zenon_H1a2 zenon_H18d zenon_H201 zenon_H141 zenon_H92 zenon_H26d zenon_H236 zenon_Hf0 zenon_Hef zenon_H8b zenon_H16a zenon_H117 zenon_H89 zenon_H91. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.42/22.49 apply (zenon_L779_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_L13_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_L2030_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L184_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.49 apply (zenon_L13_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.49 apply (zenon_L14_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L226_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 apply (zenon_L41_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.42/22.49 apply (zenon_L41_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.42/22.49 apply (zenon_L2036_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.42/22.49 apply (zenon_L151_); trivial. % 22.42/22.49 apply (zenon_L48_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.49 apply (zenon_L178_); trivial. % 22.42/22.49 apply (zenon_L154_); trivial. % 22.42/22.49 apply (zenon_L98_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L226_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 apply (zenon_L41_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.42/22.49 apply (zenon_L41_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.42/22.49 apply (zenon_L2036_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.42/22.49 apply (zenon_L47_); trivial. % 22.42/22.49 apply (zenon_L134_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.49 apply (zenon_L178_); trivial. % 22.42/22.49 apply (zenon_L154_); trivial. % 22.42/22.49 apply (zenon_L621_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.42/22.49 apply (zenon_L161_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_L376_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_L65_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L184_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.49 apply (zenon_L934_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.49 apply (zenon_L25_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L147_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 apply (zenon_L686_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.49 apply (zenon_L53_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.49 apply (zenon_L193_); trivial. % 22.42/22.49 apply (zenon_L115_); trivial. % 22.42/22.49 apply (zenon_L98_); trivial. % 22.42/22.49 apply (zenon_L2037_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.42/22.49 apply (zenon_L755_); trivial. % 22.42/22.49 apply (zenon_L2038_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.42/22.49 apply (zenon_L990_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.42/22.49 apply (zenon_L1999_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_L934_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L214_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.42/22.49 apply (zenon_L171_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.42/22.49 exact (zenon_H7b zenon_H65). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.42/22.49 apply (zenon_L116_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.42/22.49 apply (zenon_L756_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.42/22.49 apply (zenon_L274_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.42/22.49 apply (zenon_L2041_); trivial. % 22.42/22.49 apply (zenon_L80_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.42/22.49 apply (zenon_L124_); trivial. % 22.42/22.49 apply (zenon_L172_); trivial. % 22.42/22.49 apply (zenon_L621_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L184_); trivial. % 22.42/22.49 apply (zenon_L246_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.42/22.49 apply (zenon_L1008_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L1362_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 apply (zenon_L253_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.42/22.49 apply (zenon_L55_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.42/22.49 apply (zenon_L486_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.49 apply (zenon_L730_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.49 apply (zenon_L111_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.42/22.49 exact (zenon_H7b zenon_H65). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.42/22.49 exact (zenon_H1ba zenon_H6d). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.42/22.49 exact (zenon_H8b zenon_H8a). % 22.42/22.49 apply (zenon_L2006_); trivial. % 22.42/22.49 apply (zenon_L766_); trivial. % 22.42/22.49 apply (zenon_L2043_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.49 apply (zenon_L193_); trivial. % 22.42/22.49 apply (zenon_L156_); trivial. % 22.42/22.49 apply (zenon_L165_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_L2046_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L184_); trivial. % 22.42/22.49 apply (zenon_L246_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.42/22.49 apply (zenon_L779_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_L13_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_L2030_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L184_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.49 apply (zenon_L13_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.49 apply (zenon_L14_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L226_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 apply (zenon_L41_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.42/22.49 apply (zenon_L264_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.42/22.49 apply (zenon_L117_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.42/22.49 apply (zenon_L2049_); trivial. % 22.42/22.49 apply (zenon_L80_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.49 apply (zenon_L178_); trivial. % 22.42/22.49 apply (zenon_L154_); trivial. % 22.42/22.49 apply (zenon_L621_); trivial. % 22.42/22.49 apply (zenon_L2050_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.42/22.49 apply (zenon_L161_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_L934_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_L65_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.49 apply (zenon_L184_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.49 apply (zenon_L376_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.49 apply (zenon_L25_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L226_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.42/22.49 apply (zenon_L65_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.42/22.49 apply (zenon_L486_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.42/22.49 apply (zenon_L15_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.42/22.49 apply (zenon_L116_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.42/22.49 apply (zenon_L1001_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.42/22.49 apply (zenon_L117_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.42/22.49 apply (zenon_L685_); trivial. % 22.42/22.49 apply (zenon_L80_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.42/22.49 apply (zenon_L617_); trivial. % 22.42/22.49 apply (zenon_L172_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.49 apply (zenon_L53_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.49 apply (zenon_L193_); trivial. % 22.42/22.49 apply (zenon_L115_); trivial. % 22.42/22.49 apply (zenon_L621_); trivial. % 22.42/22.49 apply (zenon_L2037_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.42/22.49 apply (zenon_L755_); trivial. % 22.42/22.49 apply (zenon_L2038_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.42/22.49 apply (zenon_L1005_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.42/22.49 apply (zenon_L1999_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.49 apply (zenon_L934_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.49 apply (zenon_L1149_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.49 apply (zenon_L25_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.49 apply (zenon_L226_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.42/22.49 exact (zenon_H6c zenon_H67). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.42/22.49 apply (zenon_L171_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.42/22.49 exact (zenon_H7b zenon_H65). % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.42/22.49 apply (zenon_L116_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.49 apply (zenon_L217_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.49 apply (zenon_L2051_); trivial. % 22.42/22.49 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.49 apply (zenon_L2041_); trivial. % 22.42/22.49 apply (zenon_L77_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.42/22.50 apply (zenon_L124_); trivial. % 22.42/22.50 apply (zenon_L172_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.50 apply (zenon_L933_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.50 apply (zenon_L193_); trivial. % 22.42/22.50 apply (zenon_L156_); trivial. % 22.42/22.50 apply (zenon_L621_); trivial. % 22.42/22.50 apply (zenon_L2003_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.50 apply (zenon_L184_); trivial. % 22.42/22.50 apply (zenon_L246_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.42/22.50 apply (zenon_L755_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.50 apply (zenon_L253_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.42/22.50 apply (zenon_L55_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.42/22.50 apply (zenon_L486_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.42/22.50 apply (zenon_L998_); trivial. % 22.42/22.50 apply (zenon_L2043_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.50 apply (zenon_L178_); trivial. % 22.42/22.50 apply (zenon_L154_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.50 apply (zenon_L2046_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.50 apply (zenon_L184_); trivial. % 22.42/22.50 apply (zenon_L246_); trivial. % 22.42/22.50 apply (zenon_L130_); trivial. % 22.42/22.50 (* end of lemma zenon_L2052_ *) % 22.42/22.50 assert (zenon_L2053_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (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))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (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 (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (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). % 22.42/22.50 do 0 intro. intros zenon_H15d zenon_Hbc zenon_H131 zenon_H1f1 zenon_H13f zenon_H1a2 zenon_H6f zenon_H117 zenon_H140 zenon_H34 zenon_H16a zenon_Hf0 zenon_H8b zenon_H12e zenon_H1b7 zenon_H1cb zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H183 zenon_H11a zenon_H68 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H77 zenon_H4e zenon_Hbb zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H13a zenon_H82 zenon_H73 zenon_H4d zenon_H38 zenon_H48. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.50 exact (zenon_H6c zenon_H67). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.50 apply (zenon_L1362_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.50 apply (zenon_L253_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.50 apply (zenon_L1977_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.50 apply (zenon_L178_); trivial. % 22.42/22.50 apply (zenon_L156_); trivial. % 22.42/22.50 apply (zenon_L165_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.50 apply (zenon_L1363_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.50 apply (zenon_L14_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.50 apply (zenon_L1970_); trivial. % 22.42/22.50 apply (zenon_L456_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.50 apply (zenon_L184_); trivial. % 22.42/22.50 apply (zenon_L246_); trivial. % 22.42/22.50 (* end of lemma zenon_L2053_ *) % 22.42/22.50 assert (zenon_L2054_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 22.42/22.50 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_Hdb zenon_H156 zenon_H4d zenon_H129 zenon_H8b zenon_H77 zenon_H7b zenon_H16a zenon_H212 zenon_He0 zenon_H7d zenon_H18a zenon_H17c zenon_Hbb zenon_Hbc. % 22.42/22.50 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.42/22.50 apply (zenon_L55_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.42/22.50 apply (zenon_L486_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.42/22.50 apply (zenon_L127_); trivial. % 22.42/22.50 apply (zenon_L1375_); trivial. % 22.42/22.50 (* end of lemma zenon_L2054_ *) % 22.42/22.50 assert (zenon_L2055_ : (((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))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (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 (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 22.42/22.50 do 0 intro. intros zenon_H183 zenon_H1a2 zenon_Ha9 zenon_H66 zenon_H14c zenon_Ha0 zenon_H13f zenon_Ha8 zenon_H1f1 zenon_H131 zenon_H12e zenon_H11a zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H73 zenon_H68 zenon_H1e zenon_H93 zenon_H196 zenon_H15d zenon_He4 zenon_Hb6 zenon_Hdb zenon_H156 zenon_H4d zenon_H129 zenon_H8b zenon_H77 zenon_H7b zenon_H16a zenon_H212 zenon_He0 zenon_H7d zenon_H18a zenon_Hbb zenon_Hbc. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.42/22.50 apply (zenon_L1990_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.42/22.50 apply (zenon_L119_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.42/22.50 apply (zenon_L1982_); trivial. % 22.42/22.50 apply (zenon_L2054_); trivial. % 22.42/22.50 (* end of lemma zenon_L2055_ *) % 22.42/22.50 assert (zenon_L2056_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (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 (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (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) (e2)) = (e0)) -> (~((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) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 22.42/22.50 do 0 intro. intros zenon_H164 zenon_H48 zenon_H7e zenon_Hbc zenon_Hbb zenon_H18a zenon_H7d zenon_H212 zenon_H16a zenon_H7b zenon_H77 zenon_H8b zenon_H129 zenon_H156 zenon_Hdb zenon_Hb6 zenon_He4 zenon_H15d zenon_H196 zenon_H1e zenon_H68 zenon_H73 zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_H177 zenon_H11a zenon_H12e zenon_H131 zenon_H1f1 zenon_Ha8 zenon_H13f zenon_Ha0 zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H183 zenon_H14c zenon_H104 zenon_H25b zenon_H20f zenon_H186 zenon_H4d zenon_H195 zenon_H93 zenon_Ha6 zenon_H5d. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.42/22.50 apply (zenon_L456_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.42/22.50 apply (zenon_L2055_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.42/22.50 apply (zenon_L257_); trivial. % 22.42/22.50 apply (zenon_L2034_); trivial. % 22.42/22.50 (* end of lemma zenon_L2056_ *) % 22.42/22.50 assert (zenon_L2057_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((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) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (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) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (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)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((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))))) -> (~((e1) = (e2))) -> False). % 22.42/22.50 do 0 intro. intros zenon_Hf0 zenon_H1c6 zenon_H189 zenon_H1b7 zenon_H18d zenon_H1cd zenon_H82 zenon_H4e zenon_Hb6 zenon_Hbb zenon_H177 zenon_Hb2 zenon_H117 zenon_H191 zenon_H19a zenon_H94 zenon_H55 zenon_H140 zenon_H2c zenon_H22d zenon_H25b zenon_H20f zenon_H186 zenon_H195 zenon_H5d zenon_H13e zenon_H1ef zenon_H68 zenon_H8b zenon_H53 zenon_H7b zenon_H16a zenon_H5a zenon_H164 zenon_H33 zenon_Hbc zenon_H18a zenon_H7d zenon_H212 zenon_H129 zenon_H156 zenon_He4 zenon_H12e zenon_H131 zenon_H1f1 zenon_H13f zenon_Ha0 zenon_Ha9 zenon_H1a2 zenon_H104 zenon_H183 zenon_H11a zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H4d zenon_H73 zenon_H1e zenon_H196 zenon_H15d zenon_H48 zenon_H141 zenon_H13a zenon_H77. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.50 apply (zenon_L13_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.50 apply (zenon_L13_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.50 apply (zenon_L14_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.50 apply (zenon_L15_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.50 exact (zenon_H6c zenon_H67). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.50 apply (zenon_L226_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.50 apply (zenon_L41_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.50 apply (zenon_L55_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.50 apply (zenon_L193_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.42/22.50 apply (zenon_L55_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.42/22.50 apply (zenon_L1984_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.42/22.50 apply (zenon_L113_); trivial. % 22.42/22.50 apply (zenon_L360_); trivial. % 22.42/22.50 apply (zenon_L621_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.50 apply (zenon_L184_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.50 apply (zenon_L13_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.50 apply (zenon_L16_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.50 apply (zenon_L15_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.50 exact (zenon_H6c zenon_H67). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.50 apply (zenon_L226_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.50 apply (zenon_L41_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.42/22.50 apply (zenon_L41_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.50 apply (zenon_L755_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.50 apply (zenon_L111_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.42/22.50 exact (zenon_H7b zenon_H65). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.42/22.50 apply (zenon_L319_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.42/22.50 exact (zenon_H8b zenon_H8a). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.42/22.50 apply (zenon_L2056_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.42/22.50 apply (zenon_L113_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.42/22.50 exact (zenon_H191 zenon_H110). % 22.42/22.50 apply (zenon_L2035_); trivial. % 22.42/22.50 apply (zenon_L766_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.50 apply (zenon_L67_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.50 apply (zenon_L111_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.42/22.50 exact (zenon_H7b zenon_H65). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.42/22.50 apply (zenon_L319_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.42/22.50 exact (zenon_H8b zenon_H8a). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.42/22.50 apply (zenon_L7_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.42/22.50 apply (zenon_L2055_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.42/22.50 apply (zenon_L257_); trivial. % 22.42/22.50 apply (zenon_L1983_); trivial. % 22.42/22.50 apply (zenon_L766_); trivial. % 22.42/22.50 apply (zenon_L134_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.50 apply (zenon_L178_); trivial. % 22.42/22.50 apply (zenon_L115_); trivial. % 22.42/22.50 apply (zenon_L98_); trivial. % 22.42/22.50 (* end of lemma zenon_L2057_ *) % 22.42/22.50 assert (zenon_L2058_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (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) (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 (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) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e1)) = (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 (e1) (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 (e3) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 22.42/22.50 do 0 intro. intros zenon_H1fe zenon_H19d zenon_H125 zenon_H1d5 zenon_H13c zenon_H164 zenon_H1a2 zenon_H13f zenon_H1f1 zenon_H12e zenon_H104 zenon_H117 zenon_H141 zenon_Hf5 zenon_Hb2 zenon_Hf0 zenon_H191 zenon_H131 zenon_H1ef zenon_H13e zenon_H15d zenon_H129 zenon_H8b zenon_H53 zenon_H7b zenon_H16a zenon_H196 zenon_H11a zenon_H73 zenon_H82 zenon_Hbb zenon_H4e zenon_H5a zenon_H77 zenon_H13a zenon_H177 zenon_H68 zenon_H183 zenon_H55 zenon_H4d zenon_H156 zenon_He4 zenon_Ha0 zenon_H2a zenon_Ha9 zenon_Hb6 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H48. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.42/22.50 apply (zenon_L161_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.50 apply (zenon_L1992_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.50 apply (zenon_L65_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.50 apply (zenon_L184_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.50 apply (zenon_L635_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.50 apply (zenon_L25_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.50 apply (zenon_L15_); trivial. % 22.42/22.50 apply (zenon_L2037_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.42/22.50 apply (zenon_L755_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.50 apply (zenon_L1996_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.50 apply (zenon_L65_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.50 apply (zenon_L184_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.50 apply (zenon_L635_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.50 apply (zenon_L16_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.50 apply (zenon_L1997_); trivial. % 22.42/22.50 apply (zenon_L456_); trivial. % 22.42/22.50 (* end of lemma zenon_L2058_ *) % 22.42/22.50 assert (zenon_L2059_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (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). % 22.42/22.50 do 0 intro. intros zenon_H1fe zenon_H1d5 zenon_H125 zenon_H164 zenon_Hb2 zenon_H15d zenon_H196 zenon_H8b zenon_Hef zenon_Hf0 zenon_H7b zenon_H16a zenon_H117 zenon_H6c zenon_H173 zenon_H11a zenon_H183 zenon_H13f zenon_H1f1 zenon_H131 zenon_H6f zenon_H191 zenon_H12e zenon_H201 zenon_H186 zenon_H1cd zenon_H18d zenon_H1a2 zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H92 zenon_H1ef zenon_H13e zenon_H141 zenon_H53 zenon_H55 zenon_H5a zenon_H4e zenon_H139 zenon_H77 zenon_Hbb zenon_H177 zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H13a zenon_H68 zenon_H82 zenon_H73 zenon_H4d zenon_H38 zenon_H48. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.42/22.50 apply (zenon_L1999_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.50 exact (zenon_H6c zenon_H67). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.50 apply (zenon_L1362_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.42/22.50 exact (zenon_H6c zenon_H67). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.42/22.50 apply (zenon_L171_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.42/22.50 exact (zenon_H7b zenon_H65). % 22.42/22.50 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.42/22.50 apply (zenon_L253_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.42/22.50 apply (zenon_L116_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.50 apply (zenon_L973_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.50 apply (zenon_L111_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.42/22.50 exact (zenon_H7b zenon_H65). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.42/22.50 apply (zenon_L61_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.42/22.50 exact (zenon_H8b zenon_H8a). % 22.42/22.50 apply (zenon_L2002_); trivial. % 22.42/22.50 apply (zenon_L1162_); trivial. % 22.42/22.50 apply (zenon_L91_); trivial. % 22.42/22.50 apply (zenon_L165_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.50 apply (zenon_L1363_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.50 apply (zenon_L25_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.50 apply (zenon_L15_); trivial. % 22.42/22.50 apply (zenon_L2003_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.50 apply (zenon_L184_); trivial. % 22.42/22.50 apply (zenon_L246_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.42/22.50 apply (zenon_L973_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.42/22.50 exact (zenon_H6c zenon_H67). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.42/22.50 apply (zenon_L1362_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.50 apply (zenon_L253_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.50 apply (zenon_L2007_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.50 apply (zenon_L178_); trivial. % 22.42/22.50 apply (zenon_L156_); trivial. % 22.42/22.50 apply (zenon_L621_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.50 apply (zenon_L1363_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.50 apply (zenon_L16_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.50 apply (zenon_L15_); trivial. % 22.42/22.50 apply (zenon_L456_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.50 apply (zenon_L184_); trivial. % 22.42/22.50 apply (zenon_L246_); trivial. % 22.42/22.50 (* end of lemma zenon_L2059_ *) % 22.42/22.50 assert (zenon_L2060_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (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))))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 22.42/22.50 do 0 intro. intros zenon_H141 zenon_H109 zenon_H77 zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_H177 zenon_H38 zenon_H68 zenon_H11a zenon_H34 zenon_H183 zenon_H1a2 zenon_H66 zenon_H13f zenon_H1f1 zenon_H4d zenon_H131 zenon_Hdb zenon_H6f zenon_H48 zenon_H12e zenon_H117 zenon_Ha9 zenon_H65 zenon_Hb6 zenon_H53 zenon_H104 zenon_Hbb zenon_Ha0. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.50 apply (zenon_L359_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.50 apply (zenon_L111_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.50 apply (zenon_L1973_); trivial. % 22.42/22.50 apply (zenon_L806_); trivial. % 22.42/22.50 (* end of lemma zenon_L2060_ *) % 22.42/22.50 assert (zenon_L2061_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (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 (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) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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 (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 22.42/22.50 do 0 intro. intros zenon_He4 zenon_H156 zenon_H104 zenon_H12e zenon_H66 zenon_H1a2 zenon_H183 zenon_H34 zenon_H11a zenon_H68 zenon_H177 zenon_H173 zenon_Hef zenon_H6c zenon_H139 zenon_H109 zenon_H141 zenon_H140 zenon_H26d zenon_H38 zenon_H48 zenon_Hb6 zenon_H6f zenon_Hdb zenon_H65 zenon_Ha9 zenon_H117 zenon_H131 zenon_H4d zenon_H1f1 zenon_H77 zenon_H13f zenon_Ha0 zenon_Hbb. % 22.42/22.50 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.42/22.50 apply (zenon_L55_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.42/22.50 apply (zenon_L486_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.42/22.50 apply (zenon_L2060_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.42/22.50 apply (zenon_L756_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.42/22.50 apply (zenon_L117_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.42/22.50 apply (zenon_L1972_); trivial. % 22.42/22.50 apply (zenon_L80_); trivial. % 22.42/22.50 (* end of lemma zenon_L2061_ *) % 22.42/22.50 assert (zenon_L2062_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (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 (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (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 (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((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)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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 (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.42/22.50 do 0 intro. intros zenon_H204 zenon_H13c zenon_H15d zenon_H4e zenon_H55 zenon_H82 zenon_H73 zenon_H196 zenon_H192 zenon_H25b zenon_H195 zenon_H186 zenon_H20f zenon_H164 zenon_Hf0 zenon_H7d zenon_H23d zenon_H236 zenon_H66 zenon_H68 zenon_H1f zenon_Hb2 zenon_Hbb zenon_Hbc zenon_H65 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_Hb6 zenon_H156 zenon_H4d zenon_H141 zenon_H104 zenon_H13f zenon_H6f zenon_H117 zenon_H131 zenon_H1f1 zenon_H77 zenon_H1a2 zenon_Hef zenon_H183 zenon_H6c zenon_H173 zenon_H177 zenon_H139 zenon_H11a zenon_H12e zenon_H48 zenon_H109 zenon_H140 zenon_H26d zenon_He4 zenon_H1fe zenon_H23b. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.42/22.50 apply (zenon_L1866_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.42/22.50 exact (zenon_H1f zenon_H1e). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.42/22.50 exact (zenon_H205 zenon_H2a). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.42/22.50 apply (zenon_L264_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.42/22.50 exact (zenon_H1f zenon_H1e). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.42/22.50 exact (zenon_Ha4 zenon_H9f). % 22.42/22.50 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.42/22.50 apply (zenon_L116_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.42/22.50 apply (zenon_L43_); trivial. % 22.42/22.50 apply (zenon_L48_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.42/22.50 apply (zenon_L27_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.42/22.50 exact (zenon_Ha4 zenon_H9f). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.42/22.50 apply (zenon_L2061_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.42/22.50 apply (zenon_L178_); trivial. % 22.42/22.50 apply (zenon_L156_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.42/22.50 exact (zenon_H1f zenon_H1e). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.42/22.50 exact (zenon_H1f zenon_H1e). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.42/22.50 exact (zenon_H4c zenon_H47). % 22.42/22.50 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.42/22.50 apply (zenon_L25_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.42/22.50 apply (zenon_L30_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.42/22.50 apply (zenon_L65_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.42/22.50 apply (zenon_L486_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.42/22.50 apply (zenon_L116_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.42/22.50 apply (zenon_L27_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.42/22.50 apply (zenon_L111_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.42/22.50 apply (zenon_L43_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.42/22.50 apply (zenon_L74_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.42/22.50 apply (zenon_L278_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.42/22.50 apply (zenon_L2038_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.42/22.50 apply (zenon_L292_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.42/22.50 apply (zenon_L257_); trivial. % 22.42/22.50 apply (zenon_L684_); trivial. % 22.42/22.50 apply (zenon_L806_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.42/22.50 apply (zenon_L124_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.42/22.50 apply (zenon_L43_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.42/22.50 apply (zenon_L113_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.42/22.50 apply (zenon_L129_); trivial. % 22.42/22.50 apply (zenon_L172_); trivial. % 22.42/22.50 apply (zenon_L31_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.42/22.50 apply (zenon_L27_); trivial. % 22.42/22.50 apply (zenon_L2021_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.42/22.50 apply (zenon_L264_); trivial. % 22.42/22.50 exact (zenon_H238 zenon_H38). % 22.42/22.50 apply (zenon_L1861_); trivial. % 22.42/22.50 (* end of lemma zenon_L2062_ *) % 22.42/22.50 assert (zenon_L2063_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.42/22.50 do 0 intro. intros zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_H68 zenon_H77 zenon_H139 zenon_H48 zenon_H2a zenon_H73 zenon_H4d zenon_H1bb zenon_H1cd zenon_Hbb zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_H1b4 zenon_H181 zenon_Hc4. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.42/22.50 apply (zenon_L352_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.42/22.50 apply (zenon_L65_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.42/22.50 apply (zenon_L184_); trivial. % 22.42/22.50 apply (zenon_L816_); trivial. % 22.42/22.50 (* end of lemma zenon_L2063_ *) % 22.42/22.50 assert (zenon_L2064_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (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 (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((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) (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (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 (e3) (e3)) = (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> False). % 22.42/22.50 do 0 intro. intros zenon_H236 zenon_H181 zenon_Hbb zenon_Hca zenon_H2c zenon_H1a2 zenon_H4e zenon_H186 zenon_H189 zenon_H1a8 zenon_Hc2 zenon_H15d zenon_H24e zenon_H1cd zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1b7 zenon_H1b4 zenon_H1bb zenon_H77 zenon_H196 zenon_H93 zenon_H48 zenon_H13a zenon_Hb2 zenon_H156 zenon_H55 zenon_He4 zenon_Ha0 zenon_H117 zenon_H12e zenon_H25b zenon_H195 zenon_H20f zenon_Hf5 zenon_H25e zenon_H192 zenon_H18d zenon_H26d zenon_H19a zenon_H11a zenon_H164 zenon_H33 zenon_H104 zenon_H121 zenon_Hf0 zenon_Hb6 zenon_H4d zenon_H1c6 zenon_H13f zenon_H131 zenon_Hfa zenon_H163 zenon_H129 zenon_H179 zenon_H141 zenon_H13c zenon_H82 zenon_H94 zenon_H125 zenon_H73 zenon_H1f1 zenon_Ha9 zenon_H1cb zenon_H1fe zenon_Hcb zenon_H1c3 zenon_H109 zenon_Hc8 zenon_H209 zenon_H1c7 zenon_Hc4 zenon_H139 zenon_H6c zenon_Hef zenon_H173 zenon_H160 zenon_H177 zenon_H68. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.42/22.50 apply (zenon_L1982_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.42/22.50 apply (zenon_L2063_); trivial. % 22.42/22.50 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.42/22.50 apply (zenon_L898_); trivial. % 22.42/22.50 apply (zenon_L1967_); trivial. % 22.42/22.50 (* end of lemma zenon_L2064_ *) % 22.42/22.50 assert (zenon_L2065_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (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) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H236 zenon_H6c zenon_Hbb zenon_H160 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H12e zenon_H15d zenon_H1a8 zenon_H189 zenon_H1cd zenon_H82 zenon_H196 zenon_H13a zenon_Ha9 zenon_Ha0 zenon_Hb6 zenon_H4e zenon_H4d zenon_H139 zenon_H177 zenon_H19a zenon_H181 zenon_H164 zenon_Hef zenon_H173 zenon_H68 zenon_H73 zenon_H1b7 zenon_H179 zenon_H195 zenon_Hfa zenon_H55 zenon_H1a2 zenon_H2c zenon_H141 zenon_H24e zenon_H156 zenon_He4 zenon_H1fe zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H120. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.46/22.51 apply (zenon_L1982_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.46/22.51 apply (zenon_L2063_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.46/22.51 apply (zenon_L978_); trivial. % 22.46/22.51 apply (zenon_L555_); trivial. % 22.46/22.51 (* end of lemma zenon_L2065_ *) % 22.46/22.51 assert (zenon_L2066_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (((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) (e3)) = (e3))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H15d zenon_H173 zenon_Hef zenon_H73 zenon_H82 zenon_H196 zenon_H93 zenon_H177 zenon_H160 zenon_H13a zenon_Ha9 zenon_Hbb zenon_Hb6 zenon_H77 zenon_H139 zenon_H4e zenon_H4d zenon_H48 zenon_H2d zenon_H1bb zenon_H162 zenon_H18a zenon_H181 zenon_Hc4. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.46/22.51 apply (zenon_L975_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.46/22.51 apply (zenon_L892_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.46/22.51 apply (zenon_L184_); trivial. % 22.46/22.51 apply (zenon_L1033_); trivial. % 22.46/22.51 (* end of lemma zenon_L2066_ *) % 22.46/22.51 assert (zenon_L2067_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (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 (e1) (e2)) = (op (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)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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 (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (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 (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (((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 (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((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) (e3)) = (op (e2) (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) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (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))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H236 zenon_H19d zenon_H1a2 zenon_H271 zenon_H1d8 zenon_H111 zenon_Hcc zenon_H270 zenon_Ha0 zenon_H1d5 zenon_H156 zenon_H179 zenon_Hbc zenon_H212 zenon_H1cf zenon_H192 zenon_H25e zenon_Hf5 zenon_H25b zenon_H19a zenon_H186 zenon_He4 zenon_H164 zenon_H13c zenon_H1c6 zenon_H131 zenon_H13f zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_Hf0 zenon_H8b zenon_H16a zenon_H22d zenon_H94 zenon_H201 zenon_H141 zenon_H104 zenon_H125 zenon_H121 zenon_H109 zenon_H1c3 zenon_H1f1 zenon_H163 zenon_H33 zenon_H11a zenon_H26d zenon_H117 zenon_Hb2 zenon_H1a8 zenon_H189 zenon_H2c zenon_H5d zenon_H26a zenon_H1fe zenon_H68 zenon_Hfa zenon_H195 zenon_H6c zenon_H181 zenon_H162 zenon_H4d zenon_H4e zenon_H139 zenon_Hb6 zenon_Hbb zenon_Ha9 zenon_H13a zenon_H177 zenon_H196 zenon_H82 zenon_H73 zenon_Hef zenon_H173 zenon_H15d zenon_H12e zenon_H77 zenon_H93 zenon_H1b4 zenon_H20f zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H160 zenon_H1c7. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.46/22.51 apply (zenon_L1982_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.46/22.51 apply (zenon_L161_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.46/22.51 apply (zenon_L2026_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.46/22.51 apply (zenon_L2066_); trivial. % 22.46/22.51 apply (zenon_L870_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.46/22.51 apply (zenon_L1007_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.46/22.51 apply (zenon_L13_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.46/22.51 apply (zenon_L215_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.46/22.51 apply (zenon_L184_); trivial. % 22.46/22.51 apply (zenon_L246_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.46/22.51 exact (zenon_H6c zenon_H67). % 22.46/22.51 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.46/22.51 apply (zenon_L976_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.46/22.51 apply (zenon_L122_); trivial. % 22.46/22.51 apply (zenon_L165_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.46/22.51 apply (zenon_L2066_); trivial. % 22.46/22.51 apply (zenon_L1510_); trivial. % 22.46/22.51 (* end of lemma zenon_L2067_ *) % 22.46/22.51 assert (zenon_L2068_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H139 zenon_H6c zenon_H2a zenon_H8a zenon_H111 zenon_Hfa zenon_H68 zenon_H1b3 zenon_Hec zenon_H77 zenon_H40 zenon_H25 zenon_H48 zenon_Heb zenon_Hf5. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.46/22.51 exact (zenon_H6c zenon_H67). % 22.46/22.51 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.46/22.51 apply (zenon_L147_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.46/22.51 apply (zenon_L258_); trivial. % 22.46/22.51 apply (zenon_L303_); trivial. % 22.46/22.51 (* end of lemma zenon_L2068_ *) % 22.46/22.51 assert (zenon_L2069_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H15c zenon_H173 zenon_H158 zenon_H6c zenon_H68 zenon_H2a zenon_H111 zenon_H8a zenon_Hfa zenon_Hf5 zenon_H48 zenon_H40 zenon_H77 zenon_Heb zenon_H1b3 zenon_H25 zenon_H139. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.46/22.51 apply (zenon_L2068_); trivial. % 22.46/22.51 apply (zenon_L304_); trivial. % 22.46/22.51 (* end of lemma zenon_L2069_ *) % 22.46/22.51 assert (zenon_L2070_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((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 (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H28 zenon_H139 zenon_H1b3 zenon_Heb zenon_H77 zenon_H48 zenon_Hf5 zenon_Hfa zenon_H8a zenon_H111 zenon_H68 zenon_H6c zenon_H158 zenon_H173. % 22.46/22.51 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.46/22.51 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.46/22.51 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.46/22.51 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.46/22.51 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.46/22.51 apply (zenon_L2069_); trivial. % 22.46/22.51 apply (zenon_L2069_); trivial. % 22.46/22.51 (* end of lemma zenon_L2070_ *) % 22.46/22.51 assert (zenon_L2071_ : (((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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (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) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H139 zenon_H6c zenon_H181 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H192 zenon_H183 zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H77 zenon_H104 zenon_H48 zenon_H12e zenon_H8a zenon_H111 zenon_H38 zenon_H68. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.46/22.51 exact (zenon_H6c zenon_H67). % 22.46/22.51 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.46/22.51 apply (zenon_L1509_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.46/22.51 apply (zenon_L258_); trivial. % 22.46/22.51 apply (zenon_L165_); trivial. % 22.46/22.51 (* end of lemma zenon_L2071_ *) % 22.46/22.51 assert (zenon_L2072_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((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 (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H139 zenon_H6c zenon_H120 zenon_H183 zenon_H192 zenon_Hc4 zenon_H1cb zenon_H34 zenon_H18a zenon_H1bb zenon_H181 zenon_H77 zenon_H104 zenon_H48 zenon_H12e zenon_H8a zenon_H111 zenon_H38 zenon_H68. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.46/22.51 exact (zenon_H6c zenon_H67). % 22.46/22.51 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.46/22.51 apply (zenon_L456_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.46/22.51 apply (zenon_L420_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.46/22.51 apply (zenon_L1507_); trivial. % 22.46/22.51 exact (zenon_H120 zenon_H11f). % 22.46/22.51 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.46/22.51 apply (zenon_L258_); trivial. % 22.46/22.51 apply (zenon_L165_); trivial. % 22.46/22.51 (* end of lemma zenon_L2072_ *) % 22.46/22.51 assert (zenon_L2073_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H236 zenon_H1f zenon_H48 zenon_Hf5 zenon_H131 zenon_H8a zenon_H1b3 zenon_H3c zenon_H77 zenon_Hfa zenon_H68 zenon_H3d zenon_H6c zenon_H139 zenon_H238. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.46/22.51 exact (zenon_H1f zenon_H1e). % 22.46/22.51 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.46/22.51 apply (zenon_L65_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.46/22.51 apply (zenon_L1123_); trivial. % 22.46/22.51 exact (zenon_H238 zenon_H38). % 22.46/22.51 (* end of lemma zenon_L2073_ *) % 22.46/22.51 assert (zenon_L2074_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H204 zenon_H23d zenon_H236 zenon_H6c zenon_H77 zenon_H68 zenon_Hfa zenon_Hf5 zenon_H8a zenon_H131 zenon_H1b3 zenon_H3c zenon_H139 zenon_H3d zenon_H48 zenon_H1f zenon_H13a zenon_Ha9 zenon_Ha0 zenon_Hb6 zenon_H23b. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.46/22.51 apply (zenon_L2073_); trivial. % 22.46/22.51 apply (zenon_L1858_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.46/22.51 apply (zenon_L2073_); trivial. % 22.46/22.51 apply (zenon_L1861_); trivial. % 22.46/22.51 (* end of lemma zenon_L2074_ *) % 22.46/22.51 assert (zenon_L2075_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H1a8 zenon_H68 zenon_H2a zenon_H1b3 zenon_H190 zenon_H8a zenon_H7f zenon_H77. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.46/22.51 apply (zenon_L147_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.46/22.51 exact (zenon_H1b3 zenon_Hef). % 22.46/22.51 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.46/22.51 apply (zenon_L366_); trivial. % 22.46/22.51 apply (zenon_L169_); trivial. % 22.46/22.51 (* end of lemma zenon_L2075_ *) % 22.46/22.51 assert (zenon_L2076_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H236 zenon_Hf5 zenon_H48 zenon_H192 zenon_H7f zenon_H139 zenon_H1c2 zenon_H111 zenon_H13a zenon_Hb6 zenon_H8a zenon_H190 zenon_H1b3 zenon_H1a8 zenon_Ha0 zenon_Ha9 zenon_H15d zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H1bb zenon_H181. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.46/22.51 apply (zenon_L13_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.46/22.51 apply (zenon_L146_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.46/22.51 apply (zenon_L41_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.46/22.51 apply (zenon_L1126_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.46/22.51 apply (zenon_L95_); trivial. % 22.46/22.51 apply (zenon_L1124_); trivial. % 22.46/22.51 apply (zenon_L192_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.46/22.51 apply (zenon_L2075_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.46/22.51 apply (zenon_L1127_); trivial. % 22.46/22.51 apply (zenon_L414_); trivial. % 22.46/22.51 (* end of lemma zenon_L2076_ *) % 22.46/22.51 assert (zenon_L2077_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (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 (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H9b zenon_H139 zenon_H6c zenon_H181 zenon_H104 zenon_H192 zenon_H183 zenon_H8a zenon_H111 zenon_Ha9. % 22.46/22.51 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.46/22.51 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.46/22.51 apply (zenon_L1130_); trivial. % 22.46/22.51 (* end of lemma zenon_L2077_ *) % 22.46/22.51 assert (zenon_L2078_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 22.46/22.51 do 0 intro. intros zenon_Hb2 zenon_Ha0 zenon_H1e zenon_H5d zenon_Ha5 zenon_Hb6 zenon_H54 zenon_Hb1 zenon_H7d. % 22.46/22.51 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.46/22.51 apply (zenon_L41_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.46/22.51 apply (zenon_L42_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.46/22.51 apply (zenon_L151_); trivial. % 22.46/22.51 apply (zenon_L221_); trivial. % 22.46/22.51 (* end of lemma zenon_L2078_ *) % 22.46/22.51 assert (zenon_L2079_ : (((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 (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H183 zenon_H77 zenon_H7e zenon_Hac zenon_Ha9 zenon_H8a zenon_H104 zenon_H181. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.46/22.51 apply (zenon_L71_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.46/22.51 apply (zenon_L371_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.46/22.51 apply (zenon_L231_); trivial. % 22.46/22.51 exact (zenon_H181 zenon_H17c). % 22.46/22.51 (* end of lemma zenon_L2079_ *) % 22.46/22.51 assert (zenon_L2080_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((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 (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H82 zenon_H48 zenon_H7a zenon_H7d zenon_Hb1 zenon_Hb6 zenon_Ha5 zenon_H5d zenon_H1e zenon_Ha0 zenon_Hb2 zenon_H183 zenon_H77 zenon_Hac zenon_Ha9 zenon_H8a zenon_H104 zenon_H181. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.46/22.51 apply (zenon_L13_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.46/22.51 exact (zenon_H7a zenon_H3c). % 22.46/22.51 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.46/22.51 apply (zenon_L2078_); trivial. % 22.46/22.51 apply (zenon_L2079_); trivial. % 22.46/22.51 (* end of lemma zenon_L2080_ *) % 22.46/22.51 assert (zenon_L2081_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e2) (e1)) = (op (e2) (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) (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) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H277 zenon_Hcc zenon_H1a2 zenon_H1cd zenon_H186 zenon_H183 zenon_H104 zenon_H15d zenon_H48 zenon_H192 zenon_H13a zenon_H1c2 zenon_H1c3 zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H111 zenon_H190 zenon_H1a8 zenon_H77 zenon_H68 zenon_Hfa zenon_Hf5 zenon_H131 zenon_H139 zenon_H26d zenon_H8a zenon_H1d8 zenon_H31 zenon_H109 zenon_Heb zenon_H4e zenon_H55 zenon_H2c zenon_H141 zenon_H164 zenon_H73 zenon_H20b zenon_H129 zenon_H20f zenon_H19a zenon_H173 zenon_H1c6 zenon_H25b zenon_H189 zenon_H82 zenon_H156 zenon_H117 zenon_H13f zenon_H1f1 zenon_He4 zenon_H1cb zenon_H121 zenon_Hb2 zenon_H179 zenon_H33 zenon_H234 zenon_H18d zenon_H163 zenon_H195 zenon_H196 zenon_H1bb zenon_H1b4 zenon_H1b7 zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H24e zenon_H1fe zenon_H1ef zenon_H125 zenon_H12e zenon_H177 zenon_H271. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H4d ]. % 22.46/22.51 apply (zenon_L1142_); trivial. % 22.46/22.51 apply (zenon_L1044_); trivial. % 22.46/22.51 (* end of lemma zenon_L2081_ *) % 22.46/22.51 assert (zenon_L2082_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H139 zenon_H6c zenon_H77 zenon_H3d zenon_H8a zenon_H111 zenon_H38 zenon_H68. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.46/22.51 exact (zenon_H6c zenon_H67). % 22.46/22.51 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.46/22.51 apply (zenon_L214_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.46/22.51 apply (zenon_L258_); trivial. % 22.46/22.51 apply (zenon_L165_); trivial. % 22.46/22.51 (* end of lemma zenon_L2082_ *) % 22.46/22.51 assert (zenon_L2083_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 22.46/22.51 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_H40 zenon_H55 zenon_H54 zenon_H1a8 zenon_Ha9 zenon_Hdb zenon_H1b3 zenon_H190 zenon_H8a zenon_H77. % 22.46/22.51 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.46/22.51 apply (zenon_L55_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.46/22.51 exact (zenon_H40 zenon_H3f). % 22.46/22.51 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.46/22.51 apply (zenon_L15_); trivial. % 22.46/22.51 apply (zenon_L1126_); trivial. % 22.46/22.51 (* end of lemma zenon_L2083_ *) % 22.46/22.51 assert (zenon_L2084_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 22.46/22.51 do 0 intro. intros zenon_Hfa zenon_H68 zenon_H25 zenon_H1b3 zenon_H8a zenon_H131 zenon_Ha9 zenon_Ha5. % 22.46/22.51 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.46/22.51 apply (zenon_L171_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.46/22.51 exact (zenon_H1b3 zenon_Hef). % 22.46/22.51 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.46/22.51 apply (zenon_L87_); trivial. % 22.46/22.51 apply (zenon_L299_); trivial. % 22.46/22.51 (* end of lemma zenon_L2084_ *) % 22.46/22.51 assert (zenon_L2085_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H1fe zenon_H38 zenon_Hf5 zenon_He4 zenon_H40 zenon_H55 zenon_H1a8 zenon_H190 zenon_H13a zenon_H139 zenon_H6c zenon_H111 zenon_H15d zenon_H131 zenon_H1b3 zenon_Hfa zenon_H77 zenon_H48 zenon_H7a zenon_Hb2 zenon_Hb6 zenon_H5d zenon_Ha5 zenon_Ha0 zenon_H7d zenon_H82 zenon_H183 zenon_H68 zenon_Hac zenon_Ha9 zenon_H8a zenon_H104 zenon_H181. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.46/22.51 apply (zenon_L13_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.46/22.51 apply (zenon_L2082_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.46/22.51 apply (zenon_L13_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.46/22.51 exact (zenon_H7a zenon_H3c). % 22.46/22.51 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.46/22.51 apply (zenon_L41_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.46/22.51 apply (zenon_L2083_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.46/22.51 apply (zenon_L95_); trivial. % 22.46/22.51 apply (zenon_L262_); trivial. % 22.46/22.51 apply (zenon_L2079_); trivial. % 22.46/22.51 apply (zenon_L246_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.46/22.51 apply (zenon_L2084_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.46/22.51 apply (zenon_L355_); trivial. % 22.46/22.51 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.46/22.51 exact (zenon_H7a zenon_H3c). % 22.46/22.51 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.46/22.51 apply (zenon_L217_); trivial. % 22.46/22.51 apply (zenon_L2079_); trivial. % 22.46/22.51 apply (zenon_L1674_); trivial. % 22.46/22.51 (* end of lemma zenon_L2085_ *) % 22.46/22.51 assert (zenon_L2086_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (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) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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 (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.46/22.51 do 0 intro. intros zenon_H236 zenon_Hb1 zenon_H11a zenon_H158 zenon_H271 zenon_H177 zenon_H12e zenon_H125 zenon_H1ef zenon_H24e zenon_H18a zenon_Hbc zenon_H212 zenon_H1b7 zenon_H1b4 zenon_H1bb zenon_H196 zenon_H195 zenon_H163 zenon_H18d zenon_H234 zenon_H33 zenon_H179 zenon_H121 zenon_H1cb zenon_H1f1 zenon_H13f zenon_H117 zenon_H156 zenon_H189 zenon_H25b zenon_H1c6 zenon_H173 zenon_H19a zenon_H20f zenon_H129 zenon_H20b zenon_H73 zenon_H164 zenon_H141 zenon_H2c zenon_H4e zenon_Heb zenon_H109 zenon_H1d8 zenon_H26d zenon_H1c3 zenon_H1c2 zenon_H192 zenon_H186 zenon_H1cd zenon_H1a2 zenon_Hcc zenon_H277 zenon_H1fe zenon_Hf5 zenon_He4 zenon_H40 zenon_H55 zenon_H1a8 zenon_H190 zenon_H13a zenon_H139 zenon_H6c zenon_H111 zenon_H15d zenon_H131 zenon_H1b3 zenon_Hfa zenon_H77 zenon_H48 zenon_H7a zenon_Hb2 zenon_Hb6 zenon_H5d zenon_Ha5 zenon_Ha0 zenon_H7d zenon_H82 zenon_H183 zenon_H68 zenon_Hac zenon_Ha9 zenon_H8a zenon_H104 zenon_H181. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.46/22.52 apply (zenon_L2080_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.46/22.52 apply (zenon_L372_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.46/22.52 apply (zenon_L2081_); trivial. % 22.46/22.52 apply (zenon_L2085_); trivial. % 22.46/22.52 (* end of lemma zenon_L2086_ *) % 22.46/22.52 assert (zenon_L2087_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((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)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H36 zenon_Hbb zenon_H139 zenon_H111 zenon_H48 zenon_H183 zenon_H8a zenon_H104 zenon_H77 zenon_H68 zenon_Hb6 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H24e zenon_H192 zenon_H12e zenon_H6c. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.46/22.52 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.46/22.52 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.46/22.52 exact (zenon_H1a3 zenon_Hbb). % 22.46/22.52 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.46/22.52 exact (zenon_H6c zenon_H67). % 22.46/22.52 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.46/22.52 apply (zenon_L456_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.46/22.52 apply (zenon_L420_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.46/22.52 apply (zenon_L363_); trivial. % 22.46/22.52 apply (zenon_L1508_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.46/22.52 apply (zenon_L258_); trivial. % 22.46/22.52 apply (zenon_L165_); trivial. % 22.46/22.52 apply (zenon_L1678_); trivial. % 22.46/22.52 (* end of lemma zenon_L2087_ *) % 22.46/22.52 assert (zenon_L2088_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (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))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (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) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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 (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (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 (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H236 zenon_Hbb zenon_H7f zenon_H1b3 zenon_H271 zenon_H177 zenon_H12e zenon_H125 zenon_H1ef zenon_H1fe zenon_H24e zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1b7 zenon_H196 zenon_H195 zenon_H163 zenon_H18d zenon_H234 zenon_H33 zenon_H179 zenon_Hb2 zenon_H121 zenon_H1cb zenon_He4 zenon_H1f1 zenon_H13f zenon_H117 zenon_H156 zenon_H82 zenon_H189 zenon_H25b zenon_H1c6 zenon_H173 zenon_H19a zenon_H20b zenon_H73 zenon_H164 zenon_H141 zenon_H2c zenon_H55 zenon_H4e zenon_Heb zenon_H109 zenon_H1d8 zenon_H8a zenon_H26d zenon_H139 zenon_H131 zenon_Hf5 zenon_Hfa zenon_H1a8 zenon_H190 zenon_H111 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H1c2 zenon_H13a zenon_H192 zenon_H48 zenon_H15d zenon_H104 zenon_H183 zenon_H186 zenon_H1cd zenon_H1a2 zenon_Hcc zenon_H277 zenon_H1c3 zenon_H68 zenon_H77 zenon_Hc4 zenon_H129 zenon_H5c zenon_H20f zenon_H1b4 zenon_H1bb zenon_H181. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.46/22.52 apply (zenon_L41_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.46/22.52 apply (zenon_L1126_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.46/22.52 apply (zenon_L178_); trivial. % 22.46/22.52 apply (zenon_L1124_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.46/22.52 apply (zenon_L2075_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.46/22.52 apply (zenon_L2081_); trivial. % 22.46/22.52 apply (zenon_L414_); trivial. % 22.46/22.52 (* end of lemma zenon_L2088_ *) % 22.46/22.52 assert (zenon_L2089_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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 (e2) (e1)) = (op (e2) (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) (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) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> False). % 22.46/22.52 do 0 intro. intros zenon_H158 zenon_H6c zenon_H13a zenon_H1c2 zenon_H1c3 zenon_H177 zenon_Ha9 zenon_H1b3 zenon_H190 zenon_H77 zenon_H1a8 zenon_Ha0 zenon_H68 zenon_H277 zenon_Hcc zenon_H1a2 zenon_H186 zenon_H183 zenon_H15d zenon_H48 zenon_H192 zenon_Hb6 zenon_Hfa zenon_Hf5 zenon_H139 zenon_H26d zenon_H1d8 zenon_H109 zenon_Heb zenon_H4e zenon_H55 zenon_H2c zenon_H141 zenon_H164 zenon_H73 zenon_H20b zenon_H129 zenon_H20f zenon_H19a zenon_H173 zenon_H1c6 zenon_H25b zenon_H189 zenon_H82 zenon_H156 zenon_H117 zenon_H13f zenon_H1f1 zenon_He4 zenon_H1cb zenon_H121 zenon_Hb2 zenon_H179 zenon_H33 zenon_H234 zenon_H18d zenon_H163 zenon_H195 zenon_H196 zenon_H1bb zenon_H1b4 zenon_H1b7 zenon_H212 zenon_H7d zenon_H18a zenon_H24e zenon_H1fe zenon_H1ef zenon_H125 zenon_H12e zenon_H271 zenon_H236 zenon_H111 zenon_H131 zenon_H104 zenon_Hbc zenon_H1cd zenon_Hbb zenon_H8a. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.46/22.52 apply (zenon_L2_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.46/22.52 apply (zenon_L2070_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.46/22.52 apply (zenon_L782_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.46/22.52 apply (zenon_L2087_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.46/22.52 apply (zenon_L1133_); trivial. % 22.46/22.52 apply (zenon_L1133_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.46/22.52 apply (zenon_L11_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.46/22.52 apply (zenon_L787_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.46/22.52 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.46/22.52 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.46/22.52 exact (zenon_H1a3 zenon_Hbb). % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.46/22.52 apply (zenon_L2088_); trivial. % 22.46/22.52 apply (zenon_L2088_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.46/22.52 apply (zenon_L789_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.46/22.52 apply (zenon_L88_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.46/22.52 apply (zenon_L37_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.46/22.52 apply (zenon_L232_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.46/22.52 apply (zenon_L791_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.46/22.52 apply (zenon_L361_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.46/22.52 apply (zenon_L792_); trivial. % 22.46/22.52 apply (zenon_L51_); trivial. % 22.46/22.52 (* end of lemma zenon_L2089_ *) % 22.46/22.52 assert (zenon_L2090_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (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) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((op (e1) (e2)) = (e1)) -> False). % 22.46/22.52 do 0 intro. intros zenon_H169 zenon_H139 zenon_H25 zenon_Heb zenon_H77 zenon_H40 zenon_H48 zenon_Hf5 zenon_Hfa zenon_H8a zenon_H111 zenon_H2a zenon_H68 zenon_H6c zenon_H158 zenon_H173 zenon_H15c zenon_H4d. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.46/22.52 exact (zenon_H1d4 zenon_H4d). % 22.46/22.52 apply (zenon_L2069_); trivial. % 22.46/22.52 (* end of lemma zenon_L2090_ *) % 22.46/22.52 assert (zenon_L2091_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (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 (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H28 zenon_H4d zenon_H173 zenon_H158 zenon_H6c zenon_H68 zenon_H111 zenon_H8a zenon_Hfa zenon_Hf5 zenon_H48 zenon_H77 zenon_Heb zenon_H139. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.46/22.52 apply (zenon_L2090_); trivial. % 22.46/22.52 apply (zenon_L2090_); trivial. % 22.46/22.52 (* end of lemma zenon_L2091_ *) % 22.46/22.52 assert (zenon_L2092_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((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))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H12e zenon_H48 zenon_H104 zenon_H8a zenon_H77 zenon_H4d zenon_H163 zenon_H183 zenon_H68 zenon_H6e zenon_H192 zenon_H1c7 zenon_H1cd zenon_H1b7 zenon_H7d zenon_H34 zenon_H24e zenon_H181. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.46/22.52 apply (zenon_L456_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.46/22.52 apply (zenon_L420_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.46/22.52 apply (zenon_L285_); trivial. % 22.46/22.52 apply (zenon_L1508_); trivial. % 22.46/22.52 (* end of lemma zenon_L2092_ *) % 22.46/22.52 assert (zenon_L2093_ : (((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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((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)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H139 zenon_H6c zenon_H181 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H192 zenon_H183 zenon_H163 zenon_H4d zenon_H77 zenon_H104 zenon_H48 zenon_H12e zenon_H8a zenon_H111 zenon_H38 zenon_H68. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.46/22.52 exact (zenon_H6c zenon_H67). % 22.46/22.52 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.46/22.52 apply (zenon_L2092_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.46/22.52 apply (zenon_L258_); trivial. % 22.46/22.52 apply (zenon_L165_); trivial. % 22.46/22.52 (* end of lemma zenon_L2093_ *) % 22.46/22.52 assert (zenon_L2094_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e0) (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H36 zenon_H6c zenon_H12e zenon_H192 zenon_H24e zenon_H1cd zenon_H1b7 zenon_H7d zenon_H4d zenon_H163 zenon_H68 zenon_H77 zenon_H104 zenon_H8a zenon_H181 zenon_H183 zenon_H48 zenon_H111 zenon_H139. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.46/22.52 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.46/22.52 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.46/22.52 apply (zenon_L2093_); trivial. % 22.46/22.52 apply (zenon_L1684_); trivial. % 22.46/22.52 (* end of lemma zenon_L2094_ *) % 22.46/22.52 assert (zenon_L2095_ : (((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)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H1bb zenon_H1cb zenon_H11d zenon_H77 zenon_H68 zenon_H115 zenon_Ha9 zenon_Ha5 zenon_H9f zenon_H1c3 zenon_H181 zenon_Hac zenon_H1b7. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 22.46/22.52 apply (zenon_L266_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 22.46/22.52 apply (zenon_L885_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 22.46/22.52 exact (zenon_H181 zenon_H17c). % 22.46/22.52 apply (zenon_L1185_); trivial. % 22.46/22.52 (* end of lemma zenon_L2095_ *) % 22.46/22.52 assert (zenon_L2096_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H19a zenon_Hf6 zenon_Ha0 zenon_H1b7 zenon_Hac zenon_H181 zenon_H1c3 zenon_H9f zenon_Ha5 zenon_Ha9 zenon_H68 zenon_H77 zenon_H1bb zenon_H11d zenon_H1cb. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.46/22.52 apply (zenon_L165_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.46/22.52 apply (zenon_L90_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.46/22.52 apply (zenon_L2095_); trivial. % 22.46/22.52 apply (zenon_L266_); trivial. % 22.46/22.52 (* end of lemma zenon_L2096_ *) % 22.46/22.52 assert (zenon_L2097_ : (((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 (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H231 zenon_H1cb zenon_H167 zenon_H4d zenon_H163 zenon_Hbc zenon_H102 zenon_Hfe zenon_H177. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H11d | zenon_intro zenon_H232 ]. % 22.46/22.52 apply (zenon_L266_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H106 | zenon_intro zenon_H233 ]. % 22.46/22.52 apply (zenon_L285_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H160 | zenon_intro zenon_Hbb ]. % 22.46/22.52 apply (zenon_L104_); trivial. % 22.46/22.52 apply (zenon_L178_); trivial. % 22.46/22.52 (* end of lemma zenon_L2097_ *) % 22.46/22.52 assert (zenon_L2098_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H183 zenon_H177 zenon_Hfe zenon_Hbc zenon_H163 zenon_H4d zenon_H167 zenon_H1cb zenon_H231 zenon_Hac zenon_Ha9 zenon_H8a zenon_H104 zenon_H181. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.46/22.52 apply (zenon_L2097_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.46/22.52 apply (zenon_L371_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.46/22.52 apply (zenon_L231_); trivial. % 22.46/22.52 exact (zenon_H181 zenon_H17c). % 22.46/22.52 (* end of lemma zenon_L2098_ *) % 22.46/22.52 assert (zenon_L2099_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (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 (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H164 zenon_H1e zenon_H33 zenon_H1bb zenon_H77 zenon_H68 zenon_Ha5 zenon_H9f zenon_H1c3 zenon_H1b7 zenon_Ha0 zenon_Hf6 zenon_H19a zenon_H183 zenon_H177 zenon_Hfe zenon_Hbc zenon_H163 zenon_H4d zenon_H1cb zenon_H231 zenon_Hac zenon_Ha9 zenon_H8a zenon_H104 zenon_H181. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.46/22.52 apply (zenon_L7_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.46/22.52 apply (zenon_L107_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.46/22.52 apply (zenon_L2096_); trivial. % 22.46/22.52 apply (zenon_L2098_); trivial. % 22.46/22.52 (* end of lemma zenon_L2099_ *) % 22.46/22.52 assert (zenon_L2100_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (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) (e0)) = (op (e3) (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) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 22.46/22.52 do 0 intro. intros zenon_H13a zenon_H195 zenon_H1a2 zenon_H1cd zenon_H117 zenon_H190 zenon_H1b3 zenon_H1a8 zenon_H55 zenon_H40 zenon_He4 zenon_H7d zenon_Hac zenon_H54 zenon_Hb6 zenon_Ha5 zenon_H5d zenon_H164 zenon_H1e zenon_H33 zenon_H1bb zenon_H77 zenon_H68 zenon_H1c3 zenon_H1b7 zenon_Ha0 zenon_H19a zenon_H183 zenon_H177 zenon_Hbc zenon_H163 zenon_H4d zenon_H1cb zenon_H231 zenon_H8a zenon_H104 zenon_H181 zenon_Hb2 zenon_Ha9 zenon_Hf6. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.46/22.52 apply (zenon_L151_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.46/22.52 apply (zenon_L2099_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.46/22.52 apply (zenon_L124_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.46/22.52 apply (zenon_L163_); trivial. % 22.46/22.52 apply (zenon_L360_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.46/22.52 apply (zenon_L153_); trivial. % 22.46/22.52 apply (zenon_L172_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.46/22.52 apply (zenon_L2083_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.46/22.52 apply (zenon_L2099_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.46/22.52 apply (zenon_L42_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.46/22.52 apply (zenon_L151_); trivial. % 22.46/22.52 apply (zenon_L44_); trivial. % 22.46/22.52 apply (zenon_L92_); trivial. % 22.46/22.52 (* end of lemma zenon_L2100_ *) % 22.46/22.52 assert (zenon_L2101_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H1fe zenon_H131 zenon_H1b3 zenon_Hfa zenon_H48 zenon_H38 zenon_H4d zenon_H73 zenon_H139 zenon_H6c zenon_H77 zenon_H111 zenon_Hb2 zenon_Hb6 zenon_H5d zenon_Ha5 zenon_Ha0 zenon_H7d zenon_H15d zenon_H183 zenon_H68 zenon_Hac zenon_Ha9 zenon_H8a zenon_H104 zenon_H181. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.46/22.52 apply (zenon_L13_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.46/22.52 apply (zenon_L2082_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.46/22.52 apply (zenon_L184_); trivial. % 22.46/22.52 apply (zenon_L246_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.46/22.52 apply (zenon_L2084_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.46/22.52 apply (zenon_L355_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.46/22.52 apply (zenon_L2082_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.46/22.52 apply (zenon_L184_); trivial. % 22.46/22.52 apply (zenon_L246_); trivial. % 22.46/22.52 apply (zenon_L1674_); trivial. % 22.46/22.52 (* end of lemma zenon_L2101_ *) % 22.46/22.52 assert (zenon_L2102_ : (((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)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((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)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H19a zenon_H104 zenon_H8a zenon_H183 zenon_H15d zenon_H7d zenon_H5d zenon_Hb6 zenon_Hb2 zenon_H111 zenon_H6c zenon_H139 zenon_H73 zenon_H4d zenon_H48 zenon_Hfa zenon_H1b3 zenon_H131 zenon_H1fe zenon_Ha0 zenon_H1b7 zenon_Hac zenon_H181 zenon_H1c3 zenon_H9f zenon_Ha5 zenon_Ha9 zenon_H68 zenon_H77 zenon_H1bb zenon_H11d zenon_H1cb. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.46/22.52 apply (zenon_L2101_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.46/22.52 apply (zenon_L90_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.46/22.52 apply (zenon_L2095_); trivial. % 22.46/22.52 apply (zenon_L266_); trivial. % 22.46/22.52 (* end of lemma zenon_L2102_ *) % 22.46/22.52 assert (zenon_L2103_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (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 (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H164 zenon_H1e zenon_H33 zenon_H1bb zenon_H77 zenon_H68 zenon_Ha5 zenon_H9f zenon_H1c3 zenon_H1b7 zenon_Ha0 zenon_H1fe zenon_H131 zenon_H1b3 zenon_Hfa zenon_H48 zenon_H73 zenon_H139 zenon_H6c zenon_H111 zenon_Hb2 zenon_Hb6 zenon_H5d zenon_H7d zenon_H15d zenon_H19a zenon_H183 zenon_H177 zenon_Hfe zenon_Hbc zenon_H163 zenon_H4d zenon_H1cb zenon_H231 zenon_Hac zenon_Ha9 zenon_H8a zenon_H104 zenon_H181. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.46/22.52 apply (zenon_L7_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.46/22.52 apply (zenon_L107_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.46/22.52 apply (zenon_L2102_); trivial. % 22.46/22.52 apply (zenon_L2098_); trivial. % 22.46/22.52 (* end of lemma zenon_L2103_ *) % 22.46/22.52 assert (zenon_L2104_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((e1) = (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 (e3) (e0)) = (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 (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (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 (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))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.46/22.52 do 0 intro. intros zenon_H82 zenon_H7a zenon_Hb6 zenon_H231 zenon_H1cb zenon_H4d zenon_H163 zenon_Hbc zenon_H177 zenon_H19a zenon_H15d zenon_Hb2 zenon_H111 zenon_H6c zenon_H139 zenon_H73 zenon_H48 zenon_Hfa zenon_H1b3 zenon_H131 zenon_H1fe zenon_Ha0 zenon_H1b7 zenon_H1c3 zenon_H68 zenon_H1bb zenon_H33 zenon_H1e zenon_H164 zenon_H5d zenon_Ha5 zenon_H7d zenon_He4 zenon_H40 zenon_H55 zenon_H1a8 zenon_H190 zenon_H117 zenon_H1cd zenon_H1a2 zenon_H195 zenon_H13a zenon_H183 zenon_H77 zenon_Hac zenon_Ha9 zenon_H8a zenon_H104 zenon_H181. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.46/22.52 apply (zenon_L13_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.46/22.52 apply (zenon_L13_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.46/22.52 exact (zenon_H7a zenon_H3c). % 22.46/22.52 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.46/22.52 exact (zenon_H6c zenon_H67). % 22.46/22.52 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.46/22.52 apply (zenon_L214_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.46/22.52 apply (zenon_L258_); trivial. % 22.46/22.52 apply (zenon_L2100_); trivial. % 22.46/22.52 apply (zenon_L2079_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.46/22.52 apply (zenon_L184_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.46/22.52 apply (zenon_L13_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.46/22.52 exact (zenon_H7a zenon_H3c). % 22.46/22.52 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.46/22.52 apply (zenon_L151_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.46/22.52 apply (zenon_L2103_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.46/22.52 apply (zenon_L124_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.46/22.52 apply (zenon_L163_); trivial. % 22.46/22.52 apply (zenon_L360_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.46/22.52 apply (zenon_L153_); trivial. % 22.46/22.52 apply (zenon_L172_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.46/22.52 apply (zenon_L2083_); trivial. % 22.46/22.52 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.46/22.52 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.48/22.53 apply (zenon_L2103_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.48/22.53 apply (zenon_L42_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.48/22.53 apply (zenon_L151_); trivial. % 22.48/22.53 apply (zenon_L44_); trivial. % 22.48/22.53 apply (zenon_L115_); trivial. % 22.48/22.53 apply (zenon_L2079_); trivial. % 22.48/22.53 (* end of lemma zenon_L2104_ *) % 22.48/22.53 assert (zenon_L2105_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (((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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (((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))))) -> (~((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)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e1)) = (op (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 (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> False). % 22.48/22.53 do 0 intro. intros zenon_H169 zenon_H15d zenon_Hfa zenon_H131 zenon_H1fe zenon_H73 zenon_H7a zenon_H139 zenon_H117 zenon_H195 zenon_H164 zenon_H231 zenon_H177 zenon_Hbc zenon_H163 zenon_H104 zenon_H183 zenon_H68 zenon_Ha5 zenon_H1bb zenon_H1b7 zenon_H181 zenon_Ha9 zenon_H1c3 zenon_H1cb zenon_H19a zenon_Hac zenon_Ha0 zenon_H33 zenon_H190 zenon_H1cd zenon_H1a2 zenon_Hb6 zenon_He4 zenon_H1a8 zenon_H55 zenon_H40 zenon_Hb2 zenon_H7d zenon_H5d zenon_H13a zenon_H8a zenon_H111 zenon_H77 zenon_H6c zenon_H82 zenon_H48 zenon_H158 zenon_H11a zenon_H173 zenon_H277 zenon_Hcc zenon_H186 zenon_H192 zenon_H1c2 zenon_Hf5 zenon_H26d zenon_H1d8 zenon_H109 zenon_Heb zenon_H4e zenon_H2c zenon_H141 zenon_H20b zenon_H129 zenon_H20f zenon_H1c6 zenon_H25b zenon_H189 zenon_H156 zenon_H13f zenon_H1f1 zenon_H121 zenon_H179 zenon_H234 zenon_H18d zenon_H196 zenon_H1b4 zenon_H212 zenon_H18a zenon_H24e zenon_H1ef zenon_H125 zenon_H12e zenon_H271 zenon_H236 zenon_H4d. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.48/22.53 exact (zenon_H1d4 zenon_H4d). % 22.48/22.53 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.48/22.53 apply (zenon_L2104_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.48/22.53 apply (zenon_L372_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.48/22.53 apply (zenon_L2081_); trivial. % 22.48/22.53 apply (zenon_L2101_); trivial. % 22.48/22.53 (* end of lemma zenon_L2105_ *) % 22.48/22.53 assert (zenon_L2106_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.48/22.53 do 0 intro. intros zenon_H139 zenon_H6c zenon_Ha0 zenon_Hbb zenon_H177 zenon_Ha9 zenon_H47 zenon_Hb6 zenon_H13a zenon_H8a zenon_H111 zenon_H38 zenon_H68. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.53 exact (zenon_H6c zenon_H67). % 22.48/22.53 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.53 apply (zenon_L1362_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.53 apply (zenon_L258_); trivial. % 22.48/22.53 apply (zenon_L165_); trivial. % 22.48/22.53 (* end of lemma zenon_L2106_ *) % 22.48/22.53 assert (zenon_L2107_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> False). % 22.48/22.53 do 0 intro. intros zenon_Hcc zenon_Heb zenon_Hf5 zenon_Hfa zenon_H158 zenon_H173 zenon_H48 zenon_H73 zenon_H139 zenon_H6c zenon_H68 zenon_Ha0 zenon_H177 zenon_Ha9 zenon_Hb6 zenon_H13a zenon_H15d zenon_H4e zenon_H186 zenon_H111 zenon_H77 zenon_H4d zenon_H104 zenon_Hbc zenon_H1cd zenon_Hbb zenon_H8a. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.48/22.53 apply (zenon_L2_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.48/22.53 apply (zenon_L2091_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.48/22.53 apply (zenon_L782_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.53 apply (zenon_L2106_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.53 apply (zenon_L2082_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.53 apply (zenon_L184_); trivial. % 22.48/22.53 apply (zenon_L246_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.48/22.53 apply (zenon_L758_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.48/22.53 apply (zenon_L11_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.48/22.53 apply (zenon_L787_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.48/22.53 apply (zenon_L335_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.48/22.53 apply (zenon_L789_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.48/22.53 apply (zenon_L343_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.48/22.53 apply (zenon_L37_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.48/22.53 apply (zenon_L232_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.48/22.53 apply (zenon_L791_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.48/22.53 apply (zenon_L361_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.48/22.53 apply (zenon_L792_); trivial. % 22.48/22.53 apply (zenon_L51_); trivial. % 22.48/22.53 (* end of lemma zenon_L2107_ *) % 22.48/22.53 assert (zenon_L2108_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (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) (e2)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (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) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (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)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((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 (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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))))) -> False). % 22.48/22.53 do 0 intro. intros zenon_H139 zenon_Heb zenon_H77 zenon_H48 zenon_Hf5 zenon_Hfa zenon_H8a zenon_H111 zenon_H68 zenon_H6c zenon_H158 zenon_H173 zenon_H4d zenon_H183 zenon_H104 zenon_H163 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H24e zenon_H192 zenon_H12e zenon_H4e zenon_H186 zenon_H131 zenon_Ha9 zenon_H236 zenon_H271 zenon_H125 zenon_H1ef zenon_H18a zenon_H212 zenon_H1b4 zenon_H196 zenon_H18d zenon_H234 zenon_H179 zenon_H121 zenon_H1f1 zenon_H13f zenon_H156 zenon_H189 zenon_H25b zenon_H1c6 zenon_H20f zenon_H129 zenon_H20b zenon_H141 zenon_H2c zenon_H109 zenon_H1d8 zenon_H26d zenon_H1c2 zenon_Hcc zenon_H277 zenon_H11a zenon_H82 zenon_H13a zenon_H5d zenon_Hb2 zenon_H55 zenon_H1a8 zenon_He4 zenon_Hb6 zenon_H1a2 zenon_H190 zenon_H33 zenon_Ha0 zenon_H19a zenon_H1cb zenon_H1c3 zenon_H1bb zenon_Hbc zenon_H177 zenon_H231 zenon_H164 zenon_H195 zenon_H117 zenon_H73 zenon_H1fe zenon_H15d. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.48/22.53 apply (zenon_L2_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.48/22.53 apply (zenon_L2091_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.48/22.53 apply (zenon_L782_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.48/22.53 apply (zenon_L2094_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.48/22.53 apply (zenon_L758_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.48/22.53 apply (zenon_L11_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.48/22.53 apply (zenon_L787_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.48/22.53 apply (zenon_L335_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.48/22.53 apply (zenon_L789_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.48/22.53 apply (zenon_L88_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.48/22.53 apply (zenon_L37_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.48/22.53 apply (zenon_L232_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.48/22.53 apply (zenon_L2077_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.48/22.53 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.48/22.53 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.48/22.53 apply (zenon_L2105_); trivial. % 22.48/22.53 apply (zenon_L2105_); trivial. % 22.48/22.53 apply (zenon_L932_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.48/22.53 apply (zenon_L792_); trivial. % 22.48/22.53 apply (zenon_L51_); trivial. % 22.48/22.53 apply (zenon_L2107_); trivial. % 22.48/22.53 (* end of lemma zenon_L2108_ *) % 22.48/22.53 assert (zenon_L2109_ : (((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) (e2)) = (op (e3) (e2)))) -> (((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)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (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) (e0)) = (op (e3) (e0)))) -> (~((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((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 (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((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)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 22.48/22.53 do 0 intro. intros zenon_H231 zenon_H271 zenon_H177 zenon_H125 zenon_H1ef zenon_H1fe zenon_Hbc zenon_H212 zenon_H196 zenon_H195 zenon_H163 zenon_H18d zenon_H234 zenon_H33 zenon_H179 zenon_H121 zenon_He4 zenon_H1f1 zenon_H13f zenon_H117 zenon_H156 zenon_H189 zenon_H25b zenon_H1c6 zenon_H19a zenon_H20b zenon_H73 zenon_H164 zenon_H141 zenon_H2c zenon_H55 zenon_H4e zenon_H109 zenon_H1d8 zenon_H26d zenon_H186 zenon_H1a2 zenon_Hcc zenon_H277 zenon_H11a zenon_Hb2 zenon_H5d zenon_H82 zenon_H15d zenon_H1a8 zenon_H190 zenon_H1c3 zenon_H1c2 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H131 zenon_H236 zenon_H23d zenon_H183 zenon_H104 zenon_H18a zenon_H1cb zenon_H1bb zenon_H192 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H24e zenon_H12e zenon_H139 zenon_Heb zenon_H77 zenon_H48 zenon_Hf5 zenon_Hfa zenon_H8a zenon_H111 zenon_H68 zenon_H6c zenon_H158 zenon_H173. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H4d ]. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.48/22.53 apply (zenon_L2_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.48/22.53 apply (zenon_L2070_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.48/22.53 apply (zenon_L782_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.48/22.53 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.48/22.53 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.48/22.53 apply (zenon_L2071_); trivial. % 22.48/22.53 apply (zenon_L2071_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.48/22.53 apply (zenon_L2072_); trivial. % 22.48/22.53 apply (zenon_L2072_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.48/22.53 apply (zenon_L2074_); trivial. % 22.48/22.53 apply (zenon_L2074_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.48/22.53 apply (zenon_L11_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.48/22.53 apply (zenon_L787_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.48/22.53 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.48/22.53 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.48/22.53 apply (zenon_L2076_); trivial. % 22.48/22.53 apply (zenon_L2076_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.48/22.53 apply (zenon_L789_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.48/22.53 apply (zenon_L88_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.48/22.53 apply (zenon_L37_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.48/22.53 apply (zenon_L232_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.48/22.53 apply (zenon_L2077_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.48/22.53 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.48/22.53 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.48/22.53 apply (zenon_L2086_); trivial. % 22.48/22.53 apply (zenon_L2086_); trivial. % 22.48/22.53 apply (zenon_L374_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.48/22.53 apply (zenon_L792_); trivial. % 22.48/22.53 apply (zenon_L51_); trivial. % 22.48/22.53 apply (zenon_L2089_); trivial. % 22.48/22.53 apply (zenon_L2108_); trivial. % 22.48/22.53 (* end of lemma zenon_L2109_ *) % 22.48/22.53 assert (zenon_L2110_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> False). % 22.48/22.53 do 0 intro. intros zenon_H28 zenon_H10c zenon_H5c. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.48/22.53 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.48/22.53 apply (zenon_L1350_); trivial. % 22.48/22.53 (* end of lemma zenon_L2110_ *) % 22.48/22.53 assert (zenon_L2111_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.53 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H6e zenon_H31 zenon_H117 zenon_Ha0 zenon_H2d zenon_H10c zenon_Hf0 zenon_H191 zenon_H196. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.53 exact (zenon_Ha4 zenon_H9f). % 22.48/22.53 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.53 apply (zenon_L110_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.53 apply (zenon_L68_); trivial. % 22.48/22.53 apply (zenon_L731_); trivial. % 22.48/22.53 (* end of lemma zenon_L2111_ *) % 22.48/22.53 assert (zenon_L2112_ : (((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)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 22.48/22.53 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H173 zenon_H10c zenon_Ha0 zenon_H31 zenon_Ha9 zenon_Hf6. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.53 exact (zenon_Ha4 zenon_H9f). % 22.48/22.53 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.53 apply (zenon_L120_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.53 apply (zenon_L68_); trivial. % 22.48/22.53 apply (zenon_L92_); trivial. % 22.48/22.53 (* end of lemma zenon_L2112_ *) % 22.48/22.53 assert (zenon_L2113_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((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)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 22.48/22.53 do 0 intro. intros zenon_H139 zenon_H77 zenon_H47 zenon_H196 zenon_H191 zenon_Hf0 zenon_H2d zenon_H117 zenon_H68 zenon_H13a zenon_Ha4 zenon_H173 zenon_H10c zenon_Ha0 zenon_H31 zenon_Ha9. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.53 apply (zenon_L251_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.53 apply (zenon_L2111_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.53 apply (zenon_L264_); trivial. % 22.48/22.53 apply (zenon_L2112_); trivial. % 22.48/22.53 (* end of lemma zenon_L2113_ *) % 22.48/22.53 assert (zenon_L2114_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.53 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_H31 zenon_H117 zenon_Ha0 zenon_H2d zenon_H10c zenon_Hf0 zenon_H191 zenon_H196. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.53 exact (zenon_Ha4 zenon_H9f). % 22.48/22.53 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.53 apply (zenon_L55_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.53 apply (zenon_L68_); trivial. % 22.48/22.53 apply (zenon_L731_); trivial. % 22.48/22.53 (* end of lemma zenon_L2114_ *) % 22.48/22.53 assert (zenon_L2115_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.53 do 0 intro. intros zenon_H15d zenon_Ha9 zenon_H173 zenon_H68 zenon_H77 zenon_H139 zenon_H196 zenon_H191 zenon_Hf0 zenon_H10c zenon_H2d zenon_Ha0 zenon_H117 zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.53 apply (zenon_L2113_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.53 apply (zenon_L2114_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.53 apply (zenon_L239_); trivial. % 22.48/22.53 apply (zenon_L192_); trivial. % 22.48/22.53 (* end of lemma zenon_L2115_ *) % 22.48/22.53 assert (zenon_L2116_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.53 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H65 zenon_Ha0 zenon_Hdd zenon_Hb6 zenon_H105 zenon_H9e zenon_H196. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.48/22.53 apply (zenon_L43_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.48/22.53 apply (zenon_L152_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.48/22.53 apply (zenon_L400_); trivial. % 22.48/22.53 apply (zenon_L154_); trivial. % 22.48/22.53 (* end of lemma zenon_L2116_ *) % 22.48/22.53 assert (zenon_L2117_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((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)) = (e1)) -> False). % 22.48/22.53 do 0 intro. intros zenon_H13f zenon_H77 zenon_H7f zenon_H1f1 zenon_H196 zenon_H9e zenon_Hb6 zenon_Hdd zenon_Ha0 zenon_H65 zenon_Ha9 zenon_H117 zenon_H195 zenon_H5c. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.48/22.53 apply (zenon_L30_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.48/22.53 apply (zenon_L284_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.48/22.53 apply (zenon_L2116_); trivial. % 22.48/22.53 apply (zenon_L149_); trivial. % 22.48/22.53 (* end of lemma zenon_L2117_ *) % 22.48/22.53 assert (zenon_L2118_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((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 (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.48/22.53 do 0 intro. intros zenon_H164 zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_H9e zenon_Ha0 zenon_H19a zenon_H14c zenon_H104 zenon_H121 zenon_H11a zenon_H10c zenon_H1cd zenon_H160 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H1b7 zenon_H24e zenon_Hc4. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.48/22.53 apply (zenon_L851_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.48/22.53 apply (zenon_L724_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.48/22.53 apply (zenon_L257_); trivial. % 22.48/22.53 apply (zenon_L561_); trivial. % 22.48/22.53 (* end of lemma zenon_L2118_ *) % 22.48/22.53 assert (zenon_L2119_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((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) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 22.48/22.53 do 0 intro. intros zenon_H164 zenon_H1e zenon_H33 zenon_H1b7 zenon_H1cb zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_H9e zenon_Ha0 zenon_H19a zenon_H212 zenon_H18a zenon_H7f zenon_H7d zenon_Hbc zenon_H160 zenon_H209. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.48/22.53 apply (zenon_L7_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.48/22.53 apply (zenon_L724_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.48/22.53 apply (zenon_L267_); trivial. % 22.48/22.53 apply (zenon_L417_); trivial. % 22.48/22.53 (* end of lemma zenon_L2119_ *) % 22.48/22.53 assert (zenon_L2120_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((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) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 22.48/22.53 do 0 intro. intros zenon_He4 zenon_H196 zenon_H177 zenon_H77 zenon_H139 zenon_H234 zenon_H104 zenon_H121 zenon_H11a zenon_H10c zenon_H1cd zenon_H24e zenon_Hc4 zenon_H2c zenon_H141 zenon_H164 zenon_H1e zenon_H33 zenon_H1b7 zenon_H1cb zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_H9e zenon_Ha0 zenon_H19a zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H160 zenon_H209. % 22.48/22.53 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.48/22.53 apply (zenon_L215_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.48/22.53 apply (zenon_L484_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.53 apply (zenon_L5_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.53 apply (zenon_L111_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.53 apply (zenon_L2118_); trivial. % 22.48/22.53 apply (zenon_L158_); trivial. % 22.48/22.53 apply (zenon_L2119_); trivial. % 22.48/22.53 (* end of lemma zenon_L2120_ *) % 22.48/22.53 assert (zenon_L2121_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (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) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((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) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> False). % 22.48/22.53 do 0 intro. intros zenon_H1cf zenon_H153 zenon_H4e zenon_H76 zenon_Ha9 zenon_Hdd zenon_H54 zenon_Hb6 zenon_H117 zenon_He4 zenon_H196 zenon_H177 zenon_H77 zenon_H139 zenon_H234 zenon_H104 zenon_H121 zenon_H11a zenon_H10c zenon_H1cd zenon_H24e zenon_Hc4 zenon_H2c zenon_H141 zenon_H164 zenon_H1e zenon_H33 zenon_H1b7 zenon_H1cb zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_H9e zenon_Ha0 zenon_H19a zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.48/22.53 apply (zenon_L94_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.48/22.53 apply (zenon_L83_); trivial. % 22.48/22.53 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.48/22.53 apply (zenon_L155_); trivial. % 22.48/22.53 apply (zenon_L2120_); trivial. % 22.48/22.53 (* end of lemma zenon_L2121_ *) % 22.48/22.53 assert (zenon_L2122_ : (((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 (e3) (e1)) = (e1)) -> (((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 (e0) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (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) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((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) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H16a zenon_H195 zenon_H1f1 zenon_H7f zenon_H13f zenon_H1cf zenon_H153 zenon_H4e zenon_H76 zenon_Ha9 zenon_Hdd zenon_H54 zenon_Hb6 zenon_H117 zenon_He4 zenon_H196 zenon_H177 zenon_H77 zenon_H139 zenon_H234 zenon_H104 zenon_H121 zenon_H11a zenon_H10c zenon_H1cd zenon_H24e zenon_Hc4 zenon_H2c zenon_H141 zenon_H164 zenon_H1e zenon_H33 zenon_H1b7 zenon_H1cb zenon_H68 zenon_H48 zenon_H5c zenon_H9e zenon_Ha0 zenon_H19a zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.48/22.54 apply (zenon_L2117_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.48/22.54 apply (zenon_L54_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.48/22.54 apply (zenon_L155_); trivial. % 22.48/22.54 apply (zenon_L2121_); trivial. % 22.48/22.54 (* end of lemma zenon_L2122_ *) % 22.48/22.54 assert (zenon_L2123_ : (((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) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 22.48/22.54 do 0 intro. intros zenon_H13f zenon_Hb6 zenon_Ha8 zenon_H7f zenon_H1f1 zenon_H48 zenon_H14c zenon_H195 zenon_H5c. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.48/22.54 apply (zenon_L151_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.48/22.54 apply (zenon_L284_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.48/22.54 apply (zenon_L255_); trivial. % 22.48/22.54 apply (zenon_L149_); trivial. % 22.48/22.54 (* end of lemma zenon_L2123_ *) % 22.48/22.54 assert (zenon_L2124_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (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 (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H117 zenon_H5c zenon_H195 zenon_H48 zenon_H1f1 zenon_H7f zenon_Hb6 zenon_H13f zenon_H10c zenon_Hf0 zenon_H14c zenon_Ha0 zenon_H9e zenon_H196. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.48/22.54 apply (zenon_L2123_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.48/22.54 apply (zenon_L74_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.48/22.54 apply (zenon_L278_); trivial. % 22.48/22.54 apply (zenon_L154_); trivial. % 22.48/22.54 (* end of lemma zenon_L2124_ *) % 22.48/22.54 assert (zenon_L2125_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (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))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H6e zenon_H140 zenon_H1a3 zenon_H191 zenon_H153 zenon_H1a2 zenon_H196 zenon_Hf0 zenon_H10c zenon_H13f zenon_Hb6 zenon_H7f zenon_H1f1 zenon_H195 zenon_H117 zenon_H1c3 zenon_Ha9 zenon_H77 zenon_H1cb zenon_H68 zenon_H48 zenon_H5c zenon_Ha0 zenon_H19a zenon_H102 zenon_H18a. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.54 exact (zenon_Ha4 zenon_H9f). % 22.48/22.54 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.54 apply (zenon_L110_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.54 apply (zenon_L95_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.48/22.54 apply (zenon_L239_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.48/22.54 apply (zenon_L1265_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.48/22.54 apply (zenon_L2124_); trivial. % 22.48/22.54 apply (zenon_L269_); trivial. % 22.48/22.54 (* end of lemma zenon_L2125_ *) % 22.48/22.54 assert (zenon_L2126_ : (((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)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H117 zenon_H109 zenon_H9d zenon_Ha0 zenon_Hdd zenon_H8a zenon_Ha9 zenon_H9e zenon_H196. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.48/22.54 apply (zenon_L73_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.48/22.54 apply (zenon_L152_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.48/22.54 apply (zenon_L153_); trivial. % 22.48/22.54 apply (zenon_L154_); trivial. % 22.48/22.54 (* end of lemma zenon_L2126_ *) % 22.48/22.54 assert (zenon_L2127_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H139 zenon_H77 zenon_H47 zenon_H191 zenon_Hf0 zenon_H10c zenon_H2d zenon_Ha0 zenon_H117 zenon_Ha9 zenon_Ha4 zenon_H13a zenon_H68 zenon_H31 zenon_H93 zenon_H196. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.54 apply (zenon_L251_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.54 apply (zenon_L2111_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.54 apply (zenon_L264_); trivial. % 22.48/22.54 apply (zenon_L167_); trivial. % 22.48/22.54 (* end of lemma zenon_L2127_ *) % 22.48/22.54 assert (zenon_L2128_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H15d zenon_H1e zenon_H7f zenon_H192 zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.54 apply (zenon_L13_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.54 apply (zenon_L146_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.54 apply (zenon_L239_); trivial. % 22.48/22.54 apply (zenon_L192_); trivial. % 22.48/22.54 (* end of lemma zenon_L2128_ *) % 22.48/22.54 assert (zenon_L2129_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (e0)) = (e3))) -> False). % 22.48/22.54 do 0 intro. intros zenon_Hb2 zenon_Ha4 zenon_Ha0 zenon_H25 zenon_H1ef zenon_H110 zenon_H209. % 22.48/22.54 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.48/22.54 exact (zenon_Ha4 zenon_H9f). % 22.48/22.54 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.48/22.54 apply (zenon_L116_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.48/22.54 apply (zenon_L282_); trivial. % 22.48/22.54 exact (zenon_H209 zenon_H9d). % 22.48/22.54 (* end of lemma zenon_L2129_ *) % 22.48/22.54 assert (zenon_L2130_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H266 zenon_H2d zenon_H55 zenon_H105 zenon_H6f zenon_H6e zenon_H110 zenon_H190. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_Hdd | zenon_intro zenon_H267 ]. % 22.48/22.54 apply (zenon_L702_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H53 | zenon_intro zenon_H268 ]. % 22.48/22.54 apply (zenon_L143_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_H6d | zenon_intro zenon_H10d ]. % 22.48/22.54 apply (zenon_L21_); trivial. % 22.48/22.54 apply (zenon_L163_); trivial. % 22.48/22.54 (* end of lemma zenon_L2130_ *) % 22.48/22.54 assert (zenon_L2131_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 22.48/22.54 do 0 intro. intros zenon_H13f zenon_H48 zenon_H7f zenon_H1f1 zenon_H190 zenon_H110 zenon_H6e zenon_H6f zenon_H55 zenon_H2d zenon_H266 zenon_H195 zenon_H5c. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.48/22.54 apply (zenon_L217_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.48/22.54 apply (zenon_L284_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.48/22.54 apply (zenon_L2130_); trivial. % 22.48/22.54 apply (zenon_L149_); trivial. % 22.48/22.54 (* end of lemma zenon_L2131_ *) % 22.48/22.54 assert (zenon_L2132_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H1fe zenon_H209 zenon_H1ef zenon_Ha0 zenon_Ha4 zenon_Hb2 zenon_Hf5 zenon_H31 zenon_H192 zenon_H139 zenon_H195 zenon_H266 zenon_H55 zenon_H6f zenon_H110 zenon_H190 zenon_H1f1 zenon_H13f zenon_H196 zenon_H15d zenon_H19a zenon_H1b7 zenon_H7f zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H18a. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.54 apply (zenon_L2128_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.54 apply (zenon_L2129_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.54 apply (zenon_L251_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.54 apply (zenon_L2131_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.54 apply (zenon_L264_); trivial. % 22.48/22.54 apply (zenon_L167_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.54 apply (zenon_L146_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.54 apply (zenon_L239_); trivial. % 22.48/22.54 apply (zenon_L192_); trivial. % 22.48/22.54 apply (zenon_L1343_); trivial. % 22.48/22.54 (* end of lemma zenon_L2132_ *) % 22.48/22.54 assert (zenon_L2133_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((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) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (((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). % 22.48/22.54 do 0 intro. intros zenon_H15d zenon_H177 zenon_H196 zenon_H93 zenon_H77 zenon_H13a zenon_Ha4 zenon_Ha9 zenon_Hb6 zenon_He4 zenon_H234 zenon_H110 zenon_H2c zenon_H141 zenon_H164 zenon_H1e zenon_H33 zenon_H1b7 zenon_H1cb zenon_H68 zenon_H48 zenon_Ha0 zenon_H19a zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H160 zenon_H209 zenon_H139 zenon_H5c zenon_Hf5. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.54 apply (zenon_L13_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.54 apply (zenon_L215_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.54 apply (zenon_L20_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.54 exact (zenon_Ha4 zenon_H9f). % 22.48/22.54 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.54 apply (zenon_L110_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.54 apply (zenon_L95_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.48/22.54 apply (zenon_L214_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.48/22.54 apply (zenon_L484_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.48/22.54 apply (zenon_L858_); trivial. % 22.48/22.54 apply (zenon_L2119_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.54 apply (zenon_L94_); trivial. % 22.48/22.54 apply (zenon_L167_); trivial. % 22.48/22.54 apply (zenon_L192_); trivial. % 22.48/22.54 (* end of lemma zenon_L2133_ *) % 22.48/22.54 assert (zenon_L2134_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.48/22.54 do 0 intro. intros zenon_Hfa zenon_Hf5 zenon_H139 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H19a zenon_Ha0 zenon_H48 zenon_H1cb zenon_H1b7 zenon_H33 zenon_H1e zenon_H164 zenon_H141 zenon_H2c zenon_H110 zenon_H234 zenon_He4 zenon_Hb6 zenon_Ha9 zenon_Ha4 zenon_H13a zenon_H93 zenon_H196 zenon_H177 zenon_H15d zenon_H4e zenon_H153 zenon_H1cf zenon_H6e zenon_H173 zenon_Hf3 zenon_H68 zenon_H5c zenon_H77. % 22.48/22.54 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.48/22.54 apply (zenon_L94_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.48/22.54 apply (zenon_L83_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.48/22.54 apply (zenon_L153_); trivial. % 22.48/22.54 apply (zenon_L2133_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.48/22.54 apply (zenon_L226_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.48/22.54 apply (zenon_L62_); trivial. % 22.48/22.54 apply (zenon_L206_); trivial. % 22.48/22.54 (* end of lemma zenon_L2134_ *) % 22.48/22.54 assert (zenon_L2135_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H196 zenon_H93 zenon_H77 zenon_H140 zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H7f zenon_H13f zenon_H1f1 zenon_H190 zenon_H6f zenon_H55 zenon_H266 zenon_H195 zenon_H192 zenon_Hb2 zenon_H1ef zenon_H1fe zenon_H173 zenon_H1cf zenon_H4e zenon_H15d zenon_H177 zenon_H13a zenon_Ha4 zenon_Ha9 zenon_Hb6 zenon_He4 zenon_H234 zenon_H2c zenon_H141 zenon_H164 zenon_H1e zenon_H33 zenon_H1b7 zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H139 zenon_Hfa zenon_H110 zenon_H19a zenon_Ha0 zenon_H48 zenon_H68 zenon_H1cb zenon_H5c zenon_Hf5. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.54 apply (zenon_L13_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.54 apply (zenon_L146_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.54 apply (zenon_L20_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.54 exact (zenon_Ha4 zenon_H9f). % 22.48/22.54 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.54 apply (zenon_L110_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.54 apply (zenon_L95_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.48/22.54 apply (zenon_L2132_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.48/22.54 apply (zenon_L2134_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.48/22.54 apply (zenon_L278_); trivial. % 22.48/22.54 apply (zenon_L267_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.54 apply (zenon_L94_); trivial. % 22.48/22.54 apply (zenon_L167_); trivial. % 22.48/22.54 apply (zenon_L192_); trivial. % 22.48/22.54 (* end of lemma zenon_L2135_ *) % 22.48/22.54 assert (zenon_L2136_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H139 zenon_H1e zenon_H68 zenon_H2a zenon_H153 zenon_H77 zenon_H93 zenon_H196. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.54 apply (zenon_L20_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.54 apply (zenon_L147_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.54 apply (zenon_L94_); trivial. % 22.48/22.54 apply (zenon_L167_); trivial. % 22.48/22.54 (* end of lemma zenon_L2136_ *) % 22.48/22.54 assert (zenon_L2137_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (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). % 22.48/22.54 do 0 intro. intros zenon_H15d zenon_H48 zenon_H196 zenon_H93 zenon_H77 zenon_H2a zenon_H68 zenon_H1e zenon_H139 zenon_H5c zenon_Hf5. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.54 apply (zenon_L13_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.54 apply (zenon_L65_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.54 apply (zenon_L2136_); trivial. % 22.48/22.54 apply (zenon_L192_); trivial. % 22.48/22.54 (* end of lemma zenon_L2137_ *) % 22.48/22.54 assert (zenon_L2138_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 22.48/22.54 do 0 intro. intros zenon_H13f zenon_H48 zenon_H7f zenon_H1f1 zenon_H190 zenon_H110 zenon_Hef zenon_Hf0 zenon_H55 zenon_H2d zenon_H266 zenon_H195 zenon_H5c. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.48/22.54 apply (zenon_L217_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.48/22.54 apply (zenon_L284_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.48/22.54 apply (zenon_L1896_); trivial. % 22.48/22.54 apply (zenon_L149_); trivial. % 22.48/22.54 (* end of lemma zenon_L2138_ *) % 22.48/22.54 assert (zenon_L2139_ : (((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H1fe zenon_Hf5 zenon_H139 zenon_H196 zenon_H15d zenon_H209 zenon_H1ef zenon_Ha0 zenon_Ha4 zenon_Hb2 zenon_H189 zenon_H13f zenon_H1f1 zenon_H190 zenon_H110 zenon_Hf0 zenon_H55 zenon_H266 zenon_H195 zenon_H2a zenon_H1a8 zenon_H19a zenon_H1b7 zenon_H7f zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H18a. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.54 apply (zenon_L2137_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.54 apply (zenon_L2129_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.48/22.54 apply (zenon_L147_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.48/22.54 apply (zenon_L2138_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.48/22.54 apply (zenon_L439_); trivial. % 22.48/22.54 apply (zenon_L169_); trivial. % 22.48/22.54 apply (zenon_L1343_); trivial. % 22.48/22.54 (* end of lemma zenon_L2139_ *) % 22.48/22.54 assert (zenon_L2140_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((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 (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((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)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (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 (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H236 zenon_H1cb zenon_Hfa zenon_Hbc zenon_H7d zenon_H212 zenon_H33 zenon_H164 zenon_H141 zenon_H2c zenon_H234 zenon_He4 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H177 zenon_H4e zenon_H1cf zenon_H173 zenon_H140 zenon_H1a8 zenon_Hf0 zenon_H189 zenon_H18a zenon_H68 zenon_H5c zenon_H7f zenon_H19a zenon_H15d zenon_H196 zenon_H13f zenon_H1f1 zenon_H190 zenon_H110 zenon_H6f zenon_H55 zenon_H266 zenon_H195 zenon_H139 zenon_H192 zenon_Hf5 zenon_Hb2 zenon_Ha4 zenon_Ha0 zenon_H1ef zenon_H209 zenon_H1fe zenon_H61 zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H1b7. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.48/22.54 apply (zenon_L2135_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.48/22.54 apply (zenon_L2139_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.48/22.54 apply (zenon_L2132_); trivial. % 22.48/22.54 apply (zenon_L1717_); trivial. % 22.48/22.54 (* end of lemma zenon_L2140_ *) % 22.48/22.54 assert (zenon_L2141_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (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))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H117 zenon_H2d zenon_H10c zenon_H1b7 zenon_H77 zenon_H93 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H61 zenon_H1fe zenon_H209 zenon_H1ef zenon_Ha0 zenon_Ha4 zenon_Hb2 zenon_Hf5 zenon_H192 zenon_H139 zenon_H195 zenon_H266 zenon_H55 zenon_H6f zenon_H190 zenon_H1f1 zenon_H13f zenon_H15d zenon_H19a zenon_H7f zenon_H5c zenon_H68 zenon_H18a zenon_H189 zenon_Hf0 zenon_H1a8 zenon_H140 zenon_H173 zenon_H1cf zenon_H4e zenon_H177 zenon_H13a zenon_Ha9 zenon_Hb6 zenon_He4 zenon_H234 zenon_H2c zenon_H141 zenon_H164 zenon_H33 zenon_H212 zenon_H7d zenon_Hbc zenon_Hfa zenon_H1cb zenon_H236 zenon_H9e zenon_H196. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.48/22.54 apply (zenon_L67_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.48/22.54 apply (zenon_L74_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.48/22.54 apply (zenon_L2140_); trivial. % 22.48/22.54 apply (zenon_L154_); trivial. % 22.48/22.54 (* end of lemma zenon_L2141_ *) % 22.48/22.54 assert (zenon_L2142_ : ((op (e0) (e1)) = (e2)) -> (~((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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (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))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H6e zenon_H11a zenon_H121 zenon_H117 zenon_H2d zenon_H10c zenon_H1b7 zenon_H77 zenon_H93 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H48 zenon_H18d zenon_H61 zenon_H1fe zenon_H209 zenon_H1ef zenon_Ha0 zenon_Ha4 zenon_Hb2 zenon_Hf5 zenon_H192 zenon_H139 zenon_H195 zenon_H266 zenon_H55 zenon_H6f zenon_H190 zenon_H1f1 zenon_H13f zenon_H15d zenon_H19a zenon_H7f zenon_H5c zenon_H68 zenon_H18a zenon_H189 zenon_Hf0 zenon_H1a8 zenon_H140 zenon_H173 zenon_H1cf zenon_H4e zenon_H177 zenon_H13a zenon_Ha9 zenon_Hb6 zenon_He4 zenon_H234 zenon_H2c zenon_H141 zenon_H164 zenon_H33 zenon_H212 zenon_H7d zenon_Hbc zenon_Hfa zenon_H1cb zenon_H236 zenon_H196. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.54 exact (zenon_Ha4 zenon_H9f). % 22.48/22.54 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.54 apply (zenon_L110_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.54 apply (zenon_L393_); trivial. % 22.48/22.54 apply (zenon_L2141_); trivial. % 22.48/22.54 (* end of lemma zenon_L2142_ *) % 22.48/22.54 assert (zenon_L2143_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (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) (e1)) = (op (e3) (e1)))) -> (~((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)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((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)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((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)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 22.48/22.54 do 0 intro. intros zenon_H236 zenon_Hfa zenon_H13a zenon_H173 zenon_H140 zenon_H1a8 zenon_H189 zenon_H15d zenon_H190 zenon_H6f zenon_H55 zenon_H266 zenon_H192 zenon_Hf5 zenon_Hb2 zenon_Ha4 zenon_H1ef zenon_H1fe zenon_H61 zenon_H18d zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H6e zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H19a zenon_H1cb zenon_H1b7 zenon_H33 zenon_H1e zenon_H164 zenon_H141 zenon_H2c zenon_Hc4 zenon_H24e zenon_H1cd zenon_H11a zenon_H121 zenon_H104 zenon_H234 zenon_H139 zenon_H77 zenon_H177 zenon_He4 zenon_H54 zenon_Ha9 zenon_H76 zenon_H4e zenon_H153 zenon_H1cf zenon_H196 zenon_H9e zenon_Ha0 zenon_Hf0 zenon_H10c zenon_H13f zenon_Hb6 zenon_H7f zenon_H1f1 zenon_H48 zenon_H195 zenon_H5c zenon_H117 zenon_H68 zenon_H93. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.54 apply (zenon_L2142_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.54 apply (zenon_L2121_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.54 apply (zenon_L2124_); trivial. % 22.48/22.54 apply (zenon_L158_); trivial. % 22.48/22.54 (* end of lemma zenon_L2143_ *) % 22.48/22.54 assert (zenon_L2144_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (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))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.54 do 0 intro. intros zenon_H140 zenon_H153 zenon_H72 zenon_H196 zenon_Hf0 zenon_H10c zenon_H13f zenon_Hb6 zenon_H7f zenon_H1f1 zenon_H195 zenon_H117 zenon_H1c3 zenon_Ha9 zenon_H77 zenon_H1cb zenon_H68 zenon_H48 zenon_H5c zenon_H9e zenon_Ha0 zenon_H19a zenon_H102 zenon_H18a. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.48/22.54 apply (zenon_L239_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.48/22.54 apply (zenon_L62_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.48/22.54 apply (zenon_L2124_); trivial. % 22.48/22.54 apply (zenon_L269_); trivial. % 22.48/22.54 (* end of lemma zenon_L2144_ *) % 22.48/22.54 assert (zenon_L2145_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (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) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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) (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (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)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((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) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (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 (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (((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). % 22.48/22.54 do 0 intro. intros zenon_H1cf zenon_H4e zenon_H54 zenon_He4 zenon_H177 zenon_H139 zenon_H234 zenon_H104 zenon_H121 zenon_H11a zenon_H1cd zenon_H24e zenon_Hc4 zenon_H2c zenon_H141 zenon_H164 zenon_H1e zenon_H33 zenon_H1b7 zenon_H212 zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_H18d zenon_H61 zenon_H1fe zenon_H1ef zenon_Ha4 zenon_Hb2 zenon_Hf5 zenon_H192 zenon_H266 zenon_H55 zenon_H6f zenon_H190 zenon_H15d zenon_H189 zenon_H1a8 zenon_H13a zenon_Hfa zenon_H236 zenon_H6e zenon_H173 zenon_H18a zenon_H102 zenon_H19a zenon_Ha0 zenon_H9e zenon_H5c zenon_H48 zenon_H68 zenon_H1cb zenon_H77 zenon_Ha9 zenon_H1c3 zenon_H117 zenon_H1f1 zenon_H7f zenon_Hb6 zenon_H13f zenon_H10c zenon_Hf0 zenon_H196 zenon_H153 zenon_H140 zenon_H93 zenon_H195. % 22.48/22.54 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.48/22.54 apply (zenon_L2143_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.48/22.54 apply (zenon_L226_); trivial. % 22.48/22.54 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.48/22.54 apply (zenon_L2144_); trivial. % 22.48/22.54 apply (zenon_L228_); trivial. % 22.48/22.54 (* end of lemma zenon_L2145_ *) % 22.48/22.54 assert (zenon_L2146_ : ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (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) (e1)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (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) (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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (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))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (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) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H7f zenon_H7d zenon_H195 zenon_H140 zenon_Hf0 zenon_H10c zenon_H13f zenon_Hb6 zenon_H1f1 zenon_H117 zenon_H1c3 zenon_Ha9 zenon_H1cb zenon_H68 zenon_H48 zenon_Ha0 zenon_H19a zenon_H18a zenon_H173 zenon_H236 zenon_Hfa zenon_H13a zenon_H1a8 zenon_H189 zenon_H15d zenon_H190 zenon_H6f zenon_H55 zenon_H266 zenon_H192 zenon_Hb2 zenon_Ha4 zenon_H1ef zenon_H1fe zenon_H61 zenon_H18d zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H209 zenon_Hbc zenon_H212 zenon_H1b7 zenon_H33 zenon_H1e zenon_H164 zenon_H141 zenon_H2c zenon_Hc4 zenon_H24e zenon_H1cd zenon_H11a zenon_H121 zenon_H104 zenon_H234 zenon_H139 zenon_H177 zenon_He4 zenon_H4e zenon_H1cf zenon_H125 zenon_H77 zenon_H93 zenon_H196 zenon_H5d zenon_H82 zenon_H5c zenon_Hf5. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_L13_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L146_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.55 apply (zenon_L13_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.55 apply (zenon_L17_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_L20_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.48/22.55 apply (zenon_L20_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L120_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L393_); trivial. % 22.48/22.55 apply (zenon_L2143_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.48/22.55 apply (zenon_L30_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L110_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L95_); trivial. % 22.48/22.55 apply (zenon_L2145_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_L94_); trivial. % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 apply (zenon_L31_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 (* end of lemma zenon_L2146_ *) % 22.48/22.55 assert (zenon_L2147_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (((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)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> False). % 22.48/22.55 do 0 intro. intros zenon_H1a2 zenon_H31 zenon_Ha9 zenon_H72 zenon_Hb6 zenon_H105 zenon_H164 zenon_H25 zenon_H179 zenon_H1b7 zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_H9e zenon_H19a zenon_Ha0 zenon_H47 zenon_H102. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.48/22.55 apply (zenon_L68_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.48/22.55 apply (zenon_L436_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.48/22.55 apply (zenon_L400_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.48/22.55 apply (zenon_L297_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.48/22.55 apply (zenon_L724_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.48/22.55 apply (zenon_L80_); trivial. % 22.48/22.55 apply (zenon_L1991_); trivial. % 22.48/22.55 (* end of lemma zenon_L2147_ *) % 22.48/22.55 assert (zenon_L2148_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((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)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_Hfa zenon_H6e zenon_H173 zenon_H5c zenon_H1a2 zenon_H31 zenon_Ha9 zenon_Hb6 zenon_H164 zenon_H25 zenon_H179 zenon_H1b7 zenon_H68 zenon_H48 zenon_H9e zenon_H19a zenon_Ha0 zenon_H47 zenon_H102 zenon_H1f1 zenon_H7f zenon_Ha8 zenon_H13f zenon_H93 zenon_H195. % 22.48/22.55 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.48/22.55 apply (zenon_L171_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.48/22.55 apply (zenon_L226_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.48/22.55 apply (zenon_L151_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.48/22.55 apply (zenon_L284_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.48/22.55 apply (zenon_L2147_); trivial. % 22.48/22.55 apply (zenon_L149_); trivial. % 22.48/22.55 apply (zenon_L228_); trivial. % 22.48/22.55 (* end of lemma zenon_L2148_ *) % 22.48/22.55 assert (zenon_L2149_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (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) (e3)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((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)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H139 zenon_H209 zenon_Hfa zenon_H173 zenon_H5c zenon_H1a2 zenon_Ha9 zenon_Hb6 zenon_H164 zenon_H25 zenon_H179 zenon_H1b7 zenon_H48 zenon_H19a zenon_Ha0 zenon_H47 zenon_H1f1 zenon_H7f zenon_H13f zenon_H195 zenon_Ha4 zenon_Hb2 zenon_H13a zenon_H94 zenon_H77 zenon_H125 zenon_H68 zenon_H31 zenon_H93 zenon_H196. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_L251_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.48/22.55 apply (zenon_L251_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.48/22.55 apply (zenon_L171_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.48/22.55 apply (zenon_L38_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L110_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L68_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.48/22.55 apply (zenon_L116_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.48/22.55 apply (zenon_L2148_); trivial. % 22.48/22.55 exact (zenon_H209 zenon_H9d). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_L264_); trivial. % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 (* end of lemma zenon_L2149_ *) % 22.48/22.55 assert (zenon_L2150_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H139 zenon_H47 zenon_H68 zenon_H2a zenon_H153 zenon_H77 zenon_H93 zenon_H196. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_L251_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_L147_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_L94_); trivial. % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 (* end of lemma zenon_L2150_ *) % 22.48/22.55 assert (zenon_L2151_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (e3))) -> False). % 22.48/22.55 do 0 intro. intros zenon_Hb2 zenon_Ha4 zenon_Ha0 zenon_H25 zenon_Hb6 zenon_H54 zenon_H209. % 22.48/22.55 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.48/22.55 apply (zenon_L116_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.48/22.55 apply (zenon_L151_); trivial. % 22.48/22.55 exact (zenon_H209 zenon_H9d). % 22.48/22.55 (* end of lemma zenon_L2151_ *) % 22.48/22.55 assert (zenon_L2152_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 22.48/22.55 do 0 intro. intros zenon_H164 zenon_H18a zenon_H2a zenon_H192 zenon_H1cb zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_H9e zenon_Ha0 zenon_H19a zenon_H67 zenon_H7e. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.48/22.55 apply (zenon_L851_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.48/22.55 apply (zenon_L292_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.48/22.55 apply (zenon_L267_); trivial. % 22.48/22.55 apply (zenon_L547_); trivial. % 22.48/22.55 (* end of lemma zenon_L2152_ *) % 22.48/22.55 assert (zenon_L2153_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H139 zenon_H7e zenon_H19a zenon_Ha0 zenon_H5c zenon_H48 zenon_H1cb zenon_H192 zenon_H18a zenon_H164 zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H68 zenon_H2a zenon_H153 zenon_H77 zenon_H93 zenon_H196. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L53_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L95_); trivial. % 22.48/22.55 apply (zenon_L2152_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_L147_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_L94_); trivial. % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 (* end of lemma zenon_L2153_ *) % 22.48/22.55 assert (zenon_L2154_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (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))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e1) (e1)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H19d zenon_H125 zenon_H94 zenon_H179 zenon_H1a2 zenon_H1c3 zenon_H1d5 zenon_Hf5 zenon_H82 zenon_H5d zenon_H139 zenon_Ha0 zenon_H1cb zenon_H192 zenon_H164 zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H2a zenon_H196 zenon_H121 zenon_H11a zenon_H236 zenon_Hfa zenon_Hbc zenon_H7d zenon_H212 zenon_H33 zenon_H141 zenon_H2c zenon_H234 zenon_He4 zenon_Ha9 zenon_H177 zenon_H4e zenon_H1cf zenon_H173 zenon_H140 zenon_H1a8 zenon_Hf0 zenon_H189 zenon_H15d zenon_H13f zenon_H1f1 zenon_H190 zenon_H6f zenon_H55 zenon_H266 zenon_H195 zenon_Hb2 zenon_H1ef zenon_H209 zenon_H1fe zenon_H61 zenon_H10c zenon_H117 zenon_H19a zenon_H1b7 zenon_H7f zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H18a. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.55 apply (zenon_L161_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_L251_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_L147_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.48/22.55 apply (zenon_L252_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.48/22.55 apply (zenon_L171_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.48/22.55 apply (zenon_L38_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L53_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L193_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.48/22.55 apply (zenon_L116_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.48/22.55 apply (zenon_L2149_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.48/22.55 apply (zenon_L274_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.48/22.55 apply (zenon_L2123_); trivial. % 22.48/22.55 apply (zenon_L269_); trivial. % 22.48/22.55 exact (zenon_H209 zenon_H9d). % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L146_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.55 apply (zenon_L2150_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.55 apply (zenon_L25_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.55 apply (zenon_L2151_); trivial. % 22.48/22.55 apply (zenon_L2153_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_L251_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_L2142_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L120_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L193_); trivial. % 22.48/22.55 apply (zenon_L2141_); trivial. % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L65_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.55 apply (zenon_L2150_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.55 apply (zenon_L17_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.55 apply (zenon_L217_); trivial. % 22.48/22.55 apply (zenon_L2153_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 apply (zenon_L1343_); trivial. % 22.48/22.55 (* end of lemma zenon_L2154_ *) % 22.48/22.55 assert (zenon_L2155_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H15d zenon_H196 zenon_H93 zenon_H68 zenon_H125 zenon_H77 zenon_H94 zenon_H13a zenon_Hb2 zenon_Ha4 zenon_H195 zenon_H13f zenon_H1f1 zenon_Ha0 zenon_H19a zenon_H1b7 zenon_H179 zenon_H25 zenon_H164 zenon_Hb6 zenon_Ha9 zenon_H1a2 zenon_H173 zenon_Hfa zenon_H209 zenon_H139 zenon_H7f zenon_H192 zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_L2149_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L146_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_L239_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 (* end of lemma zenon_L2155_ *) % 22.48/22.55 assert (zenon_L2156_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (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 (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (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))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H196 zenon_H93 zenon_H68 zenon_H11a zenon_H121 zenon_H117 zenon_H2d zenon_H10c zenon_H1b7 zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H61 zenon_H1fe zenon_H209 zenon_H1ef zenon_Ha0 zenon_Ha4 zenon_Hb2 zenon_H139 zenon_H195 zenon_H266 zenon_H55 zenon_H6f zenon_H190 zenon_H1f1 zenon_H13f zenon_H15d zenon_H19a zenon_H18a zenon_H189 zenon_Hf0 zenon_H1a8 zenon_H140 zenon_H173 zenon_H1cf zenon_H4e zenon_H177 zenon_H13a zenon_Ha9 zenon_Hb6 zenon_He4 zenon_H234 zenon_H2c zenon_H141 zenon_H164 zenon_H33 zenon_H212 zenon_H7d zenon_Hbc zenon_Hfa zenon_H1cb zenon_H236 zenon_H7f zenon_H192 zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_L251_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_L2142_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_L264_); trivial. % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L146_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_L239_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 (* end of lemma zenon_L2156_ *) % 22.48/22.55 assert (zenon_L2157_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((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 (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H1a2 zenon_H179 zenon_H94 zenon_H125 zenon_Hf5 zenon_H31 zenon_H192 zenon_H236 zenon_H1cb zenon_Hfa zenon_Hbc zenon_H7d zenon_H212 zenon_H33 zenon_H164 zenon_H141 zenon_H2c zenon_H234 zenon_He4 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H177 zenon_H4e zenon_H1cf zenon_H173 zenon_H140 zenon_H1a8 zenon_Hf0 zenon_H189 zenon_H15d zenon_H13f zenon_H1f1 zenon_H190 zenon_H6f zenon_H55 zenon_H266 zenon_H195 zenon_H139 zenon_Hb2 zenon_Ha4 zenon_Ha0 zenon_H1ef zenon_H209 zenon_H1fe zenon_H61 zenon_H10c zenon_H117 zenon_H121 zenon_H11a zenon_H196 zenon_H19a zenon_H1b7 zenon_H7f zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H18a. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.55 apply (zenon_L2128_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.55 apply (zenon_L2155_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.55 apply (zenon_L2156_); trivial. % 22.48/22.55 apply (zenon_L1343_); trivial. % 22.48/22.55 (* end of lemma zenon_L2157_ *) % 22.48/22.55 assert (zenon_L2158_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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 (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (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 (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H104 zenon_H1cd zenon_H24e zenon_H5d zenon_H82 zenon_H1d5 zenon_H1c3 zenon_H19d zenon_H18a zenon_H93 zenon_H5c zenon_H18d zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H7f zenon_H1b7 zenon_H19a zenon_H196 zenon_H117 zenon_H61 zenon_H1fe zenon_H1ef zenon_Ha4 zenon_Hb2 zenon_H195 zenon_H266 zenon_H55 zenon_H6f zenon_H190 zenon_H1f1 zenon_H13f zenon_H189 zenon_Hf0 zenon_H1a8 zenon_H140 zenon_H1cf zenon_H4e zenon_He4 zenon_H234 zenon_H2c zenon_H141 zenon_H164 zenon_H212 zenon_H7d zenon_Hbc zenon_Hfa zenon_H1cb zenon_H236 zenon_H192 zenon_Hf5 zenon_H125 zenon_H94 zenon_H179 zenon_H1a2 zenon_H15d zenon_H68 zenon_Ha9 zenon_H77 zenon_H139 zenon_H209 zenon_H177 zenon_Ha0 zenon_Hb6 zenon_H10c zenon_H173 zenon_H121 zenon_H33 zenon_H11a zenon_H1a3 zenon_Hc4 zenon_H13a zenon_H48. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.48/22.55 apply (zenon_L2146_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.48/22.55 apply (zenon_L2154_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.48/22.55 apply (zenon_L2157_); trivial. % 22.48/22.55 apply (zenon_L1253_); trivial. % 22.48/22.55 (* end of lemma zenon_L2158_ *) % 22.48/22.55 assert (zenon_L2159_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H6e zenon_Hb6 zenon_H153 zenon_H19a zenon_Ha0 zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H162. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L110_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L95_); trivial. % 22.48/22.55 apply (zenon_L159_); trivial. % 22.48/22.55 (* end of lemma zenon_L2159_ *) % 22.48/22.55 assert (zenon_L2160_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H139 zenon_H1e zenon_H162 zenon_H68 zenon_H48 zenon_H5c zenon_Ha0 zenon_H19a zenon_Hb6 zenon_Ha9 zenon_Ha4 zenon_H13a zenon_H153 zenon_H77 zenon_H93 zenon_H196. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_L20_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_L2159_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_L94_); trivial. % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 (* end of lemma zenon_L2160_ *) % 22.48/22.55 assert (zenon_L2161_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e0)) = (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). % 22.48/22.55 do 0 intro. intros zenon_H15d zenon_H7f zenon_H192 zenon_H196 zenon_H93 zenon_H77 zenon_H13a zenon_Ha4 zenon_Ha9 zenon_Hb6 zenon_H19a zenon_Ha0 zenon_H48 zenon_H68 zenon_H162 zenon_H1e zenon_H139 zenon_H5c zenon_Hf5. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_L13_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L146_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_L2160_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 (* end of lemma zenon_L2161_ *) % 22.48/22.55 assert (zenon_L2162_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((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)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H139 zenon_H162 zenon_H1c3 zenon_Ha9 zenon_H77 zenon_H1cb zenon_H68 zenon_H48 zenon_H5c zenon_Ha0 zenon_H19a zenon_H18a zenon_H192 zenon_H2a zenon_H164 zenon_H47 zenon_Hb6 zenon_H13a zenon_H94 zenon_H25 zenon_H125 zenon_H93 zenon_H196. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_L251_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_L147_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.48/22.55 apply (zenon_L251_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.48/22.55 apply (zenon_L171_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.48/22.55 apply (zenon_L38_); trivial. % 22.48/22.55 apply (zenon_L340_); trivial. % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 (* end of lemma zenon_L2162_ *) % 22.48/22.55 assert (zenon_L2163_ : (((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))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H2a zenon_Hb6 zenon_H153 zenon_H19a zenon_Ha0 zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H162. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L53_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L95_); trivial. % 22.48/22.55 apply (zenon_L159_); trivial. % 22.48/22.55 (* end of lemma zenon_L2163_ *) % 22.48/22.55 assert (zenon_L2164_ : (((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 (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H164 zenon_H2d zenon_H109 zenon_H2a zenon_H192 zenon_H1cb zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_H9e zenon_Ha0 zenon_H19a zenon_H162. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.48/22.55 apply (zenon_L359_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.48/22.55 apply (zenon_L292_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.48/22.55 apply (zenon_L267_); trivial. % 22.48/22.55 exact (zenon_H162 zenon_H167). % 22.48/22.55 (* end of lemma zenon_L2164_ *) % 22.48/22.55 assert (zenon_L2165_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (((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 (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H66 zenon_H164 zenon_H2d zenon_H109 zenon_H2a zenon_H192 zenon_H1cb zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_Ha0 zenon_H19a zenon_H162. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L53_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L193_); trivial. % 22.48/22.55 apply (zenon_L2164_); trivial. % 22.48/22.55 (* end of lemma zenon_L2165_ *) % 22.48/22.55 assert (zenon_L2166_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H15d zenon_H196 zenon_Ha9 zenon_H164 zenon_H2d zenon_H109 zenon_H1cb zenon_H77 zenon_H139 zenon_H7f zenon_H192 zenon_H162 zenon_H68 zenon_H93 zenon_H48 zenon_Ha0 zenon_H19a zenon_Hb6 zenon_H2a zenon_Ha4 zenon_H13a zenon_H5c zenon_Hf5. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_L251_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_L147_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_L2165_); trivial. % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L146_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_L2163_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 (* end of lemma zenon_L2166_ *) % 22.48/22.55 assert (zenon_L2167_ : (((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) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H1fe zenon_H1c3 zenon_H94 zenon_H125 zenon_Hf5 zenon_H13a zenon_Ha4 zenon_H2a zenon_Hb6 zenon_Ha0 zenon_H162 zenon_H192 zenon_H139 zenon_H1cb zenon_H109 zenon_H164 zenon_Ha9 zenon_H196 zenon_H15d zenon_H19a zenon_H1b7 zenon_H7f zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H18a. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.55 apply (zenon_L2137_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_L2162_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L65_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_L2163_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.55 apply (zenon_L2166_); trivial. % 22.48/22.55 apply (zenon_L1343_); trivial. % 22.48/22.55 (* end of lemma zenon_L2167_ *) % 22.48/22.55 assert (zenon_L2168_ : (((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)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (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 (e3) (e3)) = (e0))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H164 zenon_H25 zenon_H179 zenon_H1b7 zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_H26d zenon_H19a zenon_H31 zenon_H177 zenon_H162. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.48/22.55 apply (zenon_L297_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.48/22.55 apply (zenon_L821_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.48/22.55 apply (zenon_L406_); trivial. % 22.48/22.55 exact (zenon_H162 zenon_H167). % 22.48/22.55 (* end of lemma zenon_L2168_ *) % 22.48/22.55 assert (zenon_L2169_ : (((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 (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (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 (e3) (e3)) = (e0))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H164 zenon_H2d zenon_H109 zenon_H1b7 zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_H26d zenon_H19a zenon_H31 zenon_H177 zenon_H162. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.48/22.55 apply (zenon_L359_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.48/22.55 apply (zenon_L821_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.48/22.55 apply (zenon_L406_); trivial. % 22.48/22.55 exact (zenon_H162 zenon_H167). % 22.48/22.55 (* end of lemma zenon_L2169_ *) % 22.48/22.55 assert (zenon_L2170_ : (((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H1fe zenon_Hf5 zenon_H139 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_Ha4 zenon_H13a zenon_H196 zenon_H192 zenon_H15d zenon_H179 zenon_H162 zenon_H177 zenon_H31 zenon_H26d zenon_H109 zenon_H164 zenon_H19a zenon_H1b7 zenon_H7f zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H18a. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.55 apply (zenon_L2161_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.55 apply (zenon_L2168_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.55 apply (zenon_L2169_); trivial. % 22.48/22.55 apply (zenon_L1343_); trivial. % 22.48/22.55 (* end of lemma zenon_L2170_ *) % 22.48/22.55 assert (zenon_L2171_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((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 (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H236 zenon_H1cb zenon_H125 zenon_H94 zenon_H1c3 zenon_H18a zenon_H68 zenon_H5c zenon_H19a zenon_H164 zenon_H109 zenon_H26d zenon_H177 zenon_H162 zenon_H179 zenon_H15d zenon_H192 zenon_H196 zenon_H13a zenon_Ha4 zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H139 zenon_Hf5 zenon_H1fe zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H7f zenon_H1b7. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.48/22.55 apply (zenon_L2161_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.48/22.55 apply (zenon_L2167_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.48/22.55 apply (zenon_L2170_); trivial. % 22.48/22.55 apply (zenon_L1276_); trivial. % 22.48/22.55 (* end of lemma zenon_L2171_ *) % 22.48/22.55 assert (zenon_L2172_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((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) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_H160 zenon_H13a zenon_Ha4 zenon_Ha9 zenon_Hb6 zenon_He4 zenon_H77 zenon_H139 zenon_H234 zenon_H104 zenon_H121 zenon_H11a zenon_H10c zenon_H1cd zenon_H24e zenon_Hc4 zenon_H2c zenon_H141 zenon_H164 zenon_H1e zenon_H33 zenon_H1b7 zenon_H1cb zenon_H68 zenon_H48 zenon_Ha0 zenon_H19a zenon_H212 zenon_H18a zenon_H7d zenon_Hbc zenon_H209 zenon_H5c zenon_Hf5. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_L13_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L215_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_L20_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L110_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L95_); trivial. % 22.48/22.55 apply (zenon_L2120_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_L122_); trivial. % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 (* end of lemma zenon_L2172_ *) % 22.48/22.55 assert (zenon_L2173_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (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). % 22.48/22.55 do 0 intro. intros zenon_H15d zenon_H177 zenon_H160 zenon_H48 zenon_H196 zenon_H93 zenon_H77 zenon_H2a zenon_H68 zenon_H1e zenon_H139 zenon_H5c zenon_Hf5. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_L352_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L65_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_L2136_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 (* end of lemma zenon_L2173_ *) % 22.48/22.55 assert (zenon_L2174_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (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). % 22.48/22.55 do 0 intro. intros zenon_H15d zenon_H196 zenon_H93 zenon_H77 zenon_H2a zenon_H68 zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H164 zenon_H18a zenon_H192 zenon_H1cb zenon_H48 zenon_Ha0 zenon_H19a zenon_H139 zenon_H2d zenon_H5d zenon_H160 zenon_H177 zenon_H82 zenon_H5c zenon_Hf5. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_L352_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L65_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.55 apply (zenon_L352_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.55 apply (zenon_L17_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.55 apply (zenon_L217_); trivial. % 22.48/22.55 apply (zenon_L2153_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 (* end of lemma zenon_L2174_ *) % 22.48/22.55 assert (zenon_L2175_ : (((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 (e3) (e3)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H12e zenon_H48 zenon_H3d zenon_H192 zenon_Hc4 zenon_H160 zenon_H1cb zenon_H34 zenon_H18a zenon_H1bb zenon_H5c zenon_H20f. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.48/22.55 apply (zenon_L456_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.48/22.55 apply (zenon_L146_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.48/22.55 apply (zenon_L847_); trivial. % 22.48/22.55 apply (zenon_L412_); trivial. % 22.48/22.55 (* end of lemma zenon_L2175_ *) % 22.48/22.55 assert (zenon_L2176_ : (((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))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H2a zenon_Hb6 zenon_H153 zenon_H19a zenon_Ha0 zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H34 zenon_H18a. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L53_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L95_); trivial. % 22.48/22.55 apply (zenon_L851_); trivial. % 22.48/22.55 (* end of lemma zenon_L2176_ *) % 22.48/22.55 assert (zenon_L2177_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H15d zenon_H196 zenon_H177 zenon_H77 zenon_H139 zenon_H20f zenon_H1bb zenon_H1cb zenon_H160 zenon_Hc4 zenon_H192 zenon_H12e zenon_H18a zenon_H34 zenon_H68 zenon_H93 zenon_H48 zenon_Ha0 zenon_H19a zenon_Hb6 zenon_H2a zenon_Ha4 zenon_H13a zenon_H5c zenon_Hf5. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_L352_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L2175_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_L2176_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 (* end of lemma zenon_L2177_ *) % 22.48/22.55 assert (zenon_L2178_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H1fe zenon_Hbc zenon_H94 zenon_H125 zenon_H209 zenon_Hb2 zenon_H82 zenon_H5d zenon_H164 zenon_H15d zenon_H196 zenon_H177 zenon_H77 zenon_H139 zenon_H20f zenon_H1bb zenon_H1cb zenon_H160 zenon_Hc4 zenon_H192 zenon_H12e zenon_H18a zenon_H68 zenon_H93 zenon_H48 zenon_Ha0 zenon_H19a zenon_Hb6 zenon_H2a zenon_Ha4 zenon_H13a zenon_H5c zenon_Hf5. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.55 apply (zenon_L2173_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_L541_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L65_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.55 apply (zenon_L541_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.55 apply (zenon_L17_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.55 apply (zenon_L2151_); trivial. % 22.48/22.55 apply (zenon_L2153_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.55 apply (zenon_L2174_); trivial. % 22.48/22.55 apply (zenon_L2177_); trivial. % 22.48/22.55 (* end of lemma zenon_L2178_ *) % 22.48/22.55 assert (zenon_L2179_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_H160 zenon_H77 zenon_H1e zenon_H68 zenon_H139 zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_L13_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L215_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_L239_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 (* end of lemma zenon_L2179_ *) % 22.48/22.55 assert (zenon_L2180_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> False). % 22.48/22.55 do 0 intro. intros zenon_H201 zenon_H48 zenon_H31 zenon_H186 zenon_H5c zenon_H190 zenon_H110 zenon_H6e zenon_H6f zenon_H55 zenon_H2d zenon_H266 zenon_H77 zenon_H160. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.48/22.55 apply (zenon_L239_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.48/22.55 apply (zenon_L138_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.48/22.55 apply (zenon_L2130_); trivial. % 22.48/22.55 apply (zenon_L367_); trivial. % 22.48/22.55 (* end of lemma zenon_L2180_ *) % 22.48/22.55 assert (zenon_L2181_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H117 zenon_Ha0 zenon_H10c zenon_Hf0 zenon_H160 zenon_H77 zenon_H266 zenon_H2d zenon_H55 zenon_H6f zenon_H6e zenon_H190 zenon_H5c zenon_H186 zenon_H31 zenon_H48 zenon_H201 zenon_H9e zenon_H196. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.48/22.55 apply (zenon_L67_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.48/22.55 apply (zenon_L74_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.48/22.55 apply (zenon_L2180_); trivial. % 22.48/22.55 apply (zenon_L154_); trivial. % 22.48/22.55 (* end of lemma zenon_L2181_ *) % 22.48/22.55 assert (zenon_L2182_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H1cf zenon_H68 zenon_H4e zenon_H76 zenon_H93 zenon_H1c2 zenon_H117 zenon_Ha0 zenon_H10c zenon_Hf0 zenon_H77 zenon_H266 zenon_H2d zenon_H55 zenon_H6f zenon_H6e zenon_H190 zenon_H5c zenon_H186 zenon_H31 zenon_H48 zenon_H201 zenon_H9e zenon_H196. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.48/22.55 apply (zenon_L264_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.48/22.55 apply (zenon_L83_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.48/22.55 apply (zenon_L207_); trivial. % 22.48/22.55 apply (zenon_L2181_); trivial. % 22.48/22.55 (* end of lemma zenon_L2182_ *) % 22.48/22.55 assert (zenon_L2183_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H1cf zenon_H68 zenon_H4e zenon_H76 zenon_H93 zenon_H1c2 zenon_H117 zenon_Ha0 zenon_H10c zenon_Hf0 zenon_H77 zenon_H266 zenon_H2d zenon_H55 zenon_H6f zenon_H6e zenon_H190 zenon_H5c zenon_H186 zenon_H31 zenon_H48 zenon_H201 zenon_H196. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L110_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L68_); trivial. % 22.48/22.55 apply (zenon_L2182_); trivial. % 22.48/22.55 (* end of lemma zenon_L2183_ *) % 22.48/22.55 assert (zenon_L2184_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e0)) = (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). % 22.48/22.55 do 0 intro. intros zenon_H139 zenon_Hbc zenon_H160 zenon_H99 zenon_H94 zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H1cf zenon_H4e zenon_H1c2 zenon_H117 zenon_Ha0 zenon_H10c zenon_Hf0 zenon_H77 zenon_H266 zenon_H2d zenon_H55 zenon_H6f zenon_H190 zenon_H5c zenon_H186 zenon_H48 zenon_H201 zenon_H47 zenon_H125 zenon_H68 zenon_H31 zenon_H93 zenon_H196. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_L251_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.48/22.55 apply (zenon_L251_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.48/22.55 apply (zenon_L2183_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.48/22.55 apply (zenon_L39_); trivial. % 22.48/22.55 apply (zenon_L104_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_L264_); trivial. % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 (* end of lemma zenon_L2184_ *) % 22.48/22.55 assert (zenon_L2185_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H6e zenon_H31 zenon_H19a zenon_Ha0 zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H34 zenon_H18a. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L110_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L68_); trivial. % 22.48/22.55 apply (zenon_L851_); trivial. % 22.48/22.55 (* end of lemma zenon_L2185_ *) % 22.48/22.55 assert (zenon_L2186_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((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 (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H19a zenon_Ha0 zenon_H68 zenon_H77 zenon_H139 zenon_H20f zenon_H1bb zenon_H18a zenon_H34 zenon_H1cb zenon_H160 zenon_Hc4 zenon_H192 zenon_H12e zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.55 apply (zenon_L251_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.55 apply (zenon_L2185_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.55 apply (zenon_L122_); trivial. % 22.48/22.55 apply (zenon_L167_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_L2175_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_L239_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 (* end of lemma zenon_L2186_ *) % 22.48/22.55 assert (zenon_L2187_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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)) = (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))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H236 zenon_H7d zenon_H212 zenon_H1b7 zenon_H141 zenon_H2c zenon_H24e zenon_H1cd zenon_H104 zenon_H234 zenon_He4 zenon_Hf5 zenon_H5c zenon_H12e zenon_H192 zenon_H160 zenon_H1cb zenon_H18a zenon_H1bb zenon_H20f zenon_H19a zenon_Ha4 zenon_H93 zenon_H196 zenon_H125 zenon_H201 zenon_H186 zenon_H190 zenon_H6f zenon_H55 zenon_H266 zenon_Hf0 zenon_H117 zenon_H1c2 zenon_H4e zenon_H1cf zenon_H94 zenon_H99 zenon_Hbc zenon_H164 zenon_H5d zenon_H82 zenon_Hb2 zenon_H1fe zenon_H15d zenon_H68 zenon_Ha9 zenon_H77 zenon_H139 zenon_H209 zenon_H177 zenon_Ha0 zenon_Hb6 zenon_H10c zenon_H173 zenon_H121 zenon_H33 zenon_H11a zenon_H1a3 zenon_Hc4 zenon_H13a zenon_H48. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.48/22.55 apply (zenon_L2172_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.48/22.55 apply (zenon_L2178_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.55 apply (zenon_L2179_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_L541_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.55 apply (zenon_L818_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.55 apply (zenon_L17_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.55 apply (zenon_L2151_); trivial. % 22.48/22.55 apply (zenon_L1931_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_L239_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.55 apply (zenon_L2184_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.55 apply (zenon_L818_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.55 apply (zenon_L17_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.55 apply (zenon_L217_); trivial. % 22.48/22.55 apply (zenon_L1931_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.55 apply (zenon_L239_); trivial. % 22.48/22.55 apply (zenon_L192_); trivial. % 22.48/22.55 apply (zenon_L2186_); trivial. % 22.48/22.55 apply (zenon_L1253_); trivial. % 22.48/22.55 (* end of lemma zenon_L2187_ *) % 22.48/22.55 assert (zenon_L2188_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 22.48/22.55 do 0 intro. intros zenon_H164 zenon_H1c7 zenon_H160 zenon_H1cd zenon_H7d zenon_H24e zenon_H1bb zenon_H18a zenon_H1cb zenon_Hc4 zenon_H1f1 zenon_H12e zenon_Hef zenon_H189 zenon_H53 zenon_H19a zenon_Ha0 zenon_H9e zenon_H48 zenon_H93 zenon_H68 zenon_H1b7 zenon_Hb6 zenon_H18d zenon_H31 zenon_H177 zenon_H67 zenon_H7e. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.48/22.55 apply (zenon_L849_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.48/22.55 apply (zenon_L759_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.48/22.55 apply (zenon_L406_); trivial. % 22.48/22.55 apply (zenon_L547_); trivial. % 22.48/22.55 (* end of lemma zenon_L2188_ *) % 22.48/22.55 assert (zenon_L2189_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_Ha0 zenon_H31 zenon_Hb9 zenon_H196. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.55 exact (zenon_Ha4 zenon_H9f). % 22.48/22.55 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.55 apply (zenon_L55_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.55 apply (zenon_L68_); trivial. % 22.48/22.55 apply (zenon_L154_); trivial. % 22.48/22.55 (* end of lemma zenon_L2189_ *) % 22.48/22.55 assert (zenon_L2190_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.55 do 0 intro. intros zenon_H117 zenon_H2d zenon_H10c zenon_Hf0 zenon_H105 zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_Ha0 zenon_H31 zenon_H196. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.48/22.55 apply (zenon_L67_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.48/22.55 apply (zenon_L74_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.48/22.55 apply (zenon_L400_); trivial. % 22.48/22.55 apply (zenon_L2189_); trivial. % 22.48/22.55 (* end of lemma zenon_L2190_ *) % 22.48/22.55 assert (zenon_L2191_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (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) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 22.48/22.55 do 0 intro. intros zenon_H13f zenon_H7e zenon_H67 zenon_H177 zenon_H18d zenon_H1b7 zenon_H68 zenon_H48 zenon_H9e zenon_H19a zenon_H189 zenon_Hef zenon_H12e zenon_H1f1 zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H24e zenon_H7d zenon_H1cd zenon_H160 zenon_H1c7 zenon_H164 zenon_H196 zenon_H31 zenon_Ha0 zenon_H3d zenon_Hb6 zenon_Ha4 zenon_H13a zenon_Hf0 zenon_H10c zenon_H2d zenon_H117 zenon_H77 zenon_H93. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.48/22.55 apply (zenon_L217_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.48/22.55 apply (zenon_L2188_); trivial. % 22.48/22.55 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.48/22.55 apply (zenon_L2190_); trivial. % 22.48/22.55 apply (zenon_L218_); trivial. % 22.48/22.55 (* end of lemma zenon_L2191_ *) % 22.48/22.55 assert (zenon_L2192_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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)) = (op (e2) (e3)))) -> ((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))))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.48/22.56 do 0 intro. intros zenon_H1a8 zenon_H201 zenon_H186 zenon_H5c zenon_H190 zenon_H6f zenon_H55 zenon_H266 zenon_H1c2 zenon_H76 zenon_H4e zenon_H1cf zenon_Ha9 zenon_H93 zenon_H77 zenon_H117 zenon_H2d zenon_H10c zenon_Hf0 zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_Ha0 zenon_H31 zenon_H196 zenon_H164 zenon_H1c7 zenon_H7d zenon_H24e zenon_H1bb zenon_H18a zenon_H1cb zenon_Hc4 zenon_H1f1 zenon_H12e zenon_H19a zenon_H9e zenon_H48 zenon_H68 zenon_H1b7 zenon_H18d zenon_H177 zenon_H67 zenon_H7e zenon_H13f zenon_H189 zenon_H99 zenon_H160 zenon_H1cd. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.48/22.56 apply (zenon_L2183_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.48/22.56 apply (zenon_L2191_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.48/22.56 apply (zenon_L458_); trivial. % 22.48/22.56 apply (zenon_L240_); trivial. % 22.48/22.56 (* end of lemma zenon_L2192_ *) % 22.48/22.56 assert (zenon_L2193_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e0)) = (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). % 22.48/22.56 do 0 intro. intros zenon_H15d zenon_H177 zenon_H160 zenon_H196 zenon_H93 zenon_H77 zenon_H13a zenon_Ha4 zenon_Ha9 zenon_Hb6 zenon_H19a zenon_Ha0 zenon_H48 zenon_H68 zenon_H162 zenon_H1e zenon_H139 zenon_H5c zenon_Hf5. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.56 apply (zenon_L13_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.56 apply (zenon_L215_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.56 apply (zenon_L2160_); trivial. % 22.48/22.56 apply (zenon_L192_); trivial. % 22.48/22.56 (* end of lemma zenon_L2193_ *) % 22.48/22.56 assert (zenon_L2194_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((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)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((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 (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.56 do 0 intro. intros zenon_H1fe zenon_H179 zenon_H162 zenon_H26d zenon_H1b7 zenon_H109 zenon_H164 zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H19a zenon_Ha0 zenon_H68 zenon_H77 zenon_H139 zenon_H20f zenon_H1bb zenon_H18a zenon_H1cb zenon_H160 zenon_Hc4 zenon_H192 zenon_H12e zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.56 apply (zenon_L2179_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.56 apply (zenon_L2168_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.56 apply (zenon_L2169_); trivial. % 22.48/22.56 apply (zenon_L2186_); trivial. % 22.48/22.56 (* end of lemma zenon_L2194_ *) % 22.48/22.56 assert (zenon_L2195_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((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 (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 (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 (e2) (e0)) = (op (e2) (e2)))) -> (((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) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (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 (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> False). % 22.48/22.56 do 0 intro. intros zenon_Hc8 zenon_H109 zenon_H284 zenon_H25e zenon_H281 zenon_H1fb zenon_Hcc zenon_H282 zenon_Heb zenon_H27e zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H13c zenon_H1ef zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H283 zenon_Hcb zenon_H1a8 zenon_H189 zenon_H18d zenon_H1f1 zenon_H13f zenon_H163 zenon_H195 zenon_Hfa zenon_H26d zenon_H179 zenon_H1c3 zenon_H1b4 zenon_H129 zenon_H15d zenon_Hf5 zenon_H13a zenon_H234 zenon_H5c zenon_H141 zenon_H19a zenon_H18a zenon_Ha0 zenon_H1b7 zenon_H104 zenon_H121 zenon_Hc4 zenon_H212 zenon_Hbc zenon_H7d zenon_H1cd zenon_H24e zenon_H10c zenon_H11a zenon_H164 zenon_H2c zenon_H1cb zenon_H33 zenon_He4 zenon_Hb6 zenon_Ha9 zenon_Ha4 zenon_H68 zenon_H77 zenon_H177 zenon_H160 zenon_H196 zenon_H93 zenon_H139 zenon_H48 zenon_H1fe zenon_H12e zenon_H20f zenon_H1bb zenon_H125 zenon_H94 zenon_H82 zenon_H192 zenon_Hb2 zenon_H5d zenon_H4e zenon_H1c2 zenon_H117 zenon_H186 zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H201 zenon_Hf0 zenon_H1cf zenon_H99 zenon_H173 zenon_H236 zenon_Hca. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.48/22.56 apply (zenon_L2187_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.48/22.56 apply (zenon_L2172_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.48/22.56 apply (zenon_L2178_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.56 apply (zenon_L2179_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.56 apply (zenon_L541_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.56 apply (zenon_L818_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.56 apply (zenon_L17_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.56 apply (zenon_L2151_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.48/22.56 apply (zenon_L297_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.48/22.56 apply (zenon_L821_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.48/22.56 apply (zenon_L406_); trivial. % 22.48/22.56 apply (zenon_L547_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.56 apply (zenon_L214_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.56 apply (zenon_L122_); trivial. % 22.48/22.56 apply (zenon_L167_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.56 apply (zenon_L239_); trivial. % 22.48/22.56 apply (zenon_L192_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.56 apply (zenon_L2184_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.56 apply (zenon_L818_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.56 apply (zenon_L17_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.56 apply (zenon_L217_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.56 exact (zenon_Ha4 zenon_H9f). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.56 apply (zenon_L55_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.56 apply (zenon_L68_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.48/22.56 apply (zenon_L2192_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.48/22.56 apply (zenon_L2191_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.48/22.56 apply (zenon_L227_); trivial. % 22.48/22.56 apply (zenon_L228_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.56 apply (zenon_L214_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.56 apply (zenon_L264_); trivial. % 22.48/22.56 apply (zenon_L1855_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.56 apply (zenon_L239_); trivial. % 22.48/22.56 apply (zenon_L192_); trivial. % 22.48/22.56 apply (zenon_L2186_); trivial. % 22.48/22.56 apply (zenon_L414_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.48/22.56 apply (zenon_L2187_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.56 apply (zenon_L13_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.56 apply (zenon_L215_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.56 apply (zenon_L20_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.56 exact (zenon_Ha4 zenon_H9f). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.56 apply (zenon_L110_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.56 apply (zenon_L393_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.48/22.56 apply (zenon_L214_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.48/22.56 apply (zenon_L540_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.56 apply (zenon_L5_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.56 apply (zenon_L111_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.56 apply (zenon_L562_); trivial. % 22.48/22.56 apply (zenon_L158_); trivial. % 22.48/22.56 apply (zenon_L2119_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.56 apply (zenon_L94_); trivial. % 22.48/22.56 apply (zenon_L167_); trivial. % 22.48/22.56 apply (zenon_L192_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.48/22.56 apply (zenon_L2178_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.56 apply (zenon_L2179_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.56 apply (zenon_L541_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.56 apply (zenon_L818_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.56 apply (zenon_L25_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.56 apply (zenon_L2151_); trivial. % 22.48/22.56 apply (zenon_L866_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.56 apply (zenon_L239_); trivial. % 22.48/22.56 apply (zenon_L192_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.56 apply (zenon_L2184_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.56 apply (zenon_L818_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.56 apply (zenon_L17_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.56 apply (zenon_L217_); trivial. % 22.48/22.56 apply (zenon_L866_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.56 apply (zenon_L239_); trivial. % 22.48/22.56 apply (zenon_L192_); trivial. % 22.48/22.56 apply (zenon_L2186_); trivial. % 22.48/22.56 apply (zenon_L414_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.48/22.56 apply (zenon_L2193_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.56 apply (zenon_L352_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.56 apply (zenon_L65_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.56 apply (zenon_L2163_); trivial. % 22.48/22.56 apply (zenon_L192_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.48/22.56 apply (zenon_L2194_); trivial. % 22.48/22.56 apply (zenon_L1236_); trivial. % 22.48/22.56 (* end of lemma zenon_L2195_ *) % 22.48/22.56 assert (zenon_L2196_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 22.48/22.56 do 0 intro. intros zenon_H125 zenon_H6c zenon_H68 zenon_H25 zenon_H94 zenon_H93 zenon_Ha9 zenon_H9d. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.48/22.56 exact (zenon_H6c zenon_H67). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.48/22.56 apply (zenon_L171_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.48/22.56 apply (zenon_L38_); trivial. % 22.48/22.56 apply (zenon_L91_); trivial. % 22.48/22.56 (* end of lemma zenon_L2196_ *) % 22.48/22.56 assert (zenon_L2197_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 22.48/22.56 do 0 intro. intros zenon_H82 zenon_H4c zenon_H5d zenon_H5c zenon_H48 zenon_H2d zenon_Hb6 zenon_H9d. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.56 exact (zenon_H4c zenon_H47). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.56 apply (zenon_L17_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.56 apply (zenon_L217_); trivial. % 22.48/22.56 apply (zenon_L134_); trivial. % 22.48/22.56 (* end of lemma zenon_L2197_ *) % 22.48/22.56 assert (zenon_L2198_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.56 do 0 intro. intros zenon_H1fe zenon_H1f zenon_H1cb zenon_H110 zenon_H4e zenon_H237 zenon_H140 zenon_H9d zenon_Hb6 zenon_H5d zenon_H4c zenon_H82 zenon_H19a zenon_Ha0 zenon_H9e zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H18a. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.56 exact (zenon_H1f zenon_H1e). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.48/22.56 exact (zenon_H237 zenon_H31). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.48/22.56 apply (zenon_L274_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.48/22.56 apply (zenon_L278_); trivial. % 22.48/22.56 apply (zenon_L267_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.56 apply (zenon_L2197_); trivial. % 22.48/22.56 apply (zenon_L851_); trivial. % 22.48/22.56 (* end of lemma zenon_L2198_ *) % 22.48/22.56 assert (zenon_L2199_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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) (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) (e0)) = (op (e2) (e2)))) -> (~((e1) = (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) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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 (e0) (e3)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((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) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 22.48/22.56 do 0 intro. intros zenon_H204 zenon_H140 zenon_H82 zenon_H109 zenon_H23d zenon_H33 zenon_H236 zenon_H9e zenon_Ha0 zenon_H1f zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H163 zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13a zenon_H13e zenon_H1ef zenon_Hb6 zenon_H13c zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H281 zenon_H25e zenon_H284 zenon_H125 zenon_H9d zenon_Ha9 zenon_H93 zenon_H94 zenon_H68 zenon_H139 zenon_H1cf zenon_Hf0 zenon_H10c zenon_H201 zenon_H77 zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H5c zenon_H186 zenon_H48 zenon_H196 zenon_H117 zenon_H1c2 zenon_H4e zenon_H19a zenon_H18a zenon_H1fe zenon_H240. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.48/22.56 apply (zenon_L1873_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.48/22.56 exact (zenon_H1f zenon_H1e). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.48/22.56 exact (zenon_H205 zenon_H2a). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.56 exact (zenon_H1f zenon_H1e). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.56 apply (zenon_L2196_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.56 exact (zenon_H6c zenon_H67). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.48/22.56 exact (zenon_H6c zenon_H67). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.48/22.56 apply (zenon_L2182_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.48/22.56 apply (zenon_L27_); trivial. % 22.48/22.56 apply (zenon_L91_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.56 apply (zenon_L264_); trivial. % 22.48/22.56 apply (zenon_L167_); trivial. % 22.48/22.56 apply (zenon_L851_); trivial. % 22.48/22.56 apply (zenon_L1236_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.48/22.56 apply (zenon_L73_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.48/22.56 apply (zenon_L74_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.48/22.56 apply (zenon_L2198_); trivial. % 22.48/22.56 apply (zenon_L154_); trivial. % 22.48/22.56 apply (zenon_L611_); trivial. % 22.48/22.56 (* end of lemma zenon_L2199_ *) % 22.48/22.56 assert (zenon_L2200_ : (((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)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.56 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H173 zenon_H10c zenon_Ha9 zenon_H66 zenon_Hb9 zenon_H196. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.56 exact (zenon_Ha4 zenon_H9f). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.56 apply (zenon_L120_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.56 apply (zenon_L193_); trivial. % 22.48/22.56 apply (zenon_L154_); trivial. % 22.48/22.56 (* end of lemma zenon_L2200_ *) % 22.48/22.56 assert (zenon_L2201_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((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) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.56 do 0 intro. intros zenon_H139 zenon_H77 zenon_Hbb zenon_H177 zenon_H47 zenon_Hb6 zenon_Hb9 zenon_Ha9 zenon_H10c zenon_H173 zenon_Ha4 zenon_H13a zenon_H93 zenon_H196. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.56 apply (zenon_L251_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.56 apply (zenon_L986_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.56 apply (zenon_L2200_); trivial. % 22.48/22.56 apply (zenon_L167_); trivial. % 22.48/22.56 (* end of lemma zenon_L2201_ *) % 22.48/22.56 assert (zenon_L2202_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.56 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha0 zenon_H2a zenon_Hb6 zenon_H153 zenon_Hb9 zenon_H196. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.56 exact (zenon_Ha4 zenon_H9f). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.56 apply (zenon_L53_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.56 apply (zenon_L95_); trivial. % 22.48/22.56 apply (zenon_L154_); trivial. % 22.48/22.56 (* end of lemma zenon_L2202_ *) % 22.48/22.56 assert (zenon_L2203_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((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)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> False). % 22.48/22.56 do 0 intro. intros zenon_H5c zenon_H10c zenon_H93 zenon_H15d zenon_Hf5 zenon_H48 zenon_Hb6 zenon_H77 zenon_H13a zenon_Hf0 zenon_H196 zenon_H117 zenon_Ha0 zenon_Ha9 zenon_Ha4 zenon_H68 zenon_H139 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_Heb zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H1a8 zenon_H140 zenon_He4 zenon_H33 zenon_H212 zenon_Hbc zenon_H7d zenon_H164 zenon_H2c zenon_H141 zenon_H234 zenon_Hfa zenon_Hb2 zenon_H13f zenon_H1f1 zenon_H18a zenon_H1fe zenon_H104 zenon_H1cd zenon_H24e zenon_H11a zenon_H177 zenon_H121 zenon_H125 zenon_H82 zenon_H192 zenon_H1d5 zenon_H179 zenon_H19d zenon_H109 zenon_H201 zenon_H1c2 zenon_H12e zenon_H23d zenon_H1d8 zenon_H111 zenon_H26a zenon_H23c zenon_H183 zenon_H231 zenon_H13b zenon_H288. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.48/22.56 apply (zenon_L2_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.48/22.56 apply (zenon_L2110_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.48/22.56 exact (zenon_H16b zenon_H93). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.56 apply (zenon_L2127_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.56 apply (zenon_L2114_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.56 apply (zenon_L239_); trivial. % 22.48/22.56 apply (zenon_L192_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.48/22.56 apply (zenon_L1241_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.48/22.56 apply (zenon_L1206_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.48/22.56 apply (zenon_L11_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.48/22.56 apply (zenon_L1207_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.48/22.56 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.48/22.56 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.48/22.56 apply (zenon_L2158_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.48/22.56 apply (zenon_L2146_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.48/22.56 apply (zenon_L2154_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.48/22.56 apply (zenon_L2157_); trivial. % 22.48/22.56 apply (zenon_L414_); trivial. % 22.48/22.56 apply (zenon_L2171_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.48/22.56 apply (zenon_L1208_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.48/22.56 apply (zenon_L1209_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.48/22.56 apply (zenon_L37_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.48/22.56 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.48/22.56 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.48/22.56 apply (zenon_L2195_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.48/22.56 apply (zenon_L2199_); trivial. % 22.48/22.56 apply (zenon_L2199_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.48/22.56 apply (zenon_L1354_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.48/22.56 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.48/22.56 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.48/22.56 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.48/22.56 exact (zenon_H16b zenon_H93). % 22.48/22.56 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.48/22.56 apply (zenon_L1355_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.56 apply (zenon_L2201_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.56 apply (zenon_L65_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.56 apply (zenon_L2202_); trivial. % 22.48/22.56 apply (zenon_L192_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.56 apply (zenon_L251_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.56 apply (zenon_L986_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.56 apply (zenon_L264_); trivial. % 22.48/22.56 apply (zenon_L167_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.56 apply (zenon_L2189_); trivial. % 22.48/22.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.56 apply (zenon_L239_); trivial. % 22.48/22.56 apply (zenon_L192_); trivial. % 22.48/22.56 apply (zenon_L1390_); trivial. % 22.48/22.56 apply (zenon_L51_); trivial. % 22.48/22.56 apply (zenon_L1234_); trivial. % 22.48/22.56 (* end of lemma zenon_L2203_ *) % 22.48/22.56 assert (zenon_L2204_ : ((op (e3) (e1)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((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)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> False). % 22.48/22.56 do 0 intro. intros zenon_H7f zenon_H9e zenon_Hdd zenon_H9d zenon_H5c zenon_H10c zenon_H15d zenon_Hf5 zenon_H48 zenon_Hb6 zenon_H77 zenon_H13a zenon_Hf0 zenon_H196 zenon_H117 zenon_Ha0 zenon_Ha9 zenon_Ha4 zenon_H68 zenon_H139 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_Heb zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H1a8 zenon_H140 zenon_He4 zenon_H33 zenon_H212 zenon_Hbc zenon_H7d zenon_H164 zenon_H2c zenon_H141 zenon_H234 zenon_Hfa zenon_Hb2 zenon_H13f zenon_H1f1 zenon_H18a zenon_H1fe zenon_H104 zenon_H1cd zenon_H24e zenon_H11a zenon_H177 zenon_H121 zenon_H125 zenon_H82 zenon_H192 zenon_H1d5 zenon_H179 zenon_H19d zenon_H109 zenon_H201 zenon_H1c2 zenon_H12e zenon_H23d zenon_H1d8 zenon_H111 zenon_H26a zenon_H23c zenon_H183 zenon_H231 zenon_H13b zenon_H288. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.48/22.57 apply (zenon_L2117_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.48/22.57 apply (zenon_L54_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.48/22.57 apply (zenon_L2126_); trivial. % 22.48/22.57 apply (zenon_L2203_); trivial. % 22.48/22.57 (* end of lemma zenon_L2204_ *) % 22.48/22.57 assert (zenon_L2205_ : (((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 (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> False). % 22.48/22.57 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H65 zenon_H10c zenon_Hf0 zenon_H191 zenon_Ha0 zenon_H115. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.48/22.57 apply (zenon_L43_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.48/22.57 apply (zenon_L74_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.48/22.57 exact (zenon_H191 zenon_H110). % 22.48/22.57 apply (zenon_L77_); trivial. % 22.48/22.57 (* end of lemma zenon_L2205_ *) % 22.48/22.57 assert (zenon_L2206_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((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) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (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) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((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) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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 (e2) (e0)) = (op (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) (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 (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((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))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> False). % 22.48/22.57 do 0 intro. intros zenon_H288 zenon_H13b zenon_H231 zenon_H183 zenon_H23c zenon_H26a zenon_H111 zenon_H1d8 zenon_H23d zenon_H12e zenon_H1c2 zenon_H201 zenon_H109 zenon_H19d zenon_H179 zenon_H1d5 zenon_H192 zenon_H82 zenon_H125 zenon_H121 zenon_H177 zenon_H11a zenon_H24e zenon_H1cd zenon_H104 zenon_H1fe zenon_H18a zenon_Hb2 zenon_Hfa zenon_H234 zenon_H141 zenon_H2c zenon_H164 zenon_H7d zenon_Hbc zenon_H212 zenon_H33 zenon_He4 zenon_H140 zenon_H1a8 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_Heb zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H139 zenon_H68 zenon_Ha4 zenon_H196 zenon_H13a zenon_Hb6 zenon_Hf5 zenon_H15d zenon_H9d zenon_H9e zenon_H5c zenon_H195 zenon_H48 zenon_H1f1 zenon_H7f zenon_H77 zenon_H13f zenon_H117 zenon_Ha9 zenon_H65 zenon_H10c zenon_Hf0 zenon_H191 zenon_Ha0. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.57 apply (zenon_L27_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.57 apply (zenon_L2204_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.57 apply (zenon_L1268_); trivial. % 22.48/22.57 apply (zenon_L2205_); trivial. % 22.48/22.57 (* end of lemma zenon_L2206_ *) % 22.48/22.57 assert (zenon_L2207_ : ((op (e1) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((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) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (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) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((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) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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 (e2) (e0)) = (op (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) (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 (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((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))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> False). % 22.48/22.57 do 0 intro. intros zenon_H25 zenon_H288 zenon_H13b zenon_H231 zenon_H183 zenon_H23c zenon_H26a zenon_H111 zenon_H1d8 zenon_H23d zenon_H12e zenon_H1c2 zenon_H201 zenon_H109 zenon_H19d zenon_H179 zenon_H1d5 zenon_H192 zenon_H82 zenon_H125 zenon_H121 zenon_H177 zenon_H11a zenon_H24e zenon_H1cd zenon_H104 zenon_H1fe zenon_H18a zenon_Hb2 zenon_Hfa zenon_H234 zenon_H141 zenon_H2c zenon_H164 zenon_H7d zenon_Hbc zenon_H212 zenon_H33 zenon_He4 zenon_H140 zenon_H1a8 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_Heb zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H139 zenon_H68 zenon_Ha4 zenon_H196 zenon_H13a zenon_Hb6 zenon_Hf5 zenon_H15d zenon_H9e zenon_H5c zenon_H195 zenon_H48 zenon_H1f1 zenon_H7f zenon_H77 zenon_H13f zenon_H117 zenon_Ha9 zenon_H65 zenon_H10c zenon_Hf0 zenon_H191 zenon_Ha0. % 22.48/22.57 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.48/22.57 exact (zenon_Ha4 zenon_H9f). % 22.48/22.57 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.48/22.57 apply (zenon_L116_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.48/22.57 apply (zenon_L43_); trivial. % 22.48/22.57 apply (zenon_L2206_); trivial. % 22.48/22.57 (* end of lemma zenon_L2207_ *) % 22.48/22.57 assert (zenon_L2208_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((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)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.57 do 0 intro. intros zenon_H16a zenon_H117 zenon_H196 zenon_H77 zenon_Hdd zenon_H72 zenon_H131 zenon_Hfa zenon_H6e zenon_H173 zenon_H5c zenon_H1a2 zenon_H31 zenon_Ha9 zenon_Hb6 zenon_H164 zenon_H25 zenon_H179 zenon_H1b7 zenon_H68 zenon_H48 zenon_H9e zenon_H19a zenon_Ha0 zenon_H47 zenon_H102 zenon_H1f1 zenon_H7f zenon_Ha8 zenon_H13f zenon_H195. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.48/22.57 apply (zenon_L2117_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.48/22.57 apply (zenon_L54_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.48/22.57 apply (zenon_L87_); trivial. % 22.48/22.57 apply (zenon_L2148_); trivial. % 22.48/22.57 (* end of lemma zenon_L2208_ *) % 22.48/22.57 assert (zenon_L2209_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((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))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (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) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((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) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (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)) = (op (e2) (e1)))) -> (((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) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((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)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 22.48/22.57 do 0 intro. intros zenon_H195 zenon_H16a zenon_H191 zenon_Hf0 zenon_H117 zenon_H6f zenon_H131 zenon_H1a2 zenon_Hb6 zenon_H164 zenon_H25 zenon_H179 zenon_H1b7 zenon_H48 zenon_H19a zenon_H47 zenon_H1f1 zenon_H7f zenon_H13f zenon_H196 zenon_Hfa zenon_H141 zenon_H5c zenon_H77 zenon_Hb2 zenon_H288 zenon_H13b zenon_H231 zenon_H183 zenon_H23c zenon_H26a zenon_H111 zenon_H1d8 zenon_H23d zenon_H12e zenon_H1c2 zenon_H201 zenon_H109 zenon_H19d zenon_H1d5 zenon_H192 zenon_H82 zenon_H125 zenon_H121 zenon_H177 zenon_H11a zenon_H24e zenon_H1cd zenon_H104 zenon_H1fe zenon_H18a zenon_H234 zenon_H2c zenon_H7d zenon_Hbc zenon_H212 zenon_H33 zenon_He4 zenon_H140 zenon_H1a8 zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_Heb zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1c6 zenon_H1cb zenon_H13c zenon_H1ef zenon_H266 zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H139 zenon_Hf5 zenon_H15d zenon_H68 zenon_H13a zenon_Ha4 zenon_H173 zenon_H10c zenon_Ha0 zenon_H31 zenon_Ha9. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.57 apply (zenon_L251_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.48/22.57 apply (zenon_L251_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.48/22.57 apply (zenon_L171_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.57 exact (zenon_Ha4 zenon_H9f). % 22.48/22.57 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.57 apply (zenon_L120_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.57 apply (zenon_L68_); trivial. % 22.48/22.57 apply (zenon_L2207_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.57 exact (zenon_Ha4 zenon_H9f). % 22.48/22.57 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.57 apply (zenon_L110_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.57 apply (zenon_L68_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.48/22.57 exact (zenon_Ha4 zenon_H9f). % 22.48/22.57 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.48/22.57 apply (zenon_L116_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.48/22.57 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.48/22.57 apply (zenon_L171_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.48/22.57 apply (zenon_L226_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.57 apply (zenon_L67_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.57 apply (zenon_L2208_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.57 apply (zenon_L2123_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.48/22.57 apply (zenon_L648_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.48/22.57 apply (zenon_L284_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.48/22.57 apply (zenon_L2205_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.48/22.57 apply (zenon_L21_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.48/22.57 apply (zenon_L87_); trivial. % 22.48/22.57 apply (zenon_L2147_); trivial. % 22.48/22.57 apply (zenon_L149_); trivial. % 22.48/22.57 apply (zenon_L206_); trivial. % 22.48/22.57 apply (zenon_L91_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.57 apply (zenon_L264_); trivial. % 22.48/22.57 apply (zenon_L2112_); trivial. % 22.48/22.57 (* end of lemma zenon_L2209_ *) % 22.48/22.57 assert (zenon_L2210_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e2) (e2)))) -> (((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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (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 (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((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)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (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))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.57 do 0 intro. intros zenon_H66 zenon_H2a zenon_Hc4 zenon_H209 zenon_H173 zenon_Ha4 zenon_H13a zenon_H15d zenon_Hf5 zenon_H139 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H73 zenon_H1ec zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H266 zenon_H1ef zenon_H13c zenon_H1c6 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H1a8 zenon_H140 zenon_He4 zenon_H33 zenon_H212 zenon_Hbc zenon_H7d zenon_H2c zenon_H234 zenon_H1fe zenon_H104 zenon_H1cd zenon_H24e zenon_H11a zenon_H177 zenon_H121 zenon_H125 zenon_H82 zenon_H192 zenon_H1d5 zenon_H19d zenon_H109 zenon_H201 zenon_H1c2 zenon_H12e zenon_H23d zenon_H1d8 zenon_H111 zenon_H26a zenon_H23c zenon_H183 zenon_H231 zenon_H13b zenon_H288 zenon_Hb2 zenon_H141 zenon_Hfa zenon_H47 zenon_H1b7 zenon_H179 zenon_H164 zenon_H1a2 zenon_H131 zenon_H6f zenon_H191 zenon_H16a zenon_H25 zenon_H4e zenon_H196 zenon_Hf0 zenon_H10c zenon_H13f zenon_Hb6 zenon_H7f zenon_H1f1 zenon_H195 zenon_H117 zenon_H1c3 zenon_Ha9 zenon_H77 zenon_H1cb zenon_H68 zenon_H48 zenon_H5c zenon_Ha0 zenon_H19a zenon_H18a. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.48/22.57 apply (zenon_L252_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.48/22.57 apply (zenon_L171_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.57 exact (zenon_Ha4 zenon_H9f). % 22.48/22.57 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.57 apply (zenon_L120_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.57 apply (zenon_L193_); trivial. % 22.48/22.57 apply (zenon_L2207_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.57 exact (zenon_Ha4 zenon_H9f). % 22.48/22.57 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.57 apply (zenon_L53_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.57 apply (zenon_L393_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.48/22.57 apply (zenon_L2209_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.48/22.57 apply (zenon_L274_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.48/22.57 apply (zenon_L2124_); trivial. % 22.48/22.57 apply (zenon_L269_); trivial. % 22.48/22.57 (* end of lemma zenon_L2210_ *) % 22.48/22.57 assert (zenon_L2211_ : (((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 (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (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))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 22.48/22.57 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H173 zenon_Hc4 zenon_H177 zenon_H10c zenon_H11a zenon_H209 zenon_H121 zenon_Ha9 zenon_Hf6. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.57 exact (zenon_Ha4 zenon_H9f). % 22.48/22.57 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.57 apply (zenon_L120_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.57 apply (zenon_L393_); trivial. % 22.48/22.57 apply (zenon_L92_); trivial. % 22.48/22.57 (* end of lemma zenon_L2211_ *) % 22.48/22.57 assert (zenon_L2212_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (((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)) -> (~((e2) = (e3))) -> False). % 22.48/22.57 do 0 intro. intros zenon_H139 zenon_H47 zenon_H68 zenon_H2a zenon_H77 zenon_H13a zenon_Ha4 zenon_H173 zenon_H10c zenon_Hb6 zenon_H153 zenon_Ha9. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.57 apply (zenon_L251_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.57 apply (zenon_L147_); trivial. % 22.48/22.57 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.57 apply (zenon_L94_); trivial. % 22.48/22.57 apply (zenon_L598_); trivial. % 22.48/22.57 (* end of lemma zenon_L2212_ *) % 22.48/22.57 assert (zenon_L2213_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((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) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (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) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((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) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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 (e2) (e0)) = (op (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) (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 (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> False). % 22.48/22.58 do 0 intro. intros zenon_H288 zenon_H13b zenon_H231 zenon_H183 zenon_H23c zenon_H26a zenon_H111 zenon_H1d8 zenon_H23d zenon_H12e zenon_H1c2 zenon_H201 zenon_H109 zenon_H19d zenon_H179 zenon_H1d5 zenon_H192 zenon_H82 zenon_H125 zenon_H121 zenon_H177 zenon_H11a zenon_H24e zenon_H1cd zenon_H104 zenon_H1fe zenon_H18a zenon_Hb2 zenon_Hfa zenon_H234 zenon_H141 zenon_H2c zenon_H164 zenon_H7d zenon_Hbc zenon_H212 zenon_H33 zenon_He4 zenon_H140 zenon_H1a8 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_Heb zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H139 zenon_H68 zenon_Ha4 zenon_Ha9 zenon_H13a zenon_H77 zenon_Hf5 zenon_H15d zenon_H9d zenon_H196 zenon_H9e zenon_H13f zenon_H7f zenon_H1f1 zenon_H48 zenon_H195 zenon_H5c zenon_H117 zenon_Hb6 zenon_H54 zenon_H10c zenon_Hf0 zenon_H191 zenon_Ha0. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.58 apply (zenon_L217_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.58 apply (zenon_L2204_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.58 apply (zenon_L2124_); trivial. % 22.48/22.58 apply (zenon_L648_); trivial. % 22.48/22.58 (* end of lemma zenon_L2213_ *) % 22.48/22.58 assert (zenon_L2214_ : (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((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)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> False). % 22.48/22.58 do 0 intro. intros zenon_Ha0 zenon_H191 zenon_Hf0 zenon_H10c zenon_Hb6 zenon_H117 zenon_H5c zenon_H195 zenon_H48 zenon_H1f1 zenon_H13f zenon_H196 zenon_H15d zenon_Hf5 zenon_H77 zenon_H13a zenon_Ha9 zenon_Ha4 zenon_H68 zenon_H139 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H1a8 zenon_H140 zenon_He4 zenon_H33 zenon_H212 zenon_Hbc zenon_H164 zenon_H2c zenon_H141 zenon_H234 zenon_Hfa zenon_Hb2 zenon_H18a zenon_H1fe zenon_H104 zenon_H1cd zenon_H24e zenon_H11a zenon_H177 zenon_H121 zenon_H125 zenon_H82 zenon_H192 zenon_H1d5 zenon_H179 zenon_H19d zenon_H109 zenon_H201 zenon_H1c2 zenon_H12e zenon_H23d zenon_H1d8 zenon_H111 zenon_H26a zenon_H23c zenon_H183 zenon_H231 zenon_H13b zenon_H288 zenon_H25 zenon_H153 zenon_H2a zenon_H7d zenon_H7f. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.58 apply (zenon_L2212_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.58 apply (zenon_L25_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.58 exact (zenon_Ha4 zenon_H9f). % 22.48/22.58 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.58 apply (zenon_L53_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.58 apply (zenon_L95_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.48/22.58 exact (zenon_Ha4 zenon_H9f). % 22.48/22.58 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.48/22.58 apply (zenon_L116_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.48/22.58 apply (zenon_L151_); trivial. % 22.48/22.58 apply (zenon_L2213_); trivial. % 22.48/22.58 apply (zenon_L31_); trivial. % 22.48/22.58 (* end of lemma zenon_L2214_ *) % 22.48/22.58 assert (zenon_L2215_ : (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((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) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (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) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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 (e2) (e0)) = (op (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) (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 (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((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 (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.58 do 0 intro. intros zenon_H209 zenon_Hc4 zenon_H7f zenon_H7d zenon_H2a zenon_H25 zenon_H288 zenon_H13b zenon_H231 zenon_H183 zenon_H23c zenon_H26a zenon_H111 zenon_H1d8 zenon_H23d zenon_H12e zenon_H1c2 zenon_H201 zenon_H109 zenon_H19d zenon_H179 zenon_H1d5 zenon_H192 zenon_H82 zenon_H125 zenon_H121 zenon_H177 zenon_H11a zenon_H24e zenon_H1cd zenon_H104 zenon_H1fe zenon_H18a zenon_Hb2 zenon_Hfa zenon_H234 zenon_H141 zenon_H2c zenon_H164 zenon_Hbc zenon_H212 zenon_H33 zenon_He4 zenon_H140 zenon_H1a8 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_Heb zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H139 zenon_H68 zenon_Ha4 zenon_Ha9 zenon_H13a zenon_H77 zenon_H15d zenon_H196 zenon_H13f zenon_H1f1 zenon_H48 zenon_H195 zenon_H117 zenon_Hb6 zenon_H10c zenon_Hf0 zenon_H191 zenon_Ha0 zenon_H5c zenon_Hf5. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.58 apply (zenon_L251_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.58 apply (zenon_L147_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.58 apply (zenon_L2210_); trivial. % 22.48/22.58 apply (zenon_L2211_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.58 apply (zenon_L65_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.58 apply (zenon_L2214_); trivial. % 22.48/22.58 apply (zenon_L192_); trivial. % 22.48/22.58 (* end of lemma zenon_L2215_ *) % 22.48/22.58 assert (zenon_L2216_ : (((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 (e3) (e3)) = (e3))) -> (~((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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.58 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H2a zenon_Hc4 zenon_H177 zenon_H11a zenon_H209 zenon_H121 zenon_H117 zenon_Ha0 zenon_H2d zenon_H10c zenon_Hf0 zenon_H191 zenon_H196. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.58 exact (zenon_Ha4 zenon_H9f). % 22.48/22.58 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.58 apply (zenon_L53_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.58 apply (zenon_L393_); trivial. % 22.48/22.58 apply (zenon_L731_); trivial. % 22.48/22.58 (* end of lemma zenon_L2216_ *) % 22.48/22.58 assert (zenon_L2217_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (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))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e1) (e1)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.58 do 0 intro. intros zenon_H16a zenon_H9e zenon_H105 zenon_Hdd zenon_H66 zenon_H111 zenon_H19d zenon_H125 zenon_H94 zenon_H179 zenon_H1a2 zenon_H1c3 zenon_H1d5 zenon_Hf5 zenon_H82 zenon_H5d zenon_H139 zenon_Ha0 zenon_H1cb zenon_H192 zenon_H164 zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H2a zenon_H196 zenon_H121 zenon_H11a zenon_H236 zenon_Hfa zenon_Hbc zenon_H7d zenon_H212 zenon_H33 zenon_H141 zenon_H2c zenon_H234 zenon_He4 zenon_Ha9 zenon_H177 zenon_H4e zenon_H1cf zenon_H173 zenon_H140 zenon_H1a8 zenon_Hf0 zenon_H189 zenon_H15d zenon_H13f zenon_H1f1 zenon_H190 zenon_H6f zenon_H55 zenon_H266 zenon_H195 zenon_Hb2 zenon_H1ef zenon_H209 zenon_H1fe zenon_H61 zenon_H10c zenon_H117 zenon_H19a zenon_H1b7 zenon_H7f zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H48 zenon_H68 zenon_H18a. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.48/22.58 apply (zenon_L2116_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.48/22.58 apply (zenon_L54_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.48/22.58 apply (zenon_L258_); trivial. % 22.48/22.58 apply (zenon_L2154_); trivial. % 22.48/22.58 (* end of lemma zenon_L2217_ *) % 22.48/22.58 assert (zenon_L2218_ : (((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))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> False). % 22.48/22.58 do 0 intro. intros zenon_H117 zenon_H109 zenon_H9d zenon_H10c zenon_Hf0 zenon_H191 zenon_Ha0 zenon_H115. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.48/22.58 apply (zenon_L73_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.48/22.58 apply (zenon_L74_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.48/22.58 exact (zenon_H191 zenon_H110). % 22.48/22.58 apply (zenon_L77_); trivial. % 22.48/22.58 (* end of lemma zenon_L2218_ *) % 22.48/22.58 assert (zenon_L2219_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((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 (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.48/22.58 do 0 intro. intros zenon_H121 zenon_H115 zenon_Ha0 zenon_H191 zenon_Hf0 zenon_H109 zenon_H117 zenon_H11a zenon_H10c zenon_H1a3 zenon_Hc4. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 22.48/22.58 apply (zenon_L2218_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 22.48/22.58 apply (zenon_L79_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 22.48/22.58 exact (zenon_H1a3 zenon_Hbb). % 22.48/22.58 exact (zenon_Hc4 zenon_Hc3). % 22.48/22.58 (* end of lemma zenon_L2219_ *) % 22.48/22.58 assert (zenon_L2220_ : (((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 (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 22.48/22.58 do 0 intro. intros zenon_H13b zenon_H34 zenon_H179 zenon_H2a zenon_H173 zenon_H1a3 zenon_H191 zenon_Ha0 zenon_H153 zenon_Hb6 zenon_H1a2 zenon_H48 zenon_H5c. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.48/22.58 apply (zenon_L297_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.48/22.58 apply (zenon_L272_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.48/22.58 apply (zenon_L1265_); trivial. % 22.48/22.58 apply (zenon_L157_); trivial. % 22.48/22.58 (* end of lemma zenon_L2220_ *) % 22.48/22.58 assert (zenon_L2221_ : (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((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))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (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 (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((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)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (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 (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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))))) -> (~((e1) = (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) (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) (e2)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.58 do 0 intro. intros zenon_Ha9 zenon_Ha0 zenon_H10c zenon_H173 zenon_Ha4 zenon_H13a zenon_H68 zenon_H15d zenon_H139 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H73 zenon_H1ec zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H266 zenon_H1ef zenon_H13c zenon_H1cb zenon_H1c6 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H1a8 zenon_H140 zenon_He4 zenon_H33 zenon_H212 zenon_Hbc zenon_H7d zenon_H2c zenon_H234 zenon_H18a zenon_H1fe zenon_H104 zenon_H1cd zenon_H24e zenon_H11a zenon_H177 zenon_H121 zenon_H125 zenon_H82 zenon_H1d5 zenon_H19d zenon_H109 zenon_H201 zenon_H1c2 zenon_H12e zenon_H23d zenon_H1d8 zenon_H111 zenon_H26a zenon_H23c zenon_H183 zenon_H231 zenon_H13b zenon_H288 zenon_Hb2 zenon_H77 zenon_H141 zenon_Hfa zenon_H196 zenon_H13f zenon_H1f1 zenon_H19a zenon_H1b7 zenon_H179 zenon_H25 zenon_H164 zenon_Hb6 zenon_H1a2 zenon_H131 zenon_H6f zenon_H117 zenon_Hf0 zenon_H191 zenon_H16a zenon_H195 zenon_H7f zenon_H192 zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.58 apply (zenon_L2209_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.58 apply (zenon_L146_); trivial. % 22.48/22.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.58 apply (zenon_L239_); trivial. % 22.48/22.58 apply (zenon_L192_); trivial. % 22.48/22.58 (* end of lemma zenon_L2221_ *) % 22.48/22.58 assert (zenon_L2222_ : (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e1) (e1)) = (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) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.59 do 0 intro. intros zenon_H68 zenon_H18d zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H7f zenon_H1b7 zenon_H19a zenon_H183 zenon_H1c2 zenon_H1c3 zenon_H6e zenon_H192 zenon_H104 zenon_H231 zenon_H105 zenon_H1cd zenon_H1cb zenon_Hdd zenon_H33 zenon_H140 zenon_H195 zenon_H1f1 zenon_H13f zenon_H61 zenon_Hbc zenon_H173 zenon_H1cf zenon_Ha9 zenon_H47 zenon_Hb6 zenon_H13a zenon_H4e zenon_H1ef zenon_Hfa zenon_H16a zenon_H5c zenon_H48 zenon_Hc4 zenon_H1a3 zenon_H10c zenon_H11a zenon_H117 zenon_H109 zenon_Hf0 zenon_H191 zenon_Ha0 zenon_H121 zenon_H34 zenon_H18a. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.48/22.59 apply (zenon_L1344_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.48/22.59 apply (zenon_L157_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.48/22.59 apply (zenon_L2219_); trivial. % 22.48/22.59 apply (zenon_L416_); trivial. % 22.48/22.59 (* end of lemma zenon_L2222_ *) % 22.48/22.59 assert (zenon_L2223_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (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) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (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) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((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))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((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)) = (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) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (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 (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> False). % 22.48/22.59 do 0 intro. intros zenon_Hf5 zenon_H5c zenon_H192 zenon_H7f zenon_H117 zenon_H109 zenon_Hf0 zenon_H191 zenon_H195 zenon_H1f1 zenon_H13f zenon_H196 zenon_H201 zenon_H186 zenon_H18a zenon_H16a zenon_Hfa zenon_H1ef zenon_H4e zenon_H1cf zenon_Hbc zenon_H61 zenon_H140 zenon_H1cb zenon_H231 zenon_H104 zenon_H1c3 zenon_H1c2 zenon_H183 zenon_H19a zenon_H1b7 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_H18d zenon_H1cd zenon_H141 zenon_Ha4 zenon_H283 zenon_H163 zenon_H73 zenon_H1ec zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H266 zenon_H13c zenon_H1c6 zenon_H25b zenon_H27e zenon_H189 zenon_H236 zenon_Heb zenon_H282 zenon_Hcc zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H25e zenon_H284 zenon_H1a8 zenon_He4 zenon_H212 zenon_H7d zenon_H2c zenon_H234 zenon_H1fe zenon_H24e zenon_H125 zenon_H82 zenon_H1d5 zenon_H19d zenon_H12e zenon_H23d zenon_H1d8 zenon_H111 zenon_H26a zenon_H23c zenon_H13b zenon_H288 zenon_Hb2 zenon_H179 zenon_H164 zenon_H1a2 zenon_H131 zenon_H6f zenon_H15d zenon_H68 zenon_Ha9 zenon_H77 zenon_H139 zenon_H209 zenon_H177 zenon_Ha0 zenon_Hb6 zenon_H10c zenon_H173 zenon_H121 zenon_H33 zenon_H11a zenon_H1a3 zenon_Hc4 zenon_H13a zenon_H48. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.59 apply (zenon_L13_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.59 apply (zenon_L146_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.59 apply (zenon_L13_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.59 apply (zenon_L17_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.59 apply (zenon_L20_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.48/22.59 apply (zenon_L20_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.59 exact (zenon_Ha4 zenon_H9f). % 22.48/22.59 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.59 apply (zenon_L110_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.59 apply (zenon_L95_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.59 apply (zenon_L731_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.59 apply (zenon_L2122_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.59 apply (zenon_L2124_); trivial. % 22.48/22.59 apply (zenon_L648_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.48/22.59 apply (zenon_L33_); trivial. % 22.48/22.59 apply (zenon_L2125_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.59 apply (zenon_L94_); trivial. % 22.48/22.59 apply (zenon_L598_); trivial. % 22.48/22.59 apply (zenon_L31_); trivial. % 22.48/22.59 apply (zenon_L192_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.59 apply (zenon_L161_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.59 apply (zenon_L2215_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.59 apply (zenon_L2216_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.59 apply (zenon_L251_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.59 apply (zenon_L147_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.59 exact (zenon_Ha4 zenon_H9f). % 22.48/22.59 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.59 apply (zenon_L120_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.59 apply (zenon_L393_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.48/22.59 apply (zenon_L2215_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.48/22.59 apply (zenon_L272_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.48/22.59 apply (zenon_L147_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.59 apply (zenon_L359_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.48/22.59 apply (zenon_L1316_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.48/22.59 apply (zenon_L117_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.48/22.59 apply (zenon_L2217_); trivial. % 22.48/22.59 apply (zenon_L331_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.59 apply (zenon_L2124_); trivial. % 22.48/22.59 apply (zenon_L2219_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.59 apply (zenon_L731_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.59 apply (zenon_L54_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.59 apply (zenon_L365_); trivial. % 22.48/22.59 apply (zenon_L2219_); trivial. % 22.48/22.59 apply (zenon_L169_); trivial. % 22.48/22.59 apply (zenon_L157_); trivial. % 22.48/22.59 apply (zenon_L2211_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.59 apply (zenon_L65_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.59 apply (zenon_L2220_); trivial. % 22.48/22.59 apply (zenon_L192_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.59 apply (zenon_L2128_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.59 apply (zenon_L2221_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.59 apply (zenon_L2115_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.59 apply (zenon_L251_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.59 exact (zenon_Ha4 zenon_H9f). % 22.48/22.59 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.59 apply (zenon_L110_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.59 apply (zenon_L68_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.59 apply (zenon_L2113_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.48/22.59 apply (zenon_L239_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.48/22.59 apply (zenon_L138_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.48/22.59 apply (zenon_L2222_); trivial. % 22.48/22.59 apply (zenon_L331_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.59 apply (zenon_L2124_); trivial. % 22.48/22.59 apply (zenon_L2219_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.59 apply (zenon_L264_); trivial. % 22.48/22.59 apply (zenon_L2112_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.59 apply (zenon_L146_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.59 apply (zenon_L239_); trivial. % 22.48/22.59 apply (zenon_L192_); trivial. % 22.48/22.59 apply (zenon_L1253_); trivial. % 22.48/22.59 (* end of lemma zenon_L2223_ *) % 22.48/22.59 assert (zenon_L2224_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (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) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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) (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (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)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((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) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (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 (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.59 do 0 intro. intros zenon_H16a zenon_Hdd zenon_H181 zenon_H1c2 zenon_H1cf zenon_H4e zenon_H54 zenon_He4 zenon_H177 zenon_H139 zenon_H234 zenon_H104 zenon_H121 zenon_H11a zenon_H1cd zenon_H24e zenon_Hc4 zenon_H2c zenon_H141 zenon_H164 zenon_H1e zenon_H33 zenon_H1b7 zenon_H212 zenon_H7d zenon_Hbc zenon_H209 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_H18d zenon_H61 zenon_H1fe zenon_H1ef zenon_Ha4 zenon_Hb2 zenon_Hf5 zenon_H192 zenon_H266 zenon_H55 zenon_H6f zenon_H190 zenon_H15d zenon_H189 zenon_H1a8 zenon_H13a zenon_Hfa zenon_H236 zenon_H6e zenon_H173 zenon_H18a zenon_H102 zenon_H19a zenon_Ha0 zenon_H9e zenon_H5c zenon_H48 zenon_H68 zenon_H1cb zenon_H77 zenon_Ha9 zenon_H1c3 zenon_H117 zenon_H1f1 zenon_H7f zenon_Hb6 zenon_H13f zenon_H10c zenon_Hf0 zenon_H196 zenon_H153 zenon_H140 zenon_H195. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.48/22.59 apply (zenon_L2117_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.48/22.59 apply (zenon_L21_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.48/22.59 apply (zenon_L1124_); trivial. % 22.48/22.59 apply (zenon_L2145_); trivial. % 22.48/22.59 (* end of lemma zenon_L2224_ *) % 22.48/22.59 assert (zenon_L2225_ : ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (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) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (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 (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (((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))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.48/22.59 do 0 intro. intros zenon_H7f zenon_H7d zenon_Ha0 zenon_H191 zenon_Hf0 zenon_H117 zenon_H195 zenon_H48 zenon_H1f1 zenon_H13f zenon_H196 zenon_H16a zenon_H181 zenon_H1c2 zenon_H1cf zenon_H4e zenon_He4 zenon_H177 zenon_H139 zenon_H234 zenon_H104 zenon_H121 zenon_H11a zenon_H1cd zenon_H24e zenon_Hc4 zenon_H2c zenon_H141 zenon_H164 zenon_H1e zenon_H33 zenon_H1b7 zenon_H212 zenon_Hbc zenon_H209 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_H18d zenon_H61 zenon_H1fe zenon_H1ef zenon_Hb2 zenon_H192 zenon_H266 zenon_H55 zenon_H6f zenon_H190 zenon_H15d zenon_H189 zenon_H1a8 zenon_Hfa zenon_H236 zenon_H18a zenon_H19a zenon_H68 zenon_H1cb zenon_H1c3 zenon_H140 zenon_H82 zenon_H5d zenon_H125 zenon_H77 zenon_H13a zenon_Ha4 zenon_H173 zenon_H10c zenon_Hb6 zenon_Ha9 zenon_H5c zenon_Hf5. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.59 apply (zenon_L13_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.59 apply (zenon_L146_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.59 apply (zenon_L13_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.59 apply (zenon_L18_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.59 apply (zenon_L20_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.48/22.59 apply (zenon_L20_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.59 exact (zenon_Ha4 zenon_H9f). % 22.48/22.59 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.59 apply (zenon_L110_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.59 apply (zenon_L393_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.59 apply (zenon_L731_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.59 apply (zenon_L2122_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.59 apply (zenon_L2124_); trivial. % 22.48/22.59 apply (zenon_L209_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.48/22.59 apply (zenon_L33_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.59 exact (zenon_Ha4 zenon_H9f). % 22.48/22.59 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.59 apply (zenon_L120_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.59 apply (zenon_L95_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.59 apply (zenon_L217_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.59 apply (zenon_L2224_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.59 apply (zenon_L2124_); trivial. % 22.48/22.59 apply (zenon_L648_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.59 apply (zenon_L94_); trivial. % 22.48/22.59 apply (zenon_L598_); trivial. % 22.48/22.59 apply (zenon_L31_); trivial. % 22.48/22.59 apply (zenon_L192_); trivial. % 22.48/22.59 (* end of lemma zenon_L2225_ *) % 22.48/22.59 assert (zenon_L2226_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (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) (e3)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> False). % 22.48/22.59 do 0 intro. intros zenon_H18a zenon_H68 zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1b7 zenon_H19a zenon_H61 zenon_H1fe zenon_H209 zenon_H1ef zenon_Hb2 zenon_H266 zenon_H55 zenon_H6f zenon_H190 zenon_H15d zenon_H189 zenon_H1a8 zenon_H140 zenon_H173 zenon_H1cf zenon_H4e zenon_H177 zenon_Ha9 zenon_He4 zenon_H234 zenon_H2c zenon_H141 zenon_H33 zenon_H212 zenon_H7d zenon_Hbc zenon_Hfa zenon_H236 zenon_H11a zenon_H121 zenon_H2a zenon_H13a zenon_Ha4 zenon_H164 zenon_H192 zenon_H1cb zenon_H139 zenon_H5d zenon_H82 zenon_Hf5 zenon_H1d5 zenon_H1c3 zenon_H1a2 zenon_H179 zenon_H94 zenon_H125 zenon_H19d zenon_Hef zenon_H153 zenon_H16a zenon_H196 zenon_H9e zenon_H13f zenon_H7f zenon_H1f1 zenon_H48 zenon_H195 zenon_H5c zenon_H117 zenon_Hb6 zenon_H54 zenon_H10c zenon_Hf0 zenon_H191 zenon_Ha0. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.59 apply (zenon_L731_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.48/22.59 apply (zenon_L497_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.48/22.59 apply (zenon_L61_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.48/22.59 apply (zenon_L155_); trivial. % 22.48/22.59 apply (zenon_L2154_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.59 apply (zenon_L2124_); trivial. % 22.48/22.59 apply (zenon_L648_); trivial. % 22.48/22.59 (* end of lemma zenon_L2226_ *) % 22.48/22.59 assert (zenon_L2227_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (((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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (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 (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 22.48/22.59 do 0 intro. intros zenon_H141 zenon_H191 zenon_H121 zenon_H209 zenon_H11a zenon_H177 zenon_Hc4 zenon_H2a zenon_Ha4 zenon_H13a zenon_H6d zenon_H196 zenon_Ha0 zenon_Hf0 zenon_H10c zenon_H13f zenon_Hb6 zenon_H7f zenon_H1f1 zenon_H48 zenon_H195 zenon_H117 zenon_H1c3 zenon_H9e zenon_Ha9 zenon_H77 zenon_H5c zenon_H68 zenon_H181. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.48/22.59 apply (zenon_L2216_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.48/22.59 apply (zenon_L54_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.48/22.59 apply (zenon_L2124_); trivial. % 22.48/22.59 apply (zenon_L209_); trivial. % 22.48/22.59 (* end of lemma zenon_L2227_ *) % 22.48/22.59 assert (zenon_L2228_ : ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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)) = (op (e3) (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) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (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))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e2) = (e3))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (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 (e2) (e1)))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((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 (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.48/22.59 do 0 intro. intros zenon_H54 zenon_H16a zenon_H153 zenon_H19d zenon_H125 zenon_H94 zenon_H179 zenon_H1a2 zenon_H1d5 zenon_Hf5 zenon_H82 zenon_H5d zenon_H139 zenon_H1cb zenon_H192 zenon_H164 zenon_H236 zenon_Hfa zenon_Hbc zenon_H7d zenon_H212 zenon_H33 zenon_H2c zenon_H234 zenon_He4 zenon_H4e zenon_H1cf zenon_H173 zenon_H140 zenon_H1a8 zenon_H189 zenon_H15d zenon_H190 zenon_H6f zenon_H55 zenon_H266 zenon_Hb2 zenon_H1ef zenon_H1fe zenon_H61 zenon_H19a zenon_H1b7 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_H18d zenon_H18a zenon_H181 zenon_H68 zenon_H5c zenon_Ha9 zenon_H1c3 zenon_H117 zenon_H195 zenon_H48 zenon_H1f1 zenon_Hb6 zenon_H13f zenon_H10c zenon_Hf0 zenon_Ha0 zenon_H196 zenon_H13a zenon_Ha4 zenon_H2a zenon_Hc4 zenon_H177 zenon_H11a zenon_H209 zenon_H121 zenon_H191 zenon_H141 zenon_H7f zenon_H77. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.59 exact (zenon_Ha4 zenon_H9f). % 22.48/22.59 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.59 apply (zenon_L53_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.59 apply (zenon_L95_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.48/22.59 apply (zenon_L147_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.48/22.59 apply (zenon_L2226_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.48/22.59 apply (zenon_L2227_); trivial. % 22.48/22.59 apply (zenon_L169_); trivial. % 22.48/22.59 (* end of lemma zenon_L2228_ *) % 22.48/22.59 assert (zenon_L2229_ : (((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) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (((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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (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) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.48/22.59 do 0 intro. intros zenon_H16a zenon_H196 zenon_H9e zenon_H105 zenon_Hb6 zenon_Hdd zenon_H117 zenon_H6f zenon_H181 zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H192 zenon_H183 zenon_Hc4 zenon_H1cb zenon_H1bb zenon_H77 zenon_H104 zenon_H12e zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H6e zenon_H31 zenon_H19a zenon_Ha0 zenon_H5c zenon_H48 zenon_H68 zenon_H34 zenon_H18a. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.48/22.59 apply (zenon_L2116_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.48/22.59 apply (zenon_L21_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.48/22.59 apply (zenon_L1509_); trivial. % 22.48/22.59 apply (zenon_L2185_); trivial. % 22.48/22.59 (* end of lemma zenon_L2229_ *) % 22.48/22.59 assert (zenon_L2230_ : ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (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) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 22.48/22.59 do 0 intro. intros zenon_Ha8 zenon_H1a3 zenon_H1cd zenon_H7f zenon_H105 zenon_H231 zenon_H104 zenon_H192 zenon_H6e zenon_H1c2 zenon_H18a zenon_H183 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H48 zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_H283 zenon_H1b4 zenon_H38 zenon_H20f zenon_H5c zenon_H129 zenon_H1bb. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.48/22.59 apply (zenon_L43_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.48/22.59 apply (zenon_L21_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.48/22.59 apply (zenon_L1275_); trivial. % 22.48/22.59 apply (zenon_L1236_); trivial. % 22.48/22.59 (* end of lemma zenon_L2230_ *) % 22.48/22.59 assert (zenon_L2231_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((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 (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (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) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (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) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 22.48/22.59 do 0 intro. intros zenon_H13f zenon_Hdd zenon_H162 zenon_H121 zenon_Ha0 zenon_H191 zenon_Hf0 zenon_H109 zenon_H117 zenon_H11a zenon_H10c zenon_H1a3 zenon_Hc4 zenon_H48 zenon_Ha8 zenon_H1cd zenon_H7f zenon_H231 zenon_H104 zenon_H192 zenon_H6e zenon_H1c2 zenon_H18a zenon_H183 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H68 zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H77 zenon_H139 zenon_H13c zenon_Hb6 zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H13a zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H195 zenon_H5c. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.48/22.59 apply (zenon_L151_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.48/22.59 apply (zenon_L111_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.48/22.59 apply (zenon_L2230_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.48/22.59 apply (zenon_L157_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.48/22.59 apply (zenon_L2219_); trivial. % 22.48/22.59 exact (zenon_H162 zenon_H167). % 22.48/22.59 apply (zenon_L149_); trivial. % 22.48/22.59 (* end of lemma zenon_L2231_ *) % 22.48/22.59 assert (zenon_L2232_ : ((op (e1) (e3)) = (e1)) -> (~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (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) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e1) (e1)) = (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.48/22.59 do 0 intro. intros zenon_H5c zenon_H195 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H18d zenon_H236 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H183 zenon_H18a zenon_H1c2 zenon_H6e zenon_H192 zenon_H104 zenon_H231 zenon_H7f zenon_H1cd zenon_H48 zenon_Hc4 zenon_H1a3 zenon_H10c zenon_H11a zenon_H117 zenon_H109 zenon_Hf0 zenon_H121 zenon_H162 zenon_H13f zenon_Ha0 zenon_Hdd zenon_H191 zenon_H9e zenon_H196. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.48/22.59 apply (zenon_L2231_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.48/22.59 apply (zenon_L152_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.48/22.59 exact (zenon_H191 zenon_H110). % 22.48/22.59 apply (zenon_L154_); trivial. % 22.48/22.59 (* end of lemma zenon_L2232_ *) % 22.48/22.59 assert (zenon_L2233_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e1) (e1)) = (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) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.48/22.59 do 0 intro. intros zenon_H19a zenon_H1fb zenon_H2a zenon_H5c zenon_H48 zenon_Hc4 zenon_H1a3 zenon_H10c zenon_H11a zenon_H117 zenon_H109 zenon_Hf0 zenon_H191 zenon_Ha0 zenon_H121 zenon_H162. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.48/22.59 apply (zenon_L316_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.48/22.59 apply (zenon_L157_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.48/22.59 apply (zenon_L2219_); trivial. % 22.48/22.59 exact (zenon_H162 zenon_H167). % 22.48/22.59 (* end of lemma zenon_L2233_ *) % 22.48/22.59 assert (zenon_L2234_ : (((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)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.48/22.59 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H173 zenon_H10c zenon_H66 zenon_H19a zenon_Ha0 zenon_H48 zenon_H181 zenon_H68 zenon_H5c zenon_H77 zenon_Ha9 zenon_H1c3 zenon_H162. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.48/22.59 exact (zenon_Ha4 zenon_H9f). % 22.48/22.59 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.48/22.59 apply (zenon_L120_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.48/22.59 apply (zenon_L193_); trivial. % 22.48/22.59 apply (zenon_L210_); trivial. % 22.48/22.59 (* end of lemma zenon_L2234_ *) % 22.48/22.59 assert (zenon_L2235_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((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)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e1)) = (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 (e1) (e3)) = (e1)) -> False). % 22.48/22.59 do 0 intro. intros zenon_H13f zenon_H48 zenon_H7f zenon_H1f1 zenon_H196 zenon_Hf6 zenon_H266 zenon_H2d zenon_H55 zenon_H190 zenon_Hf0 zenon_H10c zenon_Hef zenon_H68 zenon_H16a zenon_H195 zenon_H5c. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.48/22.59 apply (zenon_L217_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.48/22.59 apply (zenon_L284_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.48/22.59 apply (zenon_L27_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.48/22.59 apply (zenon_L61_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.48/22.59 apply (zenon_L1263_); trivial. % 22.48/22.59 apply (zenon_L167_); trivial. % 22.48/22.59 apply (zenon_L149_); trivial. % 22.48/22.59 (* end of lemma zenon_L2235_ *) % 22.48/22.59 assert (zenon_L2236_ : (((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 (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.48/22.59 do 0 intro. intros zenon_H164 zenon_H25 zenon_H179 zenon_H2a zenon_H192 zenon_H14c zenon_H104 zenon_H162. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.48/22.59 apply (zenon_L297_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.48/22.59 apply (zenon_L292_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.48/22.59 apply (zenon_L257_); trivial. % 22.48/22.59 exact (zenon_H162 zenon_H167). % 22.48/22.59 (* end of lemma zenon_L2236_ *) % 22.48/22.59 assert (zenon_L2237_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((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))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> False). % 22.48/22.59 do 0 intro. intros zenon_H82 zenon_Ha9 zenon_H153 zenon_Hb6 zenon_H10c zenon_H173 zenon_Ha4 zenon_H13a zenon_H77 zenon_H2a zenon_H68 zenon_H139 zenon_H5d zenon_H61 zenon_H48 zenon_H2d zenon_H7d zenon_H7f. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.48/22.59 apply (zenon_L2212_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.48/22.59 apply (zenon_L18_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.48/22.59 apply (zenon_L217_); trivial. % 22.48/22.59 apply (zenon_L31_); trivial. % 22.48/22.59 (* end of lemma zenon_L2237_ *) % 22.48/22.59 assert (zenon_L2238_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (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) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (((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))) -> (~((e2) = (e3))) -> (((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). % 22.48/22.59 do 0 intro. intros zenon_H15d zenon_H117 zenon_H191 zenon_H19a zenon_Ha0 zenon_H162 zenon_H13f zenon_H1f1 zenon_H196 zenon_H266 zenon_H55 zenon_H190 zenon_Hf0 zenon_H16a zenon_H195 zenon_H1a8 zenon_H181 zenon_H1c3 zenon_H7f zenon_H7d zenon_H2d zenon_H48 zenon_H61 zenon_H5d zenon_H139 zenon_H68 zenon_H2a zenon_H77 zenon_H13a zenon_Ha4 zenon_H173 zenon_H10c zenon_Hb6 zenon_Ha9 zenon_H82 zenon_H5c zenon_Hf5. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.59 apply (zenon_L251_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.59 apply (zenon_L147_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.59 apply (zenon_L2234_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.48/22.59 apply (zenon_L147_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.48/22.59 apply (zenon_L2235_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.48/22.59 apply (zenon_L67_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.48/22.59 apply (zenon_L289_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.48/22.59 exact (zenon_H191 zenon_H110). % 22.48/22.59 apply (zenon_L166_); trivial. % 22.48/22.59 apply (zenon_L169_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.59 apply (zenon_L65_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.59 apply (zenon_L2237_); trivial. % 22.48/22.59 apply (zenon_L192_); trivial. % 22.48/22.59 (* end of lemma zenon_L2238_ *) % 22.48/22.59 assert (zenon_L2239_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (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 (e3) (e1)) = (e3))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.48/22.59 do 0 intro. intros zenon_H121 zenon_H115 zenon_H191 zenon_Hf0 zenon_H10c zenon_H109 zenon_H117 zenon_H1c7 zenon_H11d zenon_Ha0 zenon_Hc4. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 22.48/22.59 apply (zenon_L2218_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 22.48/22.59 exact (zenon_H1c7 zenon_Hac). % 22.48/22.59 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 22.48/22.59 apply (zenon_L80_); trivial. % 22.48/22.59 exact (zenon_Hc4 zenon_Hc3). % 22.48/22.59 (* end of lemma zenon_L2239_ *) % 22.48/22.59 assert (zenon_L2240_ : (~((op (e0) (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))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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)) = (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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (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 (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) (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)) = (op (e2) (e1)))) -> (((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) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (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))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (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) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 22.48/22.59 do 0 intro. intros zenon_H192 zenon_H195 zenon_H16a zenon_H6f zenon_H131 zenon_H1a2 zenon_H164 zenon_H179 zenon_H1b7 zenon_H19a zenon_H1f1 zenon_H13f zenon_Hfa zenon_H141 zenon_Hb2 zenon_H288 zenon_H13b zenon_H183 zenon_H23c zenon_H26a zenon_H111 zenon_H1d8 zenon_H23d zenon_H12e zenon_H1c2 zenon_H109 zenon_H19d zenon_H1d5 zenon_H82 zenon_H125 zenon_H121 zenon_H177 zenon_H11a zenon_H24e zenon_H1fe zenon_H18a zenon_H234 zenon_H2c zenon_H7d zenon_H212 zenon_H33 zenon_He4 zenon_H140 zenon_H1a8 zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_Heb zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_H25b zenon_H1c6 zenon_H13c zenon_H1ef zenon_H266 zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hf5 zenon_H5c zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H117 zenon_Ha0 zenon_H10c zenon_Hf0 zenon_H191 zenon_H196 zenon_H139 zenon_H77 zenon_H68 zenon_H173 zenon_Ha9 zenon_H15d zenon_H201 zenon_H48 zenon_H31 zenon_H186 zenon_H61 zenon_Hc2 zenon_Hbc zenon_H104 zenon_H1bb zenon_H1cb zenon_H120 zenon_H162 zenon_H231 zenon_Hcb zenon_H1cd zenon_H7f. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.59 apply (zenon_L2128_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.48/22.59 apply (zenon_L2221_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.48/22.59 apply (zenon_L2115_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.48/22.59 apply (zenon_L239_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.48/22.59 apply (zenon_L335_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.48/22.59 apply (zenon_L1321_); trivial. % 22.48/22.59 apply (zenon_L331_); trivial. % 22.48/22.59 (* end of lemma zenon_L2240_ *) % 22.48/22.59 assert (zenon_L2241_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (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 (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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) (e1)) = (op (e2) (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 (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((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). % 22.48/22.59 do 0 intro. intros zenon_H15d zenon_H173 zenon_H10c zenon_H13f zenon_H1f1 zenon_H120 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H266 zenon_H55 zenon_H190 zenon_Hf0 zenon_H6f zenon_H16a zenon_H195 zenon_H5c zenon_H192 zenon_H7f zenon_H7d zenon_H2d zenon_H61 zenon_H5d zenon_H139 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H77 zenon_H68 zenon_H82 zenon_H38 zenon_H48. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.59 apply (zenon_L251_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.48/22.59 apply (zenon_L217_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.48/22.59 apply (zenon_L284_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.48/22.59 apply (zenon_L27_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.48/22.59 apply (zenon_L21_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.48/22.59 apply (zenon_L1263_); trivial. % 22.48/22.59 apply (zenon_L555_); trivial. % 22.48/22.59 apply (zenon_L149_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.59 apply (zenon_L1249_); trivial. % 22.48/22.59 apply (zenon_L165_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.59 apply (zenon_L146_); trivial. % 22.48/22.59 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.59 apply (zenon_L1341_); trivial. % 22.48/22.59 apply (zenon_L246_); trivial. % 22.48/22.59 (* end of lemma zenon_L2241_ *) % 22.48/22.59 assert (zenon_L2242_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (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 (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (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 (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (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) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e1)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (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 (e0) (e3)) = (op (e2) (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) (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). % 22.48/22.60 do 0 intro. intros zenon_H15d zenon_H173 zenon_H201 zenon_H186 zenon_H231 zenon_H104 zenon_Hc2 zenon_H1cd zenon_H192 zenon_H68 zenon_H38 zenon_H77 zenon_H121 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H33 zenon_H13a zenon_H11a zenon_H10c zenon_H1a3 zenon_Hc4 zenon_Hfa zenon_H1cf zenon_H1d5 zenon_H4e zenon_H190 zenon_H1bb zenon_H162 zenon_H120 zenon_H1cb zenon_Hbc zenon_H191 zenon_H48 zenon_H140 zenon_H7f zenon_H141 zenon_H34 zenon_H109 zenon_H1a2 zenon_H196 zenon_H156 zenon_H1a8 zenon_H139 zenon_H5c zenon_Hf5. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.60 apply (zenon_L251_); trivial. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.60 apply (zenon_L1311_); trivial. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.60 apply (zenon_L1249_); trivial. % 22.48/22.60 apply (zenon_L165_); trivial. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.48/22.60 apply (zenon_L146_); trivial. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.48/22.60 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.48/22.60 apply (zenon_L1558_); trivial. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.48/22.60 apply (zenon_L1316_); trivial. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.48/22.60 apply (zenon_L1312_); trivial. % 22.48/22.60 apply (zenon_L169_); trivial. % 22.48/22.60 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.48/22.60 apply (zenon_L1316_); trivial. % 22.48/22.60 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.48/22.60 apply (zenon_L1558_); trivial. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.48/22.60 apply (zenon_L100_); trivial. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.48/22.60 apply (zenon_L1479_); trivial. % 22.48/22.60 apply (zenon_L169_); trivial. % 22.48/22.60 apply (zenon_L206_); trivial. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.48/22.60 apply (zenon_L1558_); trivial. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.48/22.60 apply (zenon_L94_); trivial. % 22.48/22.60 apply (zenon_L165_); trivial. % 22.48/22.60 apply (zenon_L192_); trivial. % 22.48/22.60 (* end of lemma zenon_L2242_ *) % 22.48/22.60 assert (zenon_L2243_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((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 (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((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))))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (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 (e2) (e0)) = (op (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) (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (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 (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 22.48/22.60 do 0 intro. intros zenon_Hcb zenon_H15d zenon_H121 zenon_Hc4 zenon_H10c zenon_H11a zenon_H33 zenon_H173 zenon_Hb6 zenon_Ha0 zenon_H38 zenon_H13a zenon_H7f zenon_H192 zenon_H48 zenon_H77 zenon_H125 zenon_Ha9 zenon_Hb2 zenon_H141 zenon_H61 zenon_He4 zenon_H1f1 zenon_H195 zenon_H13f zenon_H5c zenon_H234 zenon_H109 zenon_Hf0 zenon_H191 zenon_H183 zenon_H19a zenon_H162 zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H196 zenon_H139 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H18a zenon_H140 zenon_Hfa zenon_H68 zenon_H7d zenon_H82 zenon_H120 zenon_H1d5 zenon_H1a8 zenon_H201 zenon_H1cd zenon_H231 zenon_H104 zenon_Hbc zenon_Hc2 zenon_H1fe. % 22.48/22.60 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.48/22.60 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.48/22.60 apply (zenon_L1334_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.60 apply (zenon_L1340_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.60 apply (zenon_L2241_); trivial. % 22.56/22.60 apply (zenon_L2242_); trivial. % 22.56/22.60 apply (zenon_L433_); trivial. % 22.56/22.60 (* end of lemma zenon_L2243_ *) % 22.56/22.60 assert (zenon_L2244_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 22.56/22.60 do 0 intro. intros zenon_H236 zenon_H1f zenon_H205 zenon_H68 zenon_H66 zenon_H63 zenon_H173 zenon_H10c zenon_Ha9 zenon_Ha0 zenon_H13a. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.60 exact (zenon_H1f zenon_H1e). % 22.56/22.60 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.60 exact (zenon_H205 zenon_H2a). % 22.56/22.60 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.60 apply (zenon_L264_); trivial. % 22.56/22.60 apply (zenon_L1349_); trivial. % 22.56/22.60 (* end of lemma zenon_L2244_ *) % 22.56/22.60 assert (zenon_L2245_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.56/22.60 do 0 intro. intros zenon_H204 zenon_H1d5 zenon_Ha4 zenon_H23d zenon_H1f zenon_H68 zenon_H66 zenon_H63 zenon_H13a zenon_Ha0 zenon_Ha9 zenon_H10c zenon_H173 zenon_H236. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.56/22.60 apply (zenon_L2244_); trivial. % 22.56/22.60 apply (zenon_L601_); trivial. % 22.56/22.60 (* end of lemma zenon_L2245_ *) % 22.56/22.60 assert (zenon_L2246_ : ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((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)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> False). % 22.56/22.60 do 0 intro. intros zenon_H31 zenon_H6c zenon_H9e zenon_Hdd zenon_H9d zenon_H5c zenon_H10c zenon_H15d zenon_Hf5 zenon_H48 zenon_Hb6 zenon_H77 zenon_H13a zenon_Hf0 zenon_H196 zenon_H117 zenon_Ha0 zenon_Ha9 zenon_Ha4 zenon_H68 zenon_H139 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_Heb zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H1a8 zenon_H140 zenon_He4 zenon_H33 zenon_H212 zenon_Hbc zenon_H7d zenon_H164 zenon_H2c zenon_H141 zenon_H234 zenon_Hfa zenon_Hb2 zenon_H13f zenon_H1f1 zenon_H18a zenon_H1fe zenon_H104 zenon_H1cd zenon_H24e zenon_H11a zenon_H177 zenon_H121 zenon_H125 zenon_H82 zenon_H192 zenon_H1d5 zenon_H179 zenon_H19d zenon_H109 zenon_H201 zenon_H1c2 zenon_H12e zenon_H23d zenon_H1d8 zenon_H111 zenon_H26a zenon_H23c zenon_H183 zenon_H231 zenon_H13b zenon_H288. % 22.56/22.60 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.56/22.60 apply (zenon_L1874_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.56/22.60 apply (zenon_L484_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.56/22.60 apply (zenon_L111_); trivial. % 22.56/22.60 apply (zenon_L2204_); trivial. % 22.56/22.60 (* end of lemma zenon_L2246_ *) % 22.56/22.60 assert (zenon_L2247_ : (((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)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.60 do 0 intro. intros zenon_H117 zenon_H109 zenon_H9d zenon_Hb6 zenon_H53 zenon_H14c zenon_Ha0 zenon_H9e zenon_H196. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.56/22.60 apply (zenon_L73_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.56/22.60 apply (zenon_L113_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.56/22.60 apply (zenon_L278_); trivial. % 22.56/22.60 apply (zenon_L154_); trivial. % 22.56/22.60 (* end of lemma zenon_L2247_ *) % 22.56/22.60 assert (zenon_L2248_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((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) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (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) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((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) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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 (e2) (e0)) = (op (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) (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 (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((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 (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> False). % 22.56/22.60 do 0 intro. intros zenon_H31 zenon_H6e zenon_H288 zenon_H13b zenon_H231 zenon_H183 zenon_H23c zenon_H26a zenon_H111 zenon_H1d8 zenon_H23d zenon_H12e zenon_H1c2 zenon_H201 zenon_H19d zenon_H179 zenon_H1d5 zenon_H192 zenon_H82 zenon_H125 zenon_H121 zenon_H177 zenon_H11a zenon_H24e zenon_H1cd zenon_H104 zenon_H1fe zenon_H18a zenon_Hb2 zenon_Hfa zenon_H234 zenon_H141 zenon_H2c zenon_H164 zenon_H7d zenon_Hbc zenon_H212 zenon_H33 zenon_He4 zenon_H140 zenon_H1a8 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_Heb zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H139 zenon_H68 zenon_Ha4 zenon_Ha9 zenon_H13a zenon_H77 zenon_Hf5 zenon_H15d zenon_H196 zenon_H9e zenon_H13f zenon_Hb6 zenon_H7f zenon_H1f1 zenon_H48 zenon_H195 zenon_H5c zenon_H117 zenon_H109 zenon_H9d zenon_H10c zenon_Hf0 zenon_H191 zenon_Ha0. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.56/22.60 apply (zenon_L2111_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.56/22.60 apply (zenon_L2204_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.56/22.60 apply (zenon_L2124_); trivial. % 22.56/22.60 apply (zenon_L2218_); trivial. % 22.56/22.60 (* end of lemma zenon_L2248_ *) % 22.56/22.60 assert (zenon_L2249_ : ((op (e0) (e2)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((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) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (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) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((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) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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 (e2) (e0)) = (op (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) (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 (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> False). % 22.56/22.60 do 0 intro. intros zenon_H153 zenon_H288 zenon_H13b zenon_H231 zenon_H183 zenon_H23c zenon_H26a zenon_H111 zenon_H1d8 zenon_H23d zenon_H12e zenon_H1c2 zenon_H201 zenon_H109 zenon_H19d zenon_H179 zenon_H1d5 zenon_H192 zenon_H82 zenon_H125 zenon_H121 zenon_H177 zenon_H11a zenon_H24e zenon_H1cd zenon_H104 zenon_H1fe zenon_H18a zenon_Hb2 zenon_Hfa zenon_H234 zenon_H141 zenon_H2c zenon_H164 zenon_H7d zenon_Hbc zenon_H212 zenon_H33 zenon_He4 zenon_H140 zenon_H1a8 zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_Heb zenon_H236 zenon_H18d zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H139 zenon_H68 zenon_Ha4 zenon_Ha9 zenon_H13a zenon_H77 zenon_Hf5 zenon_H15d zenon_H9d zenon_H196 zenon_H9e zenon_H13f zenon_H1f1 zenon_H48 zenon_H195 zenon_H5c zenon_H117 zenon_Hb6 zenon_H54 zenon_H10c zenon_Hf0 zenon_H191 zenon_Ha0. % 22.56/22.60 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.56/22.60 apply (zenon_L738_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.56/22.60 apply (zenon_L484_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.56/22.60 apply (zenon_L15_); trivial. % 22.56/22.60 apply (zenon_L2213_); trivial. % 22.56/22.60 (* end of lemma zenon_L2249_ *) % 22.56/22.60 assert (zenon_L2250_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (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) (e2)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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) (e2)) = (op (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 22.56/22.60 do 0 intro. intros zenon_H204 zenon_H236 zenon_H9e zenon_Ha0 zenon_H1f zenon_H9b zenon_H117 zenon_H196 zenon_H191 zenon_H10c zenon_Hf0 zenon_H13f zenon_H195 zenon_H1f1 zenon_H109 zenon_H15d zenon_Hf5 zenon_Ha4 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_H13c zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H18d zenon_Heb zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H1a8 zenon_H140 zenon_He4 zenon_H212 zenon_Hbc zenon_H7d zenon_H164 zenon_H2c zenon_H141 zenon_Hfa zenon_Hb2 zenon_H18a zenon_H1fe zenon_H104 zenon_H1cd zenon_H24e zenon_H11a zenon_H177 zenon_H121 zenon_H125 zenon_H82 zenon_H192 zenon_H1d5 zenon_H179 zenon_H19d zenon_H201 zenon_H1c2 zenon_H12e zenon_H23d zenon_H1d8 zenon_H111 zenon_H26a zenon_H23c zenon_H183 zenon_H231 zenon_H13b zenon_H288 zenon_H48 zenon_H68 zenon_H13a zenon_Ha9 zenon_Hb6 zenon_H9d zenon_H33 zenon_H139 zenon_H5c zenon_H234 zenon_H77 zenon_H240. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.60 apply (zenon_L1873_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.60 exact (zenon_H1f zenon_H1e). % 22.56/22.60 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.60 exact (zenon_H205 zenon_H2a). % 22.56/22.60 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.60 exact (zenon_H6c zenon_H67). % 22.56/22.60 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.60 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.56/22.60 apply (zenon_L214_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.56/22.60 apply (zenon_L484_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.56/22.60 apply (zenon_L731_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.56/22.60 apply (zenon_L2246_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.56/22.60 apply (zenon_L2247_); trivial. % 22.56/22.60 apply (zenon_L2218_); trivial. % 22.56/22.60 apply (zenon_L2248_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.60 apply (zenon_L264_); trivial. % 22.56/22.60 apply (zenon_L2112_); trivial. % 22.56/22.60 apply (zenon_L1353_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.60 exact (zenon_H1f zenon_H1e). % 22.56/22.60 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.60 exact (zenon_H4c zenon_H47). % 22.56/22.60 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.60 apply (zenon_L65_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.60 exact (zenon_H4c zenon_H47). % 22.56/22.60 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.60 apply (zenon_L17_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.60 apply (zenon_L2249_); trivial. % 22.56/22.60 apply (zenon_L134_); trivial. % 22.56/22.60 apply (zenon_L115_); trivial. % 22.56/22.60 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.60 exact (zenon_H237 zenon_H31). % 22.56/22.60 apply (zenon_L156_); trivial. % 22.56/22.60 apply (zenon_L1861_); trivial. % 22.56/22.60 (* end of lemma zenon_L2250_ *) % 22.56/22.60 assert (zenon_L2251_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.56/22.60 do 0 intro. intros zenon_H15d zenon_Ha9 zenon_Hbb zenon_H177 zenon_H10c zenon_H173 zenon_H77 zenon_H139 zenon_H48 zenon_H196 zenon_Hb9 zenon_Hb6 zenon_H2a zenon_Ha0 zenon_Ha4 zenon_H13a zenon_H5c zenon_Hf5. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.61 apply (zenon_L251_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.61 apply (zenon_L986_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.61 apply (zenon_L2200_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.61 exact (zenon_Ha4 zenon_H9f). % 22.56/22.61 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.61 apply (zenon_L120_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.61 apply (zenon_L178_); trivial. % 22.56/22.61 apply (zenon_L92_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.61 apply (zenon_L65_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.61 apply (zenon_L2202_); trivial. % 22.56/22.61 apply (zenon_L192_); trivial. % 22.56/22.61 (* end of lemma zenon_L2251_ *) % 22.56/22.61 assert (zenon_L2252_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H15d zenon_Ha9 zenon_H10c zenon_H173 zenon_H177 zenon_Hbb zenon_H77 zenon_H139 zenon_H196 zenon_Hb9 zenon_Ha0 zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.61 apply (zenon_L251_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.61 apply (zenon_L986_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.61 apply (zenon_L2200_); trivial. % 22.56/22.61 apply (zenon_L2112_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.61 apply (zenon_L2189_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.61 apply (zenon_L239_); trivial. % 22.56/22.61 apply (zenon_L192_); trivial. % 22.56/22.61 (* end of lemma zenon_L2252_ *) % 22.56/22.61 assert (zenon_L2253_ : (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e2) (e3)) = (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 (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (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) (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) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> False). % 22.56/22.61 do 0 intro. intros zenon_Ha4 zenon_H1fe zenon_Hb9 zenon_H13f zenon_H140 zenon_H1ba zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H1fb zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H196 zenon_H13c zenon_H1ef zenon_H266 zenon_H190 zenon_H13e zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H163 zenon_H283 zenon_Hbb zenon_H177 zenon_H139 zenon_Hfa zenon_H1cb zenon_H1c3 zenon_H4e zenon_H1d5 zenon_H1cf zenon_Hf0 zenon_H183 zenon_H288 zenon_H192 zenon_H10c zenon_H173 zenon_H179 zenon_H13b zenon_H18a zenon_H5c zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1b7 zenon_H19a zenon_H8b zenon_H6f zenon_H7b zenon_H16a zenon_H55 zenon_H234 zenon_H1d8 zenon_He4 zenon_H77 zenon_H68 zenon_H5d zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H82 zenon_H48. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.61 apply (zenon_L1355_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.61 apply (zenon_L2251_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.61 apply (zenon_L2252_); trivial. % 22.56/22.61 apply (zenon_L1372_); trivial. % 22.56/22.61 (* end of lemma zenon_L2253_ *) % 22.56/22.61 assert (zenon_L2254_ : (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e1)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (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) (e1)) = (op (e2) (e2)))) -> (((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) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (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) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.56/22.61 do 0 intro. intros zenon_Ha4 zenon_H1fe zenon_H140 zenon_H10c zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H1cb zenon_H196 zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_Hbb zenon_H177 zenon_H48 zenon_He4 zenon_H1d8 zenon_H234 zenon_H55 zenon_H141 zenon_H18a zenon_H68 zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H77 zenon_H1b7 zenon_H19a zenon_H8b zenon_H1ba zenon_H13f zenon_H111 zenon_H195 zenon_H16a zenon_H13d zenon_Ha0 zenon_Hb9 zenon_H5d zenon_H139 zenon_Hb6 zenon_Ha9 zenon_H13a zenon_H82 zenon_H5c zenon_Hf5. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.61 apply (zenon_L1355_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.61 apply (zenon_L2251_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.61 apply (zenon_L2252_); trivial. % 22.56/22.61 apply (zenon_L1388_); trivial. % 22.56/22.61 (* end of lemma zenon_L2254_ *) % 22.56/22.61 assert (zenon_L2255_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H201 zenon_H77 zenon_H48 zenon_H53 zenon_H190 zenon_H1a2 zenon_Ha9 zenon_H66 zenon_Hf3 zenon_H14c zenon_Ha0 zenon_Hb6. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.56/22.61 apply (zenon_L94_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.56/22.61 apply (zenon_L117_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.56/22.61 apply (zenon_L143_); trivial. % 22.56/22.61 apply (zenon_L364_); trivial. % 22.56/22.61 (* end of lemma zenon_L2255_ *) % 22.56/22.61 assert (zenon_L2256_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H1cf zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Ha9 zenon_H1a2 zenon_H190 zenon_H77 zenon_H201 zenon_Hf3 zenon_H68 zenon_H1ef zenon_H65 zenon_H12e zenon_H48 zenon_H53 zenon_H1f1 zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.56/22.61 apply (zenon_L2255_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.56/22.61 apply (zenon_L62_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.56/22.61 apply (zenon_L533_); trivial. % 22.56/22.61 apply (zenon_L849_); trivial. % 22.56/22.61 (* end of lemma zenon_L2256_ *) % 22.56/22.61 assert (zenon_L2257_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (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))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H13a zenon_Hc4 zenon_H104 zenon_H1c7 zenon_H33 zenon_H121 zenon_Ha9 zenon_H6e zenon_H111 zenon_H110 zenon_H38 zenon_Ha0. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.61 apply (zenon_L819_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.61 apply (zenon_L110_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.61 apply (zenon_L75_); trivial. % 22.56/22.61 apply (zenon_L156_); trivial. % 22.56/22.61 (* end of lemma zenon_L2257_ *) % 22.56/22.61 assert (zenon_L2258_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e1)) -> False). % 22.56/22.61 do 0 intro. intros zenon_H117 zenon_H65 zenon_H1a3 zenon_H190 zenon_Hf3 zenon_H153 zenon_H1a2 zenon_Ha0 zenon_H38 zenon_H111 zenon_H6e zenon_Ha9 zenon_H121 zenon_H33 zenon_H1c7 zenon_H104 zenon_Hc4 zenon_H13a zenon_Hb6 zenon_H128. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.56/22.61 apply (zenon_L43_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.56/22.61 apply (zenon_L164_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.56/22.61 apply (zenon_L2257_); trivial. % 22.56/22.61 apply (zenon_L182_); trivial. % 22.56/22.61 (* end of lemma zenon_L2258_ *) % 22.56/22.61 assert (zenon_L2259_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e1)) -> False). % 22.56/22.61 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H65 zenon_Ha0 zenon_Hdd zenon_H105 zenon_Hb6 zenon_H128. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.56/22.61 apply (zenon_L43_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.56/22.61 apply (zenon_L152_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.56/22.61 apply (zenon_L400_); trivial. % 22.56/22.61 apply (zenon_L182_); trivial. % 22.56/22.61 (* end of lemma zenon_L2259_ *) % 22.56/22.61 assert (zenon_L2260_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H1cf zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Hf3 zenon_Ha9 zenon_H1a2 zenon_Hf7 zenon_H186 zenon_H1ef zenon_H65 zenon_H1bb zenon_H18a zenon_H34 zenon_H106 zenon_H1cb zenon_Hc4. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.56/22.61 apply (zenon_L364_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.56/22.61 apply (zenon_L438_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.56/22.61 apply (zenon_L533_); trivial. % 22.56/22.61 apply (zenon_L847_); trivial. % 22.56/22.61 (* end of lemma zenon_L2260_ *) % 22.56/22.61 assert (zenon_L2261_ : (((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) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e1)) -> False). % 22.56/22.61 do 0 intro. intros zenon_H117 zenon_H109 zenon_H9d zenon_Hdd zenon_H14c zenon_Ha0 zenon_Hb6 zenon_H128. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.56/22.61 apply (zenon_L73_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.56/22.61 apply (zenon_L152_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.56/22.61 apply (zenon_L278_); trivial. % 22.56/22.61 apply (zenon_L182_); trivial. % 22.56/22.61 (* end of lemma zenon_L2261_ *) % 22.56/22.61 assert (zenon_L2262_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (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 (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H13f zenon_H65 zenon_H77 zenon_Hf0 zenon_H3f zenon_H48 zenon_H117 zenon_H109 zenon_H9d zenon_Hdd zenon_H14c zenon_Ha0 zenon_Hb6. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.56/22.61 apply (zenon_L30_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.56/22.61 apply (zenon_L118_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.56/22.61 apply (zenon_L255_); trivial. % 22.56/22.61 apply (zenon_L2261_); trivial. % 22.56/22.61 (* end of lemma zenon_L2262_ *) % 22.56/22.61 assert (zenon_L2263_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (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 (e3) (e0)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H13f zenon_H65 zenon_H77 zenon_H48 zenon_H4d zenon_H131 zenon_H117 zenon_H109 zenon_H9d zenon_Hdd zenon_H14c zenon_Ha0 zenon_Hb6. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.56/22.61 apply (zenon_L30_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.56/22.61 apply (zenon_L111_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.56/22.61 apply (zenon_L128_); trivial. % 22.56/22.61 apply (zenon_L2261_); trivial. % 22.56/22.61 (* end of lemma zenon_L2263_ *) % 22.56/22.61 assert (zenon_L2264_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (((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))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((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)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> (~((e0) = (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 (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.61 do 0 intro. intros zenon_Heb zenon_Hc2 zenon_H24 zenon_H139 zenon_H1d8 zenon_H4e zenon_H104 zenon_H1c7 zenon_H111 zenon_H68 zenon_H34 zenon_H1c3 zenon_H1a2 zenon_H25b zenon_Hf5 zenon_H26a zenon_H129 zenon_H20f zenon_H1b4 zenon_H1cf zenon_H18a zenon_H1bb zenon_H1ef zenon_H186 zenon_H33 zenon_H1b7 zenon_H190 zenon_H5d zenon_H1cb zenon_H18d zenon_H6f zenon_H201 zenon_H23c zenon_H13a zenon_H121 zenon_H38 zenon_H183 zenon_Ha9 zenon_H2c zenon_H15d zenon_H192 zenon_H7d zenon_H1cd zenon_H24e zenon_H162 zenon_Hcb zenon_H131 zenon_He4 zenon_H6e zenon_Hb6 zenon_Ha0 zenon_H9d zenon_H109 zenon_H117 zenon_Hf0 zenon_Hdd zenon_H13f zenon_H65 zenon_H77 zenon_H1f1 zenon_H48 zenon_H14c zenon_H195. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.61 apply (zenon_L1750_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.61 apply (zenon_L2262_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.61 apply (zenon_L2263_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.56/22.61 apply (zenon_L214_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.56/22.61 apply (zenon_L2262_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.56/22.61 apply (zenon_L111_); trivial. % 22.56/22.61 apply (zenon_L1268_); trivial. % 22.56/22.61 (* end of lemma zenon_L2264_ *) % 22.56/22.61 assert (zenon_L2265_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.56/22.61 do 0 intro. intros zenon_H13b zenon_H34 zenon_H179 zenon_He3 zenon_Hb6 zenon_Ha0 zenon_H14c zenon_H66 zenon_Ha9 zenon_H1a2 zenon_H48 zenon_H77 zenon_H201 zenon_Hf5 zenon_H38. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.56/22.61 apply (zenon_L297_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.56/22.61 exact (zenon_He3 zenon_He7). % 22.56/22.61 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.56/22.61 apply (zenon_L365_); trivial. % 22.56/22.61 apply (zenon_L663_); trivial. % 22.56/22.61 (* end of lemma zenon_L2265_ *) % 22.56/22.61 assert (zenon_L2266_ : ((op (e0) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (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 (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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 (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H47 zenon_H7d zenon_Heb zenon_Hc2 zenon_H24 zenon_H139 zenon_H1d8 zenon_H4e zenon_H104 zenon_H1c7 zenon_H111 zenon_H1c3 zenon_H25b zenon_H26a zenon_H129 zenon_H20f zenon_H1b4 zenon_H1cf zenon_H18a zenon_H1bb zenon_H1ef zenon_H186 zenon_H33 zenon_H1b7 zenon_H190 zenon_H5d zenon_H1cb zenon_H18d zenon_H6f zenon_H23c zenon_H13a zenon_H121 zenon_H183 zenon_H2c zenon_H15d zenon_H192 zenon_H1cd zenon_H24e zenon_H162 zenon_Hcb zenon_H131 zenon_He4 zenon_H9d zenon_H109 zenon_H117 zenon_Hf0 zenon_H13f zenon_H65 zenon_H1f1 zenon_H195 zenon_H36 zenon_H1fb zenon_He2 zenon_Hf5 zenon_H201 zenon_H77 zenon_H48 zenon_H1a2 zenon_Ha9 zenon_H14c zenon_Ha0 zenon_Hb6 zenon_He3 zenon_H179 zenon_H34 zenon_H13b zenon_H38 zenon_H68. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.61 apply (zenon_L251_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.56/22.61 apply (zenon_L317_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.56/22.61 exact (zenon_He3 zenon_He7). % 22.56/22.61 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.56/22.61 apply (zenon_L2264_); trivial. % 22.56/22.61 apply (zenon_L802_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.61 apply (zenon_L2265_); trivial. % 22.56/22.61 apply (zenon_L165_); trivial. % 22.56/22.61 (* end of lemma zenon_L2266_ *) % 22.56/22.61 assert (zenon_L2267_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((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 (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (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) (e3)) = (op (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) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((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 (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (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)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H13b zenon_H179 zenon_He3 zenon_He2 zenon_H1fb zenon_H36 zenon_Hf0 zenon_H131 zenon_Hcb zenon_H162 zenon_H24e zenon_H1cd zenon_H192 zenon_H15d zenon_H24 zenon_Hc2 zenon_Heb zenon_H7d zenon_H173 zenon_H12e zenon_H156 zenon_Hfa zenon_H234 zenon_Hb2 zenon_H34 zenon_H1cb zenon_H5d zenon_H18d zenon_H104 zenon_H111 zenon_H183 zenon_H129 zenon_H1b4 zenon_H1bb zenon_H18a zenon_H1ef zenon_H14c zenon_H6f zenon_H109 zenon_H117 zenon_H1b7 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H1c3 zenon_H26a zenon_H190 zenon_H186 zenon_H1a2 zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1d8 zenon_H82 zenon_H68 zenon_H77 zenon_H121 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H33 zenon_H13a zenon_H1c7 zenon_H1a3 zenon_Hc4 zenon_H65 zenon_H2c zenon_H139 zenon_H38 zenon_H48. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.61 apply (zenon_L251_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.61 apply (zenon_L253_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.61 apply (zenon_L110_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.56/22.61 apply (zenon_L253_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.56/22.61 apply (zenon_L116_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.56/22.61 exact (zenon_He3 zenon_He7). % 22.56/22.61 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.56/22.61 apply (zenon_L147_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.56/22.61 exact (zenon_He3 zenon_He7). % 22.56/22.61 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.61 apply (zenon_L46_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.56/22.61 apply (zenon_L30_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.56/22.61 apply (zenon_L2256_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.56/22.61 apply (zenon_L255_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.56/22.61 apply (zenon_L2258_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.56/22.61 apply (zenon_L486_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.56/22.61 apply (zenon_L2259_); trivial. % 22.56/22.61 apply (zenon_L1437_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.61 apply (zenon_L226_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.61 apply (zenon_L62_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.56/22.61 apply (zenon_L30_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.56/22.61 apply (zenon_L118_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.56/22.61 apply (zenon_L255_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.56/22.61 apply (zenon_L95_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.56/22.61 apply (zenon_L117_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.56/22.61 apply (zenon_L2259_); trivial. % 22.56/22.61 apply (zenon_L2260_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.61 apply (zenon_L117_); trivial. % 22.56/22.61 apply (zenon_L1269_); trivial. % 22.56/22.61 apply (zenon_L802_); trivial. % 22.56/22.61 apply (zenon_L663_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.56/22.61 apply (zenon_L43_); trivial. % 22.56/22.61 apply (zenon_L2266_); trivial. % 22.56/22.61 apply (zenon_L156_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.61 apply (zenon_L2265_); trivial. % 22.56/22.61 apply (zenon_L165_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.61 apply (zenon_L1302_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.61 apply (zenon_L1410_); trivial. % 22.56/22.61 apply (zenon_L246_); trivial. % 22.56/22.61 (* end of lemma zenon_L2267_ *) % 22.56/22.61 assert (zenon_L2268_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e1) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> (~((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 (e3) (e3)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e0)) = (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)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H15d zenon_H13b zenon_H179 zenon_He3 zenon_Hf5 zenon_H18a zenon_Ha0 zenon_Ha9 zenon_Hb6 zenon_H190 zenon_H1c3 zenon_H1cf zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H117 zenon_H109 zenon_H6f zenon_H14c zenon_H13a zenon_H186 zenon_H1ef zenon_H1d8 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1a2 zenon_H104 zenon_H33 zenon_H121 zenon_H18d zenon_H5d zenon_H1cb zenon_H82 zenon_H68 zenon_H77 zenon_H183 zenon_H192 zenon_Hc4 zenon_H24e zenon_H34 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H162 zenon_H1bb zenon_H181 zenon_H65 zenon_H2c zenon_H139 zenon_H38 zenon_H48. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.61 apply (zenon_L251_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.61 apply (zenon_L1701_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.61 apply (zenon_L2265_); trivial. % 22.56/22.61 apply (zenon_L165_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.61 apply (zenon_L1779_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.61 apply (zenon_L1748_); trivial. % 22.56/22.61 apply (zenon_L246_); trivial. % 22.56/22.61 (* end of lemma zenon_L2268_ *) % 22.56/22.61 assert (zenon_L2269_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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 (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 22.56/22.61 do 0 intro. intros zenon_Hc2 zenon_H139 zenon_H179 zenon_He3 zenon_H201 zenon_Ha9 zenon_Ha0 zenon_Hb6 zenon_H1a2 zenon_H14c zenon_H48 zenon_Hf5 zenon_H38 zenon_H13b zenon_H68 zenon_H34 zenon_H192 zenon_H1bb zenon_H181 zenon_H7d zenon_H1b7 zenon_H1cd zenon_H1c7 zenon_H24e zenon_H162 zenon_H183 zenon_H77 zenon_H82 zenon_H4e zenon_H104 zenon_H1c3 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1d8 zenon_H121 zenon_H23c zenon_H6f zenon_H18d zenon_H1cb zenon_H5d zenon_H117 zenon_H190 zenon_H13f zenon_H109 zenon_H1f1 zenon_He4 zenon_H33 zenon_H186 zenon_H1ef zenon_H18a zenon_H1cf zenon_H2c zenon_H65 zenon_H13a zenon_H15d. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.56/22.61 apply (zenon_L2268_); trivial. % 22.56/22.61 apply (zenon_L2268_); trivial. % 22.56/22.61 (* end of lemma zenon_L2269_ *) % 22.56/22.61 assert (zenon_L2270_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H201 zenon_Hfe zenon_H48 zenon_Hc2 zenon_Hbc zenon_H104 zenon_H120 zenon_H162 zenon_H231 zenon_Hcb zenon_H1cf zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Hf3 zenon_Ha9 zenon_H1a2 zenon_Hf7 zenon_H186 zenon_H1ef zenon_H65 zenon_H1bb zenon_H18a zenon_H34 zenon_H1cb zenon_Hc4. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.56/22.61 apply (zenon_L95_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.56/22.61 apply (zenon_L117_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.56/22.61 apply (zenon_L1321_); trivial. % 22.56/22.61 apply (zenon_L2260_); trivial. % 22.56/22.61 (* end of lemma zenon_L2270_ *) % 22.56/22.61 assert (zenon_L2271_ : (((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)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.56/22.61 do 0 intro. intros zenon_Hfa zenon_H77 zenon_H3c zenon_H6e zenon_H173 zenon_H68 zenon_H201 zenon_Hfe zenon_H48 zenon_Hc2 zenon_Hbc zenon_H104 zenon_H120 zenon_H162 zenon_H231 zenon_Hcb zenon_H1cf zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Hf3 zenon_Ha9 zenon_H1a2 zenon_H186 zenon_H1ef zenon_H65 zenon_H1bb zenon_H18a zenon_H34 zenon_H1cb zenon_Hc4. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.61 apply (zenon_L24_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.61 apply (zenon_L226_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.61 apply (zenon_L62_); trivial. % 22.56/22.61 apply (zenon_L2270_); trivial. % 22.56/22.61 (* end of lemma zenon_L2271_ *) % 22.56/22.61 assert (zenon_L2272_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H201 zenon_H77 zenon_H48 zenon_H1a3 zenon_H162 zenon_H120 zenon_H104 zenon_Hbc zenon_H231 zenon_H1cf zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Hf3 zenon_Ha9 zenon_H1a2 zenon_Hf7 zenon_H186 zenon_H1ef zenon_H65 zenon_H1bb zenon_H18a zenon_H34 zenon_H1cb zenon_Hc4. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.56/22.61 apply (zenon_L1322_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.56/22.61 apply (zenon_L117_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.56/22.61 apply (zenon_L476_); trivial. % 22.56/22.61 apply (zenon_L2260_); trivial. % 22.56/22.61 (* end of lemma zenon_L2272_ *) % 22.56/22.61 assert (zenon_L2273_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (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 (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((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)) = (e3))) -> (~((op (e3) (e2)) = (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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((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))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.56/22.61 do 0 intro. intros zenon_H15d zenon_H13b zenon_H179 zenon_He3 zenon_He2 zenon_H234 zenon_Hf0 zenon_Heb zenon_H7d zenon_H5d zenon_H18d zenon_H25b zenon_Hf5 zenon_H20f zenon_H195 zenon_H190 zenon_H26a zenon_H1c3 zenon_He4 zenon_H23c zenon_H4e zenon_H201 zenon_H13f zenon_H1f1 zenon_H117 zenon_H109 zenon_H6f zenon_H33 zenon_H18a zenon_H121 zenon_H231 zenon_Hbc zenon_H104 zenon_H1b4 zenon_H129 zenon_H1b7 zenon_H183 zenon_Hcb zenon_Hc2 zenon_H1d8 zenon_H34 zenon_H77 zenon_H65 zenon_H139 zenon_H2c zenon_Hc4 zenon_H1cb zenon_H120 zenon_H162 zenon_H1bb zenon_H1ef zenon_H186 zenon_H1cf zenon_H1a2 zenon_Hb6 zenon_Ha9 zenon_H14c zenon_Ha0 zenon_H1a3 zenon_H173 zenon_Hfa zenon_H68 zenon_H13a zenon_H82 zenon_H38 zenon_H48. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.61 apply (zenon_L251_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.61 apply (zenon_L253_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.61 apply (zenon_L110_); trivial. % 22.56/22.61 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.56/22.62 apply (zenon_L297_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.56/22.62 exact (zenon_He3 zenon_He7). % 22.56/22.62 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.56/22.62 apply (zenon_L147_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.56/22.62 exact (zenon_He3 zenon_He7). % 22.56/22.62 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.62 apply (zenon_L2271_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.56/22.62 apply (zenon_L30_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.56/22.62 apply (zenon_L118_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.56/22.62 apply (zenon_L255_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.56/22.62 apply (zenon_L1786_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.56/22.62 apply (zenon_L117_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.56/22.62 apply (zenon_L2259_); trivial. % 22.56/22.62 apply (zenon_L1437_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.62 apply (zenon_L226_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.62 apply (zenon_L62_); trivial. % 22.56/22.62 apply (zenon_L2272_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.62 apply (zenon_L117_); trivial. % 22.56/22.62 apply (zenon_L1269_); trivial. % 22.56/22.62 apply (zenon_L802_); trivial. % 22.56/22.62 apply (zenon_L663_); trivial. % 22.56/22.62 apply (zenon_L156_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.62 apply (zenon_L2265_); trivial. % 22.56/22.62 apply (zenon_L165_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.62 apply (zenon_L1326_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.62 apply (zenon_L1786_); trivial. % 22.56/22.62 apply (zenon_L246_); trivial. % 22.56/22.62 (* end of lemma zenon_L2273_ *) % 22.56/22.62 assert (zenon_L2274_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> False). % 22.56/22.62 do 0 intro. intros zenon_H1a2 zenon_H77 zenon_H65 zenon_H1ef zenon_Ha9 zenon_H31 zenon_H68 zenon_H1cf zenon_H14c zenon_Ha0 zenon_Hb6 zenon_H106. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.56/22.62 apply (zenon_L68_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.56/22.62 apply (zenon_L1849_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.56/22.62 apply (zenon_L278_); trivial. % 22.56/22.62 apply (zenon_L363_); trivial. % 22.56/22.62 (* end of lemma zenon_L2274_ *) % 22.56/22.62 assert (zenon_L2275_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (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 (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 22.56/22.62 do 0 intro. intros zenon_H1a8 zenon_H3d zenon_H156 zenon_H55 zenon_H201 zenon_H9f zenon_Hf6 zenon_H34 zenon_H48 zenon_H12e zenon_H72 zenon_H1a2 zenon_H77 zenon_H65 zenon_H1ef zenon_Ha9 zenon_H31 zenon_H68 zenon_H1cf zenon_H14c zenon_Ha0 zenon_Hb6. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.56/22.62 apply (zenon_L214_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.56/22.62 apply (zenon_L100_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.56/22.62 apply (zenon_L34_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.56/22.62 apply (zenon_L239_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.56/22.62 apply (zenon_L59_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.56/22.62 apply (zenon_L1848_); trivial. % 22.56/22.62 apply (zenon_L2274_); trivial. % 22.56/22.62 (* end of lemma zenon_L2275_ *) % 22.56/22.62 assert (zenon_L2276_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e0)) -> (~((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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e1)) -> False). % 22.56/22.62 do 0 intro. intros zenon_H204 zenon_H3a zenon_Hfa zenon_Hf5 zenon_H163 zenon_H1b4 zenon_H183 zenon_H23d zenon_H23b zenon_H139 zenon_H68 zenon_Hb6 zenon_Ha9 zenon_Ha0 zenon_H13a zenon_H77 zenon_H65 zenon_H2c zenon_H1f zenon_H48 zenon_H3d zenon_H236 zenon_H1fe zenon_H240 zenon_H24 zenon_H15d zenon_H1a8 zenon_H1a2 zenon_H12e zenon_H14c zenon_H1ef zenon_H1cf zenon_H201 zenon_H55 zenon_H156 zenon_H192 zenon_H3c. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.62 apply (zenon_L491_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.62 exact (zenon_H1f zenon_H1e). % 22.56/22.62 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.62 exact (zenon_H205 zenon_H2a). % 22.56/22.62 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.62 exact (zenon_H1f zenon_H1e). % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.62 apply (zenon_L25_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.62 apply (zenon_L27_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.62 exact (zenon_H6c zenon_H67). % 22.56/22.62 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.62 apply (zenon_L214_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.62 apply (zenon_L1868_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.56/22.62 apply (zenon_L1868_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.56/22.62 apply (zenon_L2275_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.56/22.62 apply (zenon_L533_); trivial. % 22.56/22.62 apply (zenon_L1846_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.62 apply (zenon_L55_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.62 apply (zenon_L68_); trivial. % 22.56/22.62 apply (zenon_L1853_); trivial. % 22.56/22.62 exact (zenon_H238 zenon_H38). % 22.56/22.62 apply (zenon_L1858_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.62 apply (zenon_L491_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.62 exact (zenon_H1f zenon_H1e). % 22.56/22.62 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.62 apply (zenon_L318_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.62 exact (zenon_H1f zenon_H1e). % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.62 apply (zenon_L25_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.62 apply (zenon_L405_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.62 exact (zenon_H6c zenon_H67). % 22.56/22.62 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.62 apply (zenon_L214_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.62 apply (zenon_L264_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.62 apply (zenon_L24_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.62 apply (zenon_L1864_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.56/22.62 apply (zenon_L68_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.56/22.62 apply (zenon_L436_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.56/22.62 apply (zenon_L278_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.56/22.62 apply (zenon_L456_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.56/22.62 apply (zenon_L348_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.56/22.62 apply (zenon_L363_); trivial. % 22.56/22.62 apply (zenon_L1859_); trivial. % 22.56/22.62 apply (zenon_L63_); trivial. % 22.56/22.62 exact (zenon_H238 zenon_H38). % 22.56/22.62 apply (zenon_L1861_); trivial. % 22.56/22.62 (* end of lemma zenon_L2276_ *) % 22.56/22.62 assert (zenon_L2277_ : ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> False). % 22.56/22.62 do 0 intro. intros zenon_H8f zenon_H14c zenon_H65. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.56/22.62 exact (zenon_H7b zenon_H65). % 22.56/22.62 exact (zenon_H13d zenon_H14c). % 22.56/22.62 (* end of lemma zenon_L2277_ *) % 22.56/22.62 assert (zenon_L2278_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> False). % 22.56/22.62 do 0 intro. intros zenon_H5a zenon_H14c zenon_H65. % 22.56/22.62 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.56/22.62 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.56/22.62 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.56/22.62 apply (zenon_L2277_); trivial. % 22.56/22.62 (* end of lemma zenon_L2278_ *) % 22.56/22.62 assert (zenon_L2279_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (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 (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 22.56/22.62 do 0 intro. intros zenon_H13f zenon_H65 zenon_H77 zenon_Hf0 zenon_H3f zenon_H48 zenon_H117 zenon_H109 zenon_H9d zenon_Hdb zenon_H6f zenon_H14c zenon_Ha0 zenon_Hb6. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.56/22.62 apply (zenon_L30_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.56/22.62 apply (zenon_L118_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.56/22.62 apply (zenon_L255_); trivial. % 22.56/22.62 apply (zenon_L1291_); trivial. % 22.56/22.62 (* end of lemma zenon_L2279_ *) % 22.56/22.62 assert (zenon_L2280_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((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)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.56/22.62 do 0 intro. intros zenon_Hfa zenon_H25 zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Ha9 zenon_H1a2 zenon_H48 zenon_H186 zenon_H139 zenon_H2c zenon_H65 zenon_H9d zenon_H33 zenon_H13a zenon_H38 zenon_H68 zenon_H201 zenon_H73 zenon_H66 zenon_H5c zenon_H77. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.62 apply (zenon_L171_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.56/22.62 apply (zenon_L1880_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.56/22.62 apply (zenon_L138_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.56/22.62 apply (zenon_L255_); trivial. % 22.56/22.62 apply (zenon_L687_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.62 apply (zenon_L22_); trivial. % 22.56/22.62 apply (zenon_L206_); trivial. % 22.56/22.62 (* end of lemma zenon_L2280_ *) % 22.56/22.62 assert (zenon_L2281_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((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)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 22.56/22.62 do 0 intro. intros zenon_Heb zenon_H18d zenon_H5d zenon_H1b7 zenon_H1f1 zenon_H4e zenon_H190 zenon_H1cb zenon_H23c zenon_He4 zenon_H6f zenon_Hdb zenon_H109 zenon_H117 zenon_Hf0 zenon_H13f zenon_Hbc zenon_Hfa zenon_H25 zenon_Hb6 zenon_Ha0 zenon_H14c zenon_Ha9 zenon_H1a2 zenon_H48 zenon_H186 zenon_H139 zenon_H2c zenon_H65 zenon_H9d zenon_H33 zenon_H13a zenon_H38 zenon_H68 zenon_H201 zenon_H73 zenon_H66 zenon_H77. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.62 apply (zenon_L1293_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.62 apply (zenon_L2279_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.62 apply (zenon_L279_); trivial. % 22.56/22.62 apply (zenon_L2280_); trivial. % 22.56/22.62 (* end of lemma zenon_L2281_ *) % 22.56/22.62 assert (zenon_L2282_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (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) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (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 (e2) (e0)) = (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 (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 22.56/22.62 do 0 intro. intros zenon_He4 zenon_H68 zenon_H13a zenon_Ha4 zenon_H6c zenon_H139 zenon_H23c zenon_H1cb zenon_H190 zenon_H4e zenon_H66 zenon_H201 zenon_H13f zenon_H77 zenon_H1f1 zenon_H1b7 zenon_H3c zenon_H5d zenon_H38 zenon_H48 zenon_H18d zenon_H65 zenon_Ha9 zenon_H117 zenon_H109 zenon_H9d zenon_Hdb zenon_H6f zenon_H14c zenon_Ha0 zenon_Hb6. % 22.56/22.62 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.56/22.62 apply (zenon_L1857_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.56/22.62 apply (zenon_L492_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.56/22.62 apply (zenon_L1289_); trivial. % 22.56/22.62 apply (zenon_L1292_); trivial. % 22.56/22.62 (* end of lemma zenon_L2282_ *) % 22.56/22.62 assert (zenon_L2283_ : (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (((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 (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 22.56/22.62 do 0 intro. intros zenon_H77 zenon_H73 zenon_H201 zenon_H68 zenon_H13a zenon_H33 zenon_H9d zenon_H65 zenon_H2c zenon_H139 zenon_H186 zenon_H48 zenon_H1a2 zenon_H14c zenon_Hb6 zenon_H25 zenon_Hfa zenon_Hbc zenon_H13f zenon_Hf0 zenon_H117 zenon_H109 zenon_H6f zenon_He4 zenon_Ha4 zenon_H6c zenon_H23c zenon_H1cb zenon_H190 zenon_H4e zenon_H1f1 zenon_H1b7 zenon_H5d zenon_H18d zenon_Heb zenon_Ha9 zenon_H66 zenon_H38 zenon_Ha0. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.62 exact (zenon_Ha4 zenon_H9f). % 22.56/22.62 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.62 apply (zenon_L2282_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.62 apply (zenon_L2279_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.62 apply (zenon_L279_); trivial. % 22.56/22.62 apply (zenon_L2280_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.62 apply (zenon_L193_); trivial. % 22.56/22.62 apply (zenon_L156_); trivial. % 22.56/22.62 (* end of lemma zenon_L2283_ *) % 22.56/22.62 assert (zenon_L2284_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> False). % 22.56/22.62 do 0 intro. intros zenon_H183 zenon_H68 zenon_H34 zenon_Hac zenon_Ha9 zenon_H106 zenon_H77 zenon_H23d zenon_H1f zenon_H4c zenon_H6c zenon_H155. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.56/22.62 apply (zenon_L291_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.56/22.62 apply (zenon_L371_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.56/22.62 apply (zenon_L367_); trivial. % 22.56/22.62 apply (zenon_L517_); trivial. % 22.56/22.62 (* end of lemma zenon_L2284_ *) % 22.56/22.62 assert (zenon_L2285_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((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)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.56/22.62 do 0 intro. intros zenon_H201 zenon_H66 zenon_H48 zenon_H4e zenon_H82 zenon_H190 zenon_H117 zenon_H65 zenon_H53 zenon_H14c zenon_Ha0 zenon_H121 zenon_H33 zenon_H9f zenon_H155 zenon_H6c zenon_H4c zenon_H1f zenon_H23d zenon_H77 zenon_Ha9 zenon_H34 zenon_H68 zenon_H183 zenon_Hb6 zenon_H129. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.56/22.62 apply (zenon_L94_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.56/22.62 apply (zenon_L2021_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.56/22.62 apply (zenon_L143_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.56/22.62 apply (zenon_L43_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.56/22.62 apply (zenon_L113_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.56/22.62 apply (zenon_L278_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 22.56/22.62 apply (zenon_L245_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 22.56/22.62 apply (zenon_L2284_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 22.56/22.62 apply (zenon_L363_); trivial. % 22.56/22.62 apply (zenon_L189_); trivial. % 22.56/22.62 (* end of lemma zenon_L2285_ *) % 22.56/22.62 assert (zenon_L2286_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((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)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> False). % 22.56/22.62 do 0 intro. intros zenon_H15d zenon_H13a zenon_H177 zenon_H77 zenon_H34 zenon_H68 zenon_H183 zenon_H201 zenon_H48 zenon_H4e zenon_H82 zenon_H190 zenon_H117 zenon_H65 zenon_H14c zenon_H121 zenon_H33 zenon_H6c zenon_H4c zenon_H1f zenon_H23d zenon_H129 zenon_H23c zenon_H3c zenon_He4 zenon_Ha0 zenon_H2a zenon_Ha9 zenon_H66 zenon_Hb6. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.62 exact (zenon_H4c zenon_H47). % 22.56/22.62 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.62 apply (zenon_L65_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.62 apply (zenon_L94_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.56/22.62 apply (zenon_L65_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.56/22.62 apply (zenon_L492_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.56/22.62 apply (zenon_L2285_); trivial. % 22.56/22.62 apply (zenon_L496_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.62 apply (zenon_L53_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.62 apply (zenon_L193_); trivial. % 22.56/22.62 apply (zenon_L115_); trivial. % 22.56/22.62 (* end of lemma zenon_L2286_ *) % 22.56/22.62 assert (zenon_L2287_ : (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (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 (e2) (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)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.56/22.62 do 0 intro. intros zenon_Hb6 zenon_H66 zenon_Ha9 zenon_H2a zenon_Ha0 zenon_He4 zenon_H23c zenon_H129 zenon_H23d zenon_H1f zenon_H4c zenon_H6c zenon_H33 zenon_H121 zenon_H14c zenon_H117 zenon_H190 zenon_H82 zenon_H4e zenon_H201 zenon_H183 zenon_H68 zenon_H177 zenon_H13a zenon_H15d zenon_H65 zenon_H77 zenon_H34 zenon_H48. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.62 exact (zenon_H4c zenon_H47). % 22.56/22.62 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.62 apply (zenon_L2286_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.62 apply (zenon_L30_); trivial. % 22.56/22.62 apply (zenon_L456_); trivial. % 22.56/22.62 (* end of lemma zenon_L2287_ *) % 22.56/22.62 assert (zenon_L2288_ : (((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 (e1) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 22.56/22.62 do 0 intro. intros zenon_H1a2 zenon_Ha0 zenon_H31 zenon_Ha9 zenon_H72 zenon_Hb6 zenon_H105 zenon_H9b zenon_Hbc. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.56/22.62 apply (zenon_L68_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.56/22.62 apply (zenon_L436_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.56/22.62 apply (zenon_L400_); trivial. % 22.56/22.62 apply (zenon_L791_); trivial. % 22.56/22.62 (* end of lemma zenon_L2288_ *) % 22.56/22.62 assert (zenon_L2289_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 22.56/22.62 do 0 intro. intros zenon_H201 zenon_H48 zenon_Hbc zenon_H9b zenon_H72 zenon_H1a2 zenon_H77 zenon_H65 zenon_H1ef zenon_Ha9 zenon_H31 zenon_H68 zenon_H1cf zenon_H14c zenon_Ha0 zenon_Hb6. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.56/22.62 apply (zenon_L239_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.56/22.62 apply (zenon_L59_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.56/22.62 apply (zenon_L2288_); trivial. % 22.56/22.62 apply (zenon_L2274_); trivial. % 22.56/22.62 (* end of lemma zenon_L2289_ *) % 22.56/22.62 assert (zenon_L2290_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.56/22.62 do 0 intro. intros zenon_H1c3 zenon_H9e zenon_Ha9 zenon_H77 zenon_H5c zenon_H94 zenon_H65 zenon_H68 zenon_H167. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 22.56/22.62 apply (zenon_L92_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 22.56/22.62 apply (zenon_L206_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 22.56/22.62 apply (zenon_L38_); trivial. % 22.56/22.62 apply (zenon_L295_); trivial. % 22.56/22.62 (* end of lemma zenon_L2290_ *) % 22.56/22.62 assert (zenon_L2291_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((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)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.56/22.62 do 0 intro. intros zenon_H13a zenon_H47 zenon_H73 zenon_H163 zenon_H4e zenon_H25 zenon_H1ec zenon_H131 zenon_H158 zenon_H156 zenon_H159 zenon_H1cf zenon_Heb zenon_H20f zenon_H13c zenon_H48 zenon_H5d zenon_Hb6 zenon_H18d zenon_Ha0 zenon_Hf5 zenon_H173 zenon_H2a zenon_H13b zenon_H40 zenon_H1d4 zenon_H1c3 zenon_Ha9 zenon_H77 zenon_H94 zenon_H65 zenon_H68 zenon_H167. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.62 apply (zenon_L253_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.62 apply (zenon_L53_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.62 apply (zenon_L276_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.62 apply (zenon_L1833_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.62 exact (zenon_H40 zenon_H3f). % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.62 exact (zenon_H1d4 zenon_H4d). % 22.56/22.62 apply (zenon_L2290_); trivial. % 22.56/22.62 (* end of lemma zenon_L2291_ *) % 22.56/22.62 assert (zenon_L2292_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((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)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 22.56/22.62 do 0 intro. intros zenon_H13a zenon_H33 zenon_H9d zenon_Ha0 zenon_H73 zenon_H163 zenon_H1d4 zenon_H4e zenon_H25 zenon_H1ec zenon_H131 zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_H156 zenon_H159 zenon_H1cf zenon_Ha9 zenon_Hf6. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.62 apply (zenon_L245_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.62 apply (zenon_L53_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.62 apply (zenon_L276_); trivial. % 22.56/22.62 apply (zenon_L92_); trivial. % 22.56/22.62 (* end of lemma zenon_L2292_ *) % 22.56/22.62 assert (zenon_L2293_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((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)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> False). % 22.56/22.62 do 0 intro. intros zenon_H139 zenon_H47 zenon_H68 zenon_H153 zenon_H77 zenon_H13a zenon_H33 zenon_H9d zenon_Ha0 zenon_H73 zenon_H163 zenon_H1d4 zenon_H4e zenon_H25 zenon_H1ec zenon_H131 zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_H156 zenon_H159 zenon_H1cf zenon_Ha9. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.62 apply (zenon_L251_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.62 apply (zenon_L147_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.62 apply (zenon_L94_); trivial. % 22.56/22.62 apply (zenon_L2292_); trivial. % 22.56/22.62 (* end of lemma zenon_L2293_ *) % 22.56/22.62 assert (zenon_L2294_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.56/22.62 do 0 intro. intros zenon_H141 zenon_H48 zenon_H54 zenon_Ha0 zenon_H10d zenon_H13d zenon_H167 zenon_H129. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.56/22.62 apply (zenon_L217_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.56/22.62 apply (zenon_L152_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.56/22.62 exact (zenon_H13d zenon_H14c). % 22.56/22.62 apply (zenon_L298_); trivial. % 22.56/22.62 (* end of lemma zenon_L2294_ *) % 22.56/22.62 assert (zenon_L2295_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((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)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 22.56/22.62 do 0 intro. intros zenon_H13a zenon_H33 zenon_H9d zenon_Ha0 zenon_H73 zenon_H163 zenon_H1d4 zenon_H4e zenon_H25 zenon_H1ec zenon_H131 zenon_H158 zenon_H2a zenon_H173 zenon_H40 zenon_H156 zenon_H159 zenon_Ha9 zenon_H1cf zenon_Hb6 zenon_H155. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.62 apply (zenon_L245_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.62 apply (zenon_L53_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.62 apply (zenon_L276_); trivial. % 22.56/22.62 apply (zenon_L115_); trivial. % 22.56/22.62 (* end of lemma zenon_L2295_ *) % 22.56/22.62 assert (zenon_L2296_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((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))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 22.56/22.62 do 0 intro. intros zenon_H169 zenon_Hfa zenon_He3 zenon_Heb zenon_H40 zenon_H25 zenon_H48 zenon_H15d zenon_H28 zenon_H1c6 zenon_H7d zenon_H13d zenon_H129 zenon_H141 zenon_H82 zenon_H77 zenon_H68 zenon_H2a zenon_H125 zenon_H9d zenon_Hb6 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H94 zenon_H13c zenon_Hf5 zenon_H5d zenon_H1c3 zenon_H167 zenon_H18d zenon_H20f zenon_H13b zenon_H13a zenon_H1d5 zenon_H33 zenon_H139 zenon_H15c. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.56/22.62 apply (zenon_L250_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.62 apply (zenon_L251_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.62 apply (zenon_L147_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.56/22.62 apply (zenon_L252_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.56/22.62 apply (zenon_L171_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.56/22.62 apply (zenon_L2291_); trivial. % 22.56/22.62 apply (zenon_L91_); trivial. % 22.56/22.62 apply (zenon_L2292_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.62 apply (zenon_L65_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.62 apply (zenon_L2293_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.62 apply (zenon_L26_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.56/22.62 apply (zenon_L53_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.56/22.62 exact (zenon_H159 zenon_H10c). % 22.56/22.62 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.56/22.62 apply (zenon_L2294_); trivial. % 22.56/22.62 apply (zenon_L44_); trivial. % 22.56/22.62 apply (zenon_L134_); trivial. % 22.56/22.62 apply (zenon_L2295_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.62 apply (zenon_L25_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.62 exact (zenon_H40 zenon_H3f). % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.62 apply (zenon_L171_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.62 exact (zenon_H1b3 zenon_Hef). % 22.56/22.62 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.62 apply (zenon_L59_); trivial. % 22.56/22.62 apply (zenon_L940_); trivial. % 22.56/22.62 exact (zenon_Hec zenon_H5c). % 22.56/22.62 apply (zenon_L1113_); trivial. % 22.56/22.62 (* end of lemma zenon_L2296_ *) % 22.56/22.62 assert (zenon_L2297_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 22.56/22.62 do 0 intro. intros zenon_H13a zenon_Hb6 zenon_H47 zenon_H1b7 zenon_H167 zenon_H55 zenon_H2d zenon_He3 zenon_He2 zenon_Ha0 zenon_H31 zenon_Ha9 zenon_Hf6. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.62 apply (zenon_L253_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.56/22.62 apply (zenon_L53_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.56/22.62 exact (zenon_He3 zenon_He7). % 22.56/22.62 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.56/22.62 apply (zenon_L702_); trivial. % 22.56/22.62 apply (zenon_L556_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.62 apply (zenon_L68_); trivial. % 22.56/22.62 apply (zenon_L92_); trivial. % 22.56/22.62 (* end of lemma zenon_L2297_ *) % 22.56/22.62 assert (zenon_L2298_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 22.56/22.62 do 0 intro. intros zenon_H139 zenon_H77 zenon_H68 zenon_H13a zenon_Hb6 zenon_H47 zenon_H1b7 zenon_H167 zenon_H55 zenon_H2d zenon_He3 zenon_He2 zenon_Ha0 zenon_H31 zenon_Ha9. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.62 apply (zenon_L251_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.62 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.56/22.62 apply (zenon_L147_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.56/22.62 exact (zenon_He3 zenon_He7). % 22.56/22.62 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.56/22.62 apply (zenon_L702_); trivial. % 22.56/22.62 apply (zenon_L556_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.62 apply (zenon_L264_); trivial. % 22.56/22.62 apply (zenon_L2297_); trivial. % 22.56/22.62 (* end of lemma zenon_L2298_ *) % 22.56/22.62 assert (zenon_L2299_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 22.56/22.62 do 0 intro. intros zenon_H139 zenon_H77 zenon_H3d zenon_H68 zenon_H13a zenon_Hb6 zenon_H47 zenon_H1b7 zenon_H167 zenon_H55 zenon_H2d zenon_He3 zenon_He2 zenon_Ha0 zenon_H31 zenon_Ha9. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.62 apply (zenon_L251_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.62 apply (zenon_L214_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.62 apply (zenon_L264_); trivial. % 22.56/22.62 apply (zenon_L2297_); trivial. % 22.56/22.62 (* end of lemma zenon_L2299_ *) % 22.56/22.62 assert (zenon_L2300_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e3) (e3)) = (e0)) -> ((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (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) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 22.56/22.62 do 0 intro. intros zenon_H82 zenon_He2 zenon_He3 zenon_H55 zenon_H1b7 zenon_H139 zenon_H7d zenon_H16a zenon_H68 zenon_Ha9 zenon_H8b zenon_H16b zenon_H167 zenon_H3d zenon_H1c6 zenon_H13c zenon_H1c3 zenon_H77 zenon_H5d zenon_H18d zenon_Hf5 zenon_H18a zenon_H1f zenon_H1fe zenon_Hf0 zenon_Hfa zenon_H31 zenon_Ha0 zenon_H33 zenon_H13a zenon_H48 zenon_H2d zenon_Hb6 zenon_H9d. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.62 apply (zenon_L2299_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.62 apply (zenon_L1812_); trivial. % 22.56/22.62 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.62 apply (zenon_L217_); trivial. % 22.56/22.62 apply (zenon_L134_); trivial. % 22.56/22.62 (* end of lemma zenon_L2300_ *) % 22.56/22.62 assert (zenon_L2301_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H139 zenon_H77 zenon_H155 zenon_H9d zenon_H33 zenon_H68 zenon_H13a zenon_Hb6 zenon_H47 zenon_H1b7 zenon_H167 zenon_H55 zenon_H2d zenon_He3 zenon_He2 zenon_Ha0 zenon_H31 zenon_Ha9. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.63 apply (zenon_L251_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.63 apply (zenon_L871_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.63 apply (zenon_L264_); trivial. % 22.56/22.63 apply (zenon_L2297_); trivial. % 22.56/22.63 (* end of lemma zenon_L2301_ *) % 22.56/22.63 assert (zenon_L2302_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((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) (e2)) = (op (e3) (e2)))) -> (((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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (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)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H92 zenon_H1ba zenon_H89 zenon_H139 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H31 zenon_H68 zenon_He3 zenon_H55 zenon_H2d zenon_H1b7 zenon_H167 zenon_He2 zenon_H77 zenon_H82 zenon_H33 zenon_H9d zenon_Hfa zenon_H7d zenon_H1c6 zenon_H18d zenon_H1c3 zenon_H5d zenon_Hf5 zenon_H13c zenon_H1fe zenon_H18a zenon_H48 zenon_H1f zenon_Hf0 zenon_H8b zenon_H16a zenon_H266 zenon_H6f zenon_H1f1 zenon_He4 zenon_H15d zenon_H13e zenon_H190 zenon_H13d zenon_H125 zenon_H183 zenon_H163 zenon_H13f zenon_H26a zenon_H100 zenon_H129 zenon_H141 zenon_H23c zenon_H1ef zenon_H73 zenon_H236 zenon_H4e zenon_H13b zenon_H20f zenon_Heb zenon_H156 zenon_H158 zenon_H173 zenon_Hbc zenon_Hcc. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.63 apply (zenon_L2298_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.63 apply (zenon_L2300_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.63 apply (zenon_L239_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.63 apply (zenon_L2301_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.63 apply (zenon_L1835_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.63 apply (zenon_L217_); trivial. % 22.56/22.63 apply (zenon_L134_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.63 apply (zenon_L2298_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.63 apply (zenon_L2299_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.63 apply (zenon_L1806_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.63 apply (zenon_L217_); trivial. % 22.56/22.63 apply (zenon_L134_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.63 apply (zenon_L239_); trivial. % 22.56/22.63 apply (zenon_L1807_); trivial. % 22.56/22.63 (* end of lemma zenon_L2302_ *) % 22.56/22.63 assert (zenon_L2303_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((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 (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (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) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H139 zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H31 zenon_H68 zenon_He3 zenon_H55 zenon_H2d zenon_H1b7 zenon_H167 zenon_He2 zenon_H77 zenon_H82 zenon_H33 zenon_H9d zenon_Hfa zenon_H7d zenon_H1c6 zenon_H18d zenon_H1c3 zenon_H5d zenon_Hf5 zenon_H13c zenon_H1fe zenon_H18a zenon_H48 zenon_H1f zenon_Hf0 zenon_H8b zenon_H16a zenon_He4 zenon_H183 zenon_H163 zenon_H13f zenon_H26a zenon_H1bf zenon_H1f1 zenon_H100 zenon_H92 zenon_H190 zenon_H13e zenon_H13d zenon_H129 zenon_H141 zenon_H89 zenon_H23c zenon_H15d. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.63 apply (zenon_L2298_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.63 apply (zenon_L2300_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.63 apply (zenon_L239_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.63 apply (zenon_L2301_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.63 apply (zenon_L1816_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.63 apply (zenon_L217_); trivial. % 22.56/22.63 apply (zenon_L134_); trivial. % 22.56/22.63 apply (zenon_L1389_); trivial. % 22.56/22.63 (* end of lemma zenon_L2303_ *) % 22.56/22.63 assert (zenon_L2304_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H1fe zenon_H18a zenon_H9d zenon_H125 zenon_H236 zenon_H48 zenon_H1f zenon_Hb6 zenon_H13c zenon_Ha9 zenon_H73 zenon_H68 zenon_H167 zenon_H18d zenon_H77 zenon_H5d zenon_H1c3 zenon_Ha0 zenon_H13a zenon_H3a. % 22.56/22.63 apply (zenon_L1826_); trivial. % 22.56/22.63 (* end of lemma zenon_L2304_ *) % 22.56/22.63 assert (zenon_L2305_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((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) (e2)))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H5a zenon_H141 zenon_H167 zenon_H129 zenon_H13d zenon_H48 zenon_H68 zenon_H77 zenon_H16a zenon_H13e zenon_H190. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.56/22.63 apply (zenon_L1814_); trivial. % 22.56/22.63 (* end of lemma zenon_L2305_ *) % 22.56/22.63 assert (zenon_L2306_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> False). % 22.56/22.63 do 0 intro. intros zenon_H61 zenon_H167 zenon_H9d. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.56/22.63 apply (zenon_L1818_); trivial. % 22.56/22.63 (* end of lemma zenon_L2306_ *) % 22.56/22.63 assert (zenon_L2307_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.56/22.63 do 0 intro. intros zenon_H1c3 zenon_H38 zenon_H77 zenon_H5c zenon_H94 zenon_H65 zenon_H68 zenon_H167. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1c4 ]. % 22.56/22.63 apply (zenon_L165_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1c5 ]. % 22.56/22.63 apply (zenon_L206_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H93 | zenon_intro zenon_H17c ]. % 22.56/22.63 apply (zenon_L38_); trivial. % 22.56/22.63 apply (zenon_L295_); trivial. % 22.56/22.63 (* end of lemma zenon_L2307_ *) % 22.56/22.63 assert (zenon_L2308_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.56/22.63 do 0 intro. intros zenon_H18d zenon_Hb6 zenon_H31 zenon_Ha0 zenon_H6e zenon_H9d zenon_H33 zenon_H13a zenon_H65 zenon_H94 zenon_H68 zenon_H77 zenon_H10c zenon_Ha9 zenon_H9e zenon_H1c3 zenon_H48 zenon_H167. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.56/22.63 apply (zenon_L871_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.56/22.63 apply (zenon_L2290_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.56/22.63 apply (zenon_L296_); trivial. % 22.56/22.63 apply (zenon_L1803_); trivial. % 22.56/22.63 (* end of lemma zenon_L2308_ *) % 22.56/22.63 assert (zenon_L2309_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e1)) = (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)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.56/22.63 do 0 intro. intros zenon_He2 zenon_H205 zenon_He3 zenon_H7d zenon_H9d zenon_Ha0 zenon_H18d zenon_Hb6 zenon_H31 zenon_H6e zenon_H33 zenon_H13a zenon_H65 zenon_H94 zenon_H68 zenon_H77 zenon_Ha9 zenon_H9e zenon_H1c3 zenon_H48 zenon_H1c6 zenon_H167 zenon_H1b7. % 22.56/22.63 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.56/22.63 exact (zenon_H205 zenon_H2a). % 22.56/22.63 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.56/22.63 exact (zenon_He3 zenon_He7). % 22.56/22.63 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.56/22.63 apply (zenon_L110_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.56/22.63 apply (zenon_L2308_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.56/22.63 apply (zenon_L152_); trivial. % 22.56/22.63 apply (zenon_L44_); trivial. % 22.56/22.63 apply (zenon_L556_); trivial. % 22.56/22.63 (* end of lemma zenon_L2309_ *) % 22.56/22.63 assert (zenon_L2310_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H240 zenon_H139 zenon_He3 zenon_H1c6 zenon_H7d zenon_H13a zenon_Hb6 zenon_H9d zenon_H33 zenon_H1c3 zenon_H167 zenon_H68 zenon_H65 zenon_H94 zenon_H77 zenon_H48 zenon_H18d zenon_Ha9 zenon_H1b7 zenon_He2 zenon_H1f zenon_H205 zenon_Ha0 zenon_H9e zenon_H236. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.63 apply (zenon_L1873_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.63 exact (zenon_H1f zenon_H1e). % 22.56/22.63 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.63 exact (zenon_H205 zenon_H2a). % 22.56/22.63 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.63 exact (zenon_H6c zenon_H67). % 22.56/22.63 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.63 apply (zenon_L2309_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.63 apply (zenon_L264_); trivial. % 22.56/22.63 apply (zenon_L92_); trivial. % 22.56/22.63 apply (zenon_L156_); trivial. % 22.56/22.63 (* end of lemma zenon_L2310_ *) % 22.56/22.63 assert (zenon_L2311_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.56/22.63 do 0 intro. intros zenon_H26a zenon_H236 zenon_H205 zenon_H1f zenon_He2 zenon_H1b7 zenon_H18d zenon_H48 zenon_H94 zenon_H65 zenon_H33 zenon_H9d zenon_H13a zenon_H7d zenon_H1c6 zenon_He3 zenon_H139 zenon_H240 zenon_H68 zenon_H77 zenon_Ha9 zenon_H38 zenon_H1c3 zenon_H128 zenon_Hb6 zenon_Ha0 zenon_H167. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H9e | zenon_intro zenon_H26b ]. % 22.56/22.63 apply (zenon_L2310_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H26c ]. % 22.56/22.63 apply (zenon_L1822_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc3 ]. % 22.56/22.63 apply (zenon_L182_); trivial. % 22.56/22.63 apply (zenon_L505_); trivial. % 22.56/22.63 (* end of lemma zenon_L2311_ *) % 22.56/22.63 assert (zenon_L2312_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H204 zenon_H23b zenon_H1d5 zenon_H23d zenon_H15d zenon_H1f zenon_H68 zenon_H66 zenon_H240 zenon_H139 zenon_He3 zenon_H1c6 zenon_H7d zenon_H13a zenon_Hb6 zenon_H9d zenon_H33 zenon_H18d zenon_Ha9 zenon_H1b7 zenon_He2 zenon_Ha0 zenon_H236 zenon_H26a zenon_H77 zenon_H94 zenon_H65 zenon_H167 zenon_H1c3 zenon_H48. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.63 exact (zenon_H1f zenon_H1e). % 22.56/22.63 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.63 exact (zenon_H205 zenon_H2a). % 22.56/22.63 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.63 apply (zenon_L264_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.56/22.63 apply (zenon_L246_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.56/22.63 apply (zenon_L2307_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.56/22.63 apply (zenon_L2311_); trivial. % 22.56/22.63 apply (zenon_L1803_); trivial. % 22.56/22.63 apply (zenon_L1886_); trivial. % 22.56/22.63 (* end of lemma zenon_L2312_ *) % 22.56/22.63 assert (zenon_L2313_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H87 zenon_H13b zenon_H167 zenon_H20f zenon_H68 zenon_He3 zenon_H48 zenon_H77 zenon_Heb zenon_H156 zenon_H158. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.56/22.63 apply (zenon_L1829_); trivial. % 22.56/22.63 (* end of lemma zenon_L2313_ *) % 22.56/22.63 assert (zenon_L2314_ : (((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 (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H27e zenon_H129 zenon_H167 zenon_H53 zenon_H189 zenon_H94 zenon_H65 zenon_H9e zenon_H196. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H115 | zenon_intro zenon_H27f ]. % 22.56/22.63 apply (zenon_L298_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H128 | zenon_intro zenon_H280 ]. % 22.56/22.63 apply (zenon_L139_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H93 | zenon_intro zenon_Hb9 ]. % 22.56/22.63 apply (zenon_L38_); trivial. % 22.56/22.63 apply (zenon_L154_); trivial. % 22.56/22.63 (* end of lemma zenon_L2314_ *) % 22.56/22.63 assert (zenon_L2315_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((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 (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 22.56/22.63 do 0 intro. intros zenon_He4 zenon_H48 zenon_H2a zenon_H40 zenon_H196 zenon_H9e zenon_H65 zenon_H94 zenon_H189 zenon_H167 zenon_H129 zenon_H27e zenon_H7d zenon_H7e. % 22.56/22.63 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.56/22.63 apply (zenon_L65_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.56/22.63 exact (zenon_H40 zenon_H3f). % 22.56/22.63 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.56/22.63 apply (zenon_L2314_); trivial. % 22.56/22.63 apply (zenon_L31_); trivial. % 22.56/22.63 (* end of lemma zenon_L2315_ *) % 22.56/22.63 assert (zenon_L2316_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((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)) = (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) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((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 (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 22.56/22.63 do 0 intro. intros zenon_H13a zenon_H33 zenon_H9d zenon_Ha0 zenon_H73 zenon_H163 zenon_H1d4 zenon_H4e zenon_H25 zenon_H1ec zenon_H131 zenon_H158 zenon_H173 zenon_H156 zenon_H159 zenon_Ha9 zenon_H1cf zenon_He4 zenon_H48 zenon_H2a zenon_H40 zenon_H196 zenon_H65 zenon_H94 zenon_H189 zenon_H167 zenon_H129 zenon_H27e zenon_H7d zenon_H7e. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.63 apply (zenon_L245_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.63 apply (zenon_L53_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.63 apply (zenon_L276_); trivial. % 22.56/22.63 apply (zenon_L2315_); trivial. % 22.56/22.63 (* end of lemma zenon_L2316_ *) % 22.56/22.63 assert (zenon_L2317_ : (((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 (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H27e zenon_H129 zenon_H167 zenon_H53 zenon_H189 zenon_H94 zenon_H65 zenon_Ha5 zenon_H195. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H115 | zenon_intro zenon_H27f ]. % 22.56/22.63 apply (zenon_L298_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H128 | zenon_intro zenon_H280 ]. % 22.56/22.63 apply (zenon_L139_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H93 | zenon_intro zenon_Hb9 ]. % 22.56/22.63 apply (zenon_L38_); trivial. % 22.56/22.63 apply (zenon_L172_); trivial. % 22.56/22.63 (* end of lemma zenon_L2317_ *) % 22.56/22.63 assert (zenon_L2318_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H25b zenon_H20f zenon_Hec zenon_H10c zenon_H167 zenon_Hb9 zenon_H195. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H136 | zenon_intro zenon_H25c ]. % 22.56/22.63 apply (zenon_L421_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H5c | zenon_intro zenon_H25d ]. % 22.56/22.63 exact (zenon_Hec zenon_H5c). % 22.56/22.63 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Ha5 ]. % 22.56/22.63 apply (zenon_L294_); trivial. % 22.56/22.63 apply (zenon_L172_); trivial. % 22.56/22.63 (* end of lemma zenon_L2318_ *) % 22.56/22.63 assert (zenon_L2319_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (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 (e3) (e3)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H13c zenon_Ha0 zenon_H25 zenon_H18a zenon_H9d zenon_H25b zenon_H20f zenon_Hec zenon_H196 zenon_H26a zenon_Hb6 zenon_H4d zenon_H27e zenon_H129 zenon_H167 zenon_H53 zenon_H189 zenon_H94 zenon_H65 zenon_H195. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.56/22.63 apply (zenon_L116_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H9e | zenon_intro zenon_H26b ]. % 22.56/22.63 apply (zenon_L2314_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H26c ]. % 22.56/22.63 apply (zenon_L2317_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc3 ]. % 22.56/22.63 apply (zenon_L2318_); trivial. % 22.56/22.63 apply (zenon_L747_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.56/22.63 apply (zenon_L124_); trivial. % 22.56/22.63 apply (zenon_L2317_); trivial. % 22.56/22.63 (* end of lemma zenon_L2319_ *) % 22.56/22.63 assert (zenon_L2320_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (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))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H15c zenon_H173 zenon_H158 zenon_H1fe zenon_H167 zenon_H18a zenon_H65 zenon_H68 zenon_H48 zenon_H1f zenon_H40 zenon_He4 zenon_H1b3 zenon_H55 zenon_H77 zenon_H1a8 zenon_Ha0 zenon_H25 zenon_H26a zenon_H9d zenon_H20f zenon_H25b zenon_H195 zenon_H129 zenon_H189 zenon_H94 zenon_H196 zenon_H27e zenon_Hb6 zenon_H13c zenon_H2a zenon_Heb. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.63 apply (zenon_L1802_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.63 exact (zenon_H40 zenon_H3f). % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.56/22.63 apply (zenon_L65_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.56/22.63 exact (zenon_H40 zenon_H3f). % 22.56/22.63 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.56/22.63 apply (zenon_L2319_); trivial. % 22.56/22.63 apply (zenon_L288_); trivial. % 22.56/22.63 exact (zenon_Hec zenon_H5c). % 22.56/22.63 apply (zenon_L304_); trivial. % 22.56/22.63 (* end of lemma zenon_L2320_ *) % 22.56/22.63 assert (zenon_L2321_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (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) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H169 zenon_H195 zenon_H25b zenon_H26a zenon_H1a8 zenon_H55 zenon_Heb zenon_H40 zenon_H25 zenon_H48 zenon_H15d zenon_H139 zenon_H33 zenon_H9d zenon_H1fe zenon_H18a zenon_H1f zenon_H27e zenon_H196 zenon_H189 zenon_H129 zenon_H7d zenon_He4 zenon_H82 zenon_Hb6 zenon_Ha0 zenon_H2a zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H94 zenon_H65 zenon_H13c zenon_Hf5 zenon_H5d zenon_H1c3 zenon_H68 zenon_H77 zenon_H167 zenon_H18d zenon_H20f zenon_H13b zenon_H13a zenon_H15c. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.56/22.63 apply (zenon_L250_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.63 apply (zenon_L2291_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.63 apply (zenon_L65_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.63 apply (zenon_L2293_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.63 apply (zenon_L1802_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.63 apply (zenon_L30_); trivial. % 22.56/22.63 apply (zenon_L2316_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.63 apply (zenon_L251_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.63 apply (zenon_L147_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.63 apply (zenon_L502_); trivial. % 22.56/22.63 apply (zenon_L2292_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.63 apply (zenon_L25_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.63 apply (zenon_L30_); trivial. % 22.56/22.63 apply (zenon_L2316_); trivial. % 22.56/22.63 apply (zenon_L2320_); trivial. % 22.56/22.63 (* end of lemma zenon_L2321_ *) % 22.56/22.63 assert (zenon_L2322_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> False). % 22.56/22.63 do 0 intro. intros zenon_H5a zenon_H190 zenon_H13e zenon_H16a zenon_H77 zenon_H68 zenon_H48 zenon_H129 zenon_H167 zenon_H141 zenon_H65. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.56/22.63 exact (zenon_H7b zenon_H65). % 22.56/22.63 apply (zenon_L1814_); trivial. % 22.56/22.63 (* end of lemma zenon_L2322_ *) % 22.56/22.63 assert (zenon_L2323_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (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) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((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) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((op (e3) (e3)) = (e0)) -> False). % 22.56/22.63 do 0 intro. intros zenon_H1c0 zenon_H195 zenon_H25b zenon_H26a zenon_H1a8 zenon_H55 zenon_Heb zenon_H48 zenon_H15d zenon_H139 zenon_H33 zenon_H1fe zenon_H18a zenon_H1f zenon_H27e zenon_H196 zenon_H189 zenon_H129 zenon_H7d zenon_He4 zenon_H82 zenon_Hb6 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H94 zenon_H65 zenon_H13c zenon_Hf5 zenon_H5d zenon_H1c3 zenon_H68 zenon_H77 zenon_H18d zenon_H20f zenon_H13b zenon_H13a zenon_H125 zenon_H236 zenon_H141 zenon_H16a zenon_H13e zenon_H190 zenon_He2 zenon_H1b7 zenon_H1c6 zenon_He3 zenon_H23d zenon_H1d5 zenon_H2c zenon_Hbc zenon_Hcc zenon_H167. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 22.56/22.63 exact (zenon_H162 zenon_H167). % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.56/22.63 apply (zenon_L2_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.56/22.63 apply (zenon_L2321_); trivial. % 22.56/22.63 apply (zenon_L2321_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.56/22.63 apply (zenon_L28_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.56/22.63 apply (zenon_L1819_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.56/22.63 apply (zenon_L2304_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.56/22.63 apply (zenon_L11_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.56/22.63 apply (zenon_L2322_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.56/22.63 apply (zenon_L2306_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.56/22.63 apply (zenon_L2312_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.56/22.63 apply (zenon_L2313_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.56/22.63 apply (zenon_L37_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.56/22.63 apply (zenon_L39_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.56/22.63 apply (zenon_L2310_); trivial. % 22.56/22.63 apply (zenon_L1876_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.56/22.63 apply (zenon_L221_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.56/22.63 apply (zenon_L201_); trivial. % 22.56/22.63 apply (zenon_L51_); trivial. % 22.56/22.63 (* end of lemma zenon_L2323_ *) % 22.56/22.63 assert (zenon_L2324_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((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))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (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)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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 (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e3)) = (e0)) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H28f zenon_Hfa zenon_Heb zenon_H48 zenon_H15d zenon_H1c6 zenon_H7d zenon_H129 zenon_H141 zenon_H82 zenon_H77 zenon_H68 zenon_H125 zenon_Hb6 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H94 zenon_H13c zenon_Hf5 zenon_H5d zenon_H1c3 zenon_H18d zenon_H20f zenon_H13b zenon_H13a zenon_H1d5 zenon_H33 zenon_H139 zenon_Hcc zenon_Hbc zenon_H236 zenon_H1ef zenon_H23c zenon_H100 zenon_H26a zenon_H13f zenon_H183 zenon_H190 zenon_H13e zenon_He4 zenon_H1f1 zenon_H6f zenon_H266 zenon_H16a zenon_Hf0 zenon_H1f zenon_H18a zenon_H1fe zenon_He2 zenon_H1b7 zenon_H55 zenon_H23d zenon_H2c zenon_H189 zenon_H196 zenon_H27e zenon_H1a8 zenon_H25b zenon_H195 zenon_H1c0 zenon_H1cb zenon_H140 zenon_H167 zenon_H1ca. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_He3 | zenon_intro zenon_H3c ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H13d | zenon_intro zenon_H65 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 22.56/22.63 exact (zenon_H162 zenon_H167). % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.56/22.63 apply (zenon_L2_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.56/22.63 apply (zenon_L2296_); trivial. % 22.56/22.63 apply (zenon_L2296_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.56/22.63 apply (zenon_L2302_); trivial. % 22.56/22.63 apply (zenon_L2302_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.56/22.63 apply (zenon_L2303_); trivial. % 22.56/22.63 apply (zenon_L2303_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.56/22.63 apply (zenon_L1819_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.56/22.63 apply (zenon_L2304_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.56/22.63 apply (zenon_L11_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.56/22.63 apply (zenon_L2305_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.56/22.63 apply (zenon_L2306_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.56/22.63 apply (zenon_L2312_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.56/22.63 apply (zenon_L2313_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.56/22.63 apply (zenon_L37_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.56/22.63 apply (zenon_L1831_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.56/22.63 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.63 apply (zenon_L1873_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.63 exact (zenon_H1f zenon_H1e). % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.56/22.63 exact (zenon_H6c zenon_H67). % 22.56/22.63 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.56/22.63 apply (zenon_L171_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.56/22.63 apply (zenon_L2323_); trivial. % 22.56/22.63 apply (zenon_L91_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.56/22.63 exact (zenon_H205 zenon_H2a). % 22.56/22.63 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.56/22.63 exact (zenon_He3 zenon_He7). % 22.56/22.63 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.56/22.63 apply (zenon_L702_); trivial. % 22.56/22.63 apply (zenon_L556_); trivial. % 22.56/22.63 apply (zenon_L416_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.63 exact (zenon_H1f zenon_H1e). % 22.56/22.63 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.63 exact (zenon_H1f zenon_H1e). % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.56/22.63 exact (zenon_H237 zenon_H31). % 22.56/22.63 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.56/22.63 apply (zenon_L274_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.56/22.63 exact (zenon_H13d zenon_H14c). % 22.56/22.63 apply (zenon_L266_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.63 exact (zenon_H4c zenon_H47). % 22.56/22.63 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.63 apply (zenon_L1833_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.63 apply (zenon_L217_); trivial. % 22.56/22.63 apply (zenon_L134_); trivial. % 22.56/22.63 apply (zenon_L416_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.63 exact (zenon_H237 zenon_H31). % 22.56/22.63 apply (zenon_L156_); trivial. % 22.56/22.63 apply (zenon_L611_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.56/22.63 apply (zenon_L221_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.56/22.63 apply (zenon_L201_); trivial. % 22.56/22.63 apply (zenon_L51_); trivial. % 22.56/22.63 apply (zenon_L2323_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H13d | zenon_intro zenon_H65 ]. % 22.56/22.63 apply (zenon_L1836_); trivial. % 22.56/22.63 apply (zenon_L1802_); trivial. % 22.56/22.63 (* end of lemma zenon_L2324_ *) % 22.56/22.63 assert (zenon_L2325_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((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 (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((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)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (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 (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.56/22.63 do 0 intro. intros zenon_H1bb zenon_H1ca zenon_H140 zenon_H1c0 zenon_H195 zenon_H25b zenon_H1a8 zenon_H27e zenon_H196 zenon_H189 zenon_H2c zenon_H23d zenon_H55 zenon_H1b7 zenon_He2 zenon_H1fe zenon_H18a zenon_H1f zenon_Hf0 zenon_H16a zenon_H266 zenon_H6f zenon_H1f1 zenon_He4 zenon_H13e zenon_H190 zenon_H183 zenon_H13f zenon_H26a zenon_H100 zenon_H23c zenon_H1ef zenon_H236 zenon_Hbc zenon_Hcc zenon_H139 zenon_H33 zenon_H1d5 zenon_H13a zenon_H13b zenon_H20f zenon_H18d zenon_H1c3 zenon_H5d zenon_Hf5 zenon_H13c zenon_H94 zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_Hb6 zenon_H125 zenon_H68 zenon_H77 zenon_H82 zenon_H141 zenon_H7d zenon_H1c6 zenon_H15d zenon_H48 zenon_Heb zenon_Hfa zenon_H28f zenon_H129 zenon_H128 zenon_H1cb zenon_H160 zenon_H9b zenon_H1b4. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 22.56/22.63 apply (zenon_L2324_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 22.56/22.63 apply (zenon_L85_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 22.56/22.63 apply (zenon_L236_); trivial. % 22.56/22.63 apply (zenon_L1202_); trivial. % 22.56/22.63 (* end of lemma zenon_L2325_ *) % 22.56/22.63 assert (zenon_L2326_ : ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((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 (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((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 (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((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)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (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 (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.56/22.63 do 0 intro. intros zenon_Hf7 zenon_H186 zenon_H4d zenon_H31 zenon_H1a2 zenon_H1bb zenon_H1ca zenon_H140 zenon_H1c0 zenon_H195 zenon_H25b zenon_H1a8 zenon_H27e zenon_H196 zenon_H189 zenon_H2c zenon_H23d zenon_H55 zenon_H1b7 zenon_He2 zenon_H1fe zenon_H18a zenon_H1f zenon_Hf0 zenon_H16a zenon_H266 zenon_H6f zenon_H1f1 zenon_He4 zenon_H13e zenon_H190 zenon_H183 zenon_H13f zenon_H26a zenon_H100 zenon_H23c zenon_H1ef zenon_H236 zenon_Hbc zenon_Hcc zenon_H139 zenon_H33 zenon_H1d5 zenon_H13a zenon_H13b zenon_H20f zenon_H18d zenon_H1c3 zenon_H5d zenon_Hf5 zenon_H13c zenon_H94 zenon_Ha9 zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_Ha0 zenon_Hb6 zenon_H125 zenon_H68 zenon_H77 zenon_H82 zenon_H141 zenon_H7d zenon_H1c6 zenon_H15d zenon_H48 zenon_Heb zenon_Hfa zenon_H28f zenon_H129 zenon_H128 zenon_H1cb zenon_H9b zenon_H1b4. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.56/22.63 apply (zenon_L264_); trivial. % 22.56/22.63 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.56/22.64 apply (zenon_L438_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.56/22.64 apply (zenon_L1040_); trivial. % 22.56/22.64 apply (zenon_L2325_); trivial. % 22.56/22.64 (* end of lemma zenon_L2326_ *) % 22.56/22.64 assert (zenon_L2327_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (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) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 22.56/22.64 do 0 intro. intros zenon_He4 zenon_H77 zenon_H6e zenon_H23c zenon_H48 zenon_H13f zenon_H3c zenon_H100 zenon_H1f1 zenon_H196 zenon_H9e zenon_H65 zenon_Ha9 zenon_H117 zenon_H109 zenon_H9d zenon_Hdd zenon_H14c zenon_Ha0 zenon_Hb6. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.56/22.64 apply (zenon_L214_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.56/22.64 apply (zenon_L492_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.56/22.64 apply (zenon_L111_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.56/22.64 apply (zenon_L69_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.56/22.64 apply (zenon_L284_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.56/22.64 apply (zenon_L2116_); trivial. % 22.56/22.64 apply (zenon_L2261_); trivial. % 22.56/22.64 (* end of lemma zenon_L2327_ *) % 22.56/22.64 assert (zenon_L2328_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((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)) = (e1)) -> False). % 22.56/22.64 do 0 intro. intros zenon_He4 zenon_H6e zenon_H234 zenon_H48 zenon_H13f zenon_H77 zenon_H1f1 zenon_H196 zenon_H9e zenon_Hb6 zenon_Hdd zenon_Ha0 zenon_H65 zenon_Ha9 zenon_H117 zenon_H195 zenon_H5c. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.56/22.64 apply (zenon_L214_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.56/22.64 apply (zenon_L484_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.56/22.64 apply (zenon_L111_); trivial. % 22.56/22.64 apply (zenon_L2117_); trivial. % 22.56/22.64 (* end of lemma zenon_L2328_ *) % 22.56/22.64 assert (zenon_L2329_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (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)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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 (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H236 zenon_Ha0 zenon_H1f zenon_H68 zenon_H173 zenon_H201 zenon_H1cf zenon_H65 zenon_H1ef zenon_H14c zenon_Ha9 zenon_Hb6 zenon_H9b zenon_Hbc zenon_H1a2 zenon_H77 zenon_H48 zenon_H28f zenon_Hfa zenon_Heb zenon_H15d zenon_H1c6 zenon_H7d zenon_H129 zenon_H141 zenon_H82 zenon_H125 zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H156 zenon_H158 zenon_H94 zenon_H13c zenon_Hf5 zenon_H5d zenon_H1c3 zenon_H18d zenon_H20f zenon_H13b zenon_H13a zenon_H1d5 zenon_H33 zenon_H139 zenon_Hcc zenon_H23c zenon_H100 zenon_H26a zenon_H13f zenon_H183 zenon_H190 zenon_H13e zenon_He4 zenon_H1f1 zenon_H6f zenon_H266 zenon_H16a zenon_Hf0 zenon_H18a zenon_H1fe zenon_He2 zenon_H1b7 zenon_H55 zenon_H23d zenon_H2c zenon_H189 zenon_H27e zenon_H1a8 zenon_H25b zenon_H195 zenon_H1c0 zenon_H1cb zenon_H140 zenon_H1ca zenon_H1b4 zenon_H1bb zenon_H186 zenon_H109 zenon_H196 zenon_H117 zenon_H179 zenon_He3 zenon_H234. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.64 apply (zenon_L1873_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.64 exact (zenon_H205 zenon_H2a). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.64 exact (zenon_H6c zenon_H67). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.64 apply (zenon_L171_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.64 apply (zenon_L226_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.64 apply (zenon_L2289_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.56/22.64 apply (zenon_L30_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.56/22.64 apply (zenon_L2247_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.56/22.64 apply (zenon_L255_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.56/22.64 apply (zenon_L239_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.56/22.64 apply (zenon_L2326_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.56/22.64 apply (zenon_L255_); trivial. % 22.56/22.64 apply (zenon_L2274_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.64 apply (zenon_L264_); trivial. % 22.56/22.64 apply (zenon_L92_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.64 apply (zenon_L405_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.64 exact (zenon_H6c zenon_H67). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.56/22.64 apply (zenon_L297_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.56/22.64 exact (zenon_He3 zenon_He7). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.56/22.64 exact (zenon_H205 zenon_H2a). % 22.56/22.64 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.56/22.64 exact (zenon_He3 zenon_He7). % 22.56/22.64 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.64 apply (zenon_L2327_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.64 apply (zenon_L2262_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.64 apply (zenon_L117_); trivial. % 22.56/22.64 apply (zenon_L2328_); trivial. % 22.56/22.64 apply (zenon_L802_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.56/22.64 exact (zenon_H205 zenon_H2a). % 22.56/22.64 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.56/22.64 exact (zenon_He3 zenon_He7). % 22.56/22.64 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.64 apply (zenon_L2327_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.64 apply (zenon_L2262_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.64 apply (zenon_L2263_); trivial. % 22.56/22.64 apply (zenon_L157_); trivial. % 22.56/22.64 apply (zenon_L802_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.64 apply (zenon_L264_); trivial. % 22.56/22.64 apply (zenon_L92_); trivial. % 22.56/22.64 apply (zenon_L156_); trivial. % 22.56/22.64 apply (zenon_L1876_); trivial. % 22.56/22.64 (* end of lemma zenon_L2329_ *) % 22.56/22.64 assert (zenon_L2330_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 22.56/22.64 do 0 intro. intros zenon_H13b zenon_H34 zenon_H179 zenon_He3 zenon_H1cd zenon_Hb1 zenon_H14c zenon_H153 zenon_Hb6 zenon_H1a2 zenon_Ha0 zenon_Ha5. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.56/22.64 apply (zenon_L297_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.56/22.64 exact (zenon_He3 zenon_He7). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.56/22.64 apply (zenon_L362_); trivial. % 22.56/22.64 apply (zenon_L90_); trivial. % 22.56/22.64 (* end of lemma zenon_L2330_ *) % 22.56/22.64 assert (zenon_L2331_ : (((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)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H139 zenon_H2c zenon_H65 zenon_H68 zenon_H2a zenon_Ha5 zenon_Ha0 zenon_H1a2 zenon_Ha9 zenon_H14c zenon_Hac zenon_H1cd zenon_He3 zenon_H179 zenon_H34 zenon_H13b zenon_H155 zenon_H77. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.64 apply (zenon_L180_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.64 apply (zenon_L147_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.56/22.64 apply (zenon_L297_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.56/22.64 exact (zenon_He3 zenon_He7). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.56/22.64 apply (zenon_L1552_); trivial. % 22.56/22.64 apply (zenon_L90_); trivial. % 22.56/22.64 apply (zenon_L98_); trivial. % 22.56/22.64 (* end of lemma zenon_L2331_ *) % 22.56/22.64 assert (zenon_L2332_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((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 (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H15d zenon_H7d zenon_H5d zenon_Hb2 zenon_H48 zenon_Hb6 zenon_Hb1 zenon_H139 zenon_H2c zenon_H65 zenon_H68 zenon_H2a zenon_Ha5 zenon_Ha0 zenon_H1a2 zenon_Ha9 zenon_H14c zenon_Hac zenon_H1cd zenon_He3 zenon_H179 zenon_H34 zenon_H13b zenon_H77. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.64 apply (zenon_L356_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.64 apply (zenon_L65_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.64 apply (zenon_L2330_); trivial. % 22.56/22.64 apply (zenon_L2331_); trivial. % 22.56/22.64 (* end of lemma zenon_L2332_ *) % 22.56/22.64 assert (zenon_L2333_ : (((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)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H65 zenon_Hdd zenon_H14c zenon_Ha0 zenon_Ha5 zenon_H195. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.56/22.64 apply (zenon_L43_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.56/22.64 apply (zenon_L152_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.56/22.64 apply (zenon_L278_); trivial. % 22.56/22.64 apply (zenon_L172_); trivial. % 22.56/22.64 (* end of lemma zenon_L2333_ *) % 22.56/22.64 assert (zenon_L2334_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.56/22.64 do 0 intro. intros zenon_He2 zenon_H1d8 zenon_H31 zenon_He3 zenon_H195 zenon_Ha5 zenon_H14c zenon_H65 zenon_Ha9 zenon_H117 zenon_Ha0 zenon_Hac. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.56/22.64 apply (zenon_L254_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.56/22.64 exact (zenon_He3 zenon_He7). % 22.56/22.64 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.56/22.64 apply (zenon_L2333_); trivial. % 22.56/22.64 apply (zenon_L107_); trivial. % 22.56/22.64 (* end of lemma zenon_L2334_ *) % 22.56/22.64 assert (zenon_L2335_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.56/22.64 do 0 intro. intros zenon_H13b zenon_H34 zenon_H179 zenon_He3 zenon_H1cd zenon_Hac zenon_Ha0 zenon_H14c zenon_H66 zenon_Ha9 zenon_H1a2 zenon_Hf5 zenon_H38. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.56/22.64 apply (zenon_L297_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.56/22.64 exact (zenon_He3 zenon_He7). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.56/22.64 apply (zenon_L1552_); trivial. % 22.56/22.64 apply (zenon_L663_); trivial. % 22.56/22.64 (* end of lemma zenon_L2335_ *) % 22.56/22.64 assert (zenon_L2336_ : (((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)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H139 zenon_H2c zenon_H65 zenon_H77 zenon_H3d zenon_Hf5 zenon_H1a2 zenon_Ha9 zenon_H14c zenon_Ha0 zenon_Hac zenon_H1cd zenon_He3 zenon_H179 zenon_H34 zenon_H13b zenon_H38 zenon_H68. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.64 apply (zenon_L180_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.64 apply (zenon_L214_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.64 apply (zenon_L2335_); trivial. % 22.56/22.64 apply (zenon_L165_); trivial. % 22.56/22.64 (* end of lemma zenon_L2336_ *) % 22.56/22.64 assert (zenon_L2337_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 22.56/22.64 do 0 intro. intros zenon_H13b zenon_H186 zenon_H158 zenon_H40 zenon_H156 zenon_H159 zenon_H1d4 zenon_H4e zenon_H1ec zenon_He3 zenon_H1cd zenon_Hac zenon_H14c zenon_H66 zenon_Ha9 zenon_H1a2 zenon_Ha0 zenon_Ha5. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.56/22.64 apply (zenon_L309_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.56/22.64 exact (zenon_He3 zenon_He7). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.56/22.64 apply (zenon_L1552_); trivial. % 22.56/22.64 apply (zenon_L90_); trivial. % 22.56/22.64 (* end of lemma zenon_L2337_ *) % 22.56/22.64 assert (zenon_L2338_ : (((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)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H139 zenon_H2c zenon_H65 zenon_H173 zenon_Ha5 zenon_Ha0 zenon_H1a2 zenon_Ha9 zenon_H14c zenon_Hac zenon_H1cd zenon_He3 zenon_H1ec zenon_H4e zenon_H1d4 zenon_H159 zenon_H156 zenon_H40 zenon_H158 zenon_H186 zenon_H13b zenon_H38 zenon_H68. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.64 apply (zenon_L180_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.64 apply (zenon_L306_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.64 apply (zenon_L2337_); trivial. % 22.56/22.64 apply (zenon_L165_); trivial. % 22.56/22.64 (* end of lemma zenon_L2338_ *) % 22.56/22.64 assert (zenon_L2339_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H169 zenon_H11a zenon_H3e zenon_H236 zenon_H55 zenon_H1fb zenon_Hf5 zenon_H1d8 zenon_H117 zenon_H195 zenon_He2 zenon_Heb zenon_H40 zenon_H48 zenon_H1ef zenon_H14c zenon_H15d zenon_H2c zenon_H68 zenon_H77 zenon_H139 zenon_H179 zenon_He3 zenon_H1a2 zenon_H1cd zenon_Hb1 zenon_Ha0 zenon_H13b zenon_Hb6 zenon_H5d zenon_Ha5 zenon_Ha9 zenon_H65 zenon_H7d zenon_Hac zenon_Hb2 zenon_H1fe zenon_H1f zenon_H173 zenon_H1ec zenon_H186 zenon_H156 zenon_H158 zenon_H4e zenon_H15c. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.64 apply (zenon_L250_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.64 apply (zenon_L405_); trivial. % 22.56/22.64 apply (zenon_L2332_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.64 apply (zenon_L2334_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.64 apply (zenon_L250_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.64 apply (zenon_L1594_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.64 apply (zenon_L356_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.64 apply (zenon_L2336_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.64 apply (zenon_L2330_); trivial. % 22.56/22.64 apply (zenon_L246_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.64 apply (zenon_L309_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.64 apply (zenon_L405_); trivial. % 22.56/22.64 apply (zenon_L2332_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.64 apply (zenon_L2334_); trivial. % 22.56/22.64 apply (zenon_L2338_); trivial. % 22.56/22.64 apply (zenon_L374_); trivial. % 22.56/22.64 (* end of lemma zenon_L2339_ *) % 22.56/22.64 assert (zenon_L2340_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> False). % 22.56/22.64 do 0 intro. intros zenon_Hc0 zenon_H14c zenon_H65. % 22.56/22.64 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.56/22.64 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.56/22.64 apply (zenon_L2277_); trivial. % 22.56/22.64 (* end of lemma zenon_L2340_ *) % 22.56/22.64 assert (zenon_L2341_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((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)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((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 (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((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 (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H169 zenon_H2c zenon_Hbc zenon_H1a2 zenon_H24 zenon_Hfa zenon_Hf5 zenon_Heb zenon_H40 zenon_H25 zenon_H48 zenon_H15d zenon_H68 zenon_H28 zenon_H82 zenon_H77 zenon_H158 zenon_H173 zenon_He3 zenon_H13a zenon_He4 zenon_H65 zenon_H1f1 zenon_H195 zenon_H13f zenon_H109 zenon_Hb6 zenon_H14c zenon_H196 zenon_H117 zenon_Ha9 zenon_H2a zenon_Ha0 zenon_H9d zenon_H33 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H139 zenon_H15c. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.56/22.64 apply (zenon_L250_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.64 apply (zenon_L251_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.64 apply (zenon_L306_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.64 apply (zenon_L245_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.64 apply (zenon_L53_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.64 apply (zenon_L193_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.64 apply (zenon_L25_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.64 exact (zenon_H40 zenon_H3f). % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.64 exact (zenon_H1d4 zenon_H4d). % 22.56/22.64 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.56/22.64 apply (zenon_L65_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.56/22.64 exact (zenon_H40 zenon_H3f). % 22.56/22.64 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.56/22.64 apply (zenon_L2247_); trivial. % 22.56/22.64 apply (zenon_L1268_); trivial. % 22.56/22.64 apply (zenon_L2292_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.64 apply (zenon_L65_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.64 apply (zenon_L2293_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.64 apply (zenon_L26_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.64 apply (zenon_L30_); trivial. % 22.56/22.64 apply (zenon_L134_); trivial. % 22.56/22.64 apply (zenon_L2295_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.64 apply (zenon_L180_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.64 apply (zenon_L147_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.64 apply (zenon_L1475_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.64 exact (zenon_H40 zenon_H3f). % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.64 apply (zenon_L279_); trivial. % 22.56/22.64 exact (zenon_Hec zenon_H5c). % 22.56/22.64 apply (zenon_L303_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.64 apply (zenon_L65_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.64 apply (zenon_L251_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.64 apply (zenon_L147_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.64 apply (zenon_L94_); trivial. % 22.56/22.64 apply (zenon_L303_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.64 apply (zenon_L26_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.64 apply (zenon_L30_); trivial. % 22.56/22.64 apply (zenon_L134_); trivial. % 22.56/22.64 apply (zenon_L503_); trivial. % 22.56/22.64 apply (zenon_L1113_); trivial. % 22.56/22.64 (* end of lemma zenon_L2341_ *) % 22.56/22.64 assert (zenon_L2342_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (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) (e3)) = (op (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) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((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 (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (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)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H13b zenon_H179 zenon_He3 zenon_He2 zenon_H1fb zenon_H36 zenon_Hf0 zenon_H9d zenon_H131 zenon_Hcb zenon_H162 zenon_H24e zenon_H1cd zenon_H192 zenon_H15d zenon_H24 zenon_Hc2 zenon_Heb zenon_H7d zenon_H34 zenon_H1cb zenon_H5d zenon_H18d zenon_H104 zenon_H111 zenon_H183 zenon_H129 zenon_H1b4 zenon_H1bb zenon_H18a zenon_H1ef zenon_H14c zenon_H6f zenon_H109 zenon_H117 zenon_H1b7 zenon_H1f1 zenon_H13f zenon_H201 zenon_H4e zenon_H23c zenon_He4 zenon_H1cf zenon_H1c3 zenon_H26a zenon_H190 zenon_H186 zenon_H1a2 zenon_H195 zenon_H20f zenon_Hf5 zenon_H25b zenon_H1d8 zenon_H82 zenon_H68 zenon_H77 zenon_H121 zenon_Ha0 zenon_Hb6 zenon_Ha9 zenon_H33 zenon_H13a zenon_H1c7 zenon_H1a3 zenon_Hc4 zenon_H65 zenon_H2c zenon_H139 zenon_H38 zenon_H48. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.64 apply (zenon_L2266_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.64 apply (zenon_L1302_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.64 apply (zenon_L1410_); trivial. % 22.56/22.64 apply (zenon_L246_); trivial. % 22.56/22.64 (* end of lemma zenon_L2342_ *) % 22.56/22.64 assert (zenon_L2343_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((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)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (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) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 22.56/22.64 do 0 intro. intros zenon_He2 zenon_H1fb zenon_H38 zenon_He3 zenon_Hb6 zenon_Ha0 zenon_H14c zenon_H9d zenon_H109 zenon_H117 zenon_Hc2 zenon_Hbc zenon_H104 zenon_H1bb zenon_H1cb zenon_H120 zenon_H162 zenon_H1a3 zenon_H231 zenon_H48 zenon_H77 zenon_H65 zenon_H13f zenon_H7d zenon_H34. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.56/22.64 apply (zenon_L316_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.56/22.64 exact (zenon_He3 zenon_He7). % 22.56/22.64 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.56/22.64 apply (zenon_L30_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.56/22.64 apply (zenon_L111_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.56/22.64 apply (zenon_L477_); trivial. % 22.56/22.64 apply (zenon_L2261_); trivial. % 22.56/22.64 apply (zenon_L802_); trivial. % 22.56/22.64 (* end of lemma zenon_L2343_ *) % 22.56/22.64 assert (zenon_L2344_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (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)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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 (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H31 zenon_H6e zenon_Hf7 zenon_H1b4 zenon_H9b zenon_H1cb zenon_H129 zenon_H28f zenon_Hfa zenon_Heb zenon_H48 zenon_H15d zenon_H1c6 zenon_H141 zenon_H82 zenon_H77 zenon_H68 zenon_H125 zenon_Hb6 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H94 zenon_H13c zenon_Hf5 zenon_H5d zenon_H1c3 zenon_H18d zenon_H20f zenon_H13b zenon_H13a zenon_H1d5 zenon_H33 zenon_H139 zenon_Hcc zenon_Hbc zenon_H236 zenon_H1ef zenon_H23c zenon_H100 zenon_H26a zenon_H13f zenon_H183 zenon_H190 zenon_H13e zenon_He4 zenon_H1f1 zenon_H6f zenon_H266 zenon_H16a zenon_Hf0 zenon_H1f zenon_H18a zenon_H1fe zenon_He2 zenon_H55 zenon_H23d zenon_H2c zenon_H189 zenon_H196 zenon_H27e zenon_H1a8 zenon_H25b zenon_H195 zenon_H1c0 zenon_H140 zenon_H1ca zenon_H1bb zenon_H24e zenon_H34 zenon_H1b7 zenon_H1cd zenon_H160 zenon_H9d zenon_H7d. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.56/22.64 apply (zenon_L871_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.56/22.64 apply (zenon_L206_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.56/22.64 apply (zenon_L2325_); trivial. % 22.56/22.64 apply (zenon_L803_); trivial. % 22.56/22.64 (* end of lemma zenon_L2344_ *) % 22.56/22.64 assert (zenon_L2345_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((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 (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((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)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H236 zenon_Ha0 zenon_H1f zenon_H48 zenon_H3c zenon_H1ef zenon_H14c zenon_H77 zenon_H173 zenon_H201 zenon_H1cf zenon_H65 zenon_H68 zenon_Ha9 zenon_Hb6 zenon_H9b zenon_Hbc zenon_H1a2 zenon_H13a zenon_H33 zenon_H1bb zenon_H1b4 zenon_H1ca zenon_H140 zenon_H1cb zenon_H1c0 zenon_H195 zenon_H25b zenon_H1a8 zenon_H27e zenon_H196 zenon_H189 zenon_H2c zenon_H23d zenon_H55 zenon_H1b7 zenon_He2 zenon_H1fe zenon_H18a zenon_Hf0 zenon_H16a zenon_H266 zenon_H6f zenon_H1f1 zenon_He4 zenon_H13e zenon_H190 zenon_H183 zenon_H13f zenon_H26a zenon_H100 zenon_H23c zenon_Hcc zenon_H139 zenon_H1d5 zenon_H13b zenon_H20f zenon_H18d zenon_H1c3 zenon_H5d zenon_Hf5 zenon_H13c zenon_H94 zenon_H158 zenon_H156 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H82 zenon_H141 zenon_H129 zenon_H7d zenon_H1c6 zenon_H15d zenon_Heb zenon_Hfa zenon_H28f zenon_H24e zenon_H1cd zenon_H125 zenon_H186. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.64 apply (zenon_L1873_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.64 exact (zenon_H205 zenon_H2a). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.64 apply (zenon_L25_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.64 apply (zenon_L405_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.64 exact (zenon_H6c zenon_H67). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.64 apply (zenon_L24_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.64 apply (zenon_L226_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.64 apply (zenon_L2289_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.56/22.64 apply (zenon_L264_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.56/22.64 apply (zenon_L438_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.56/22.64 apply (zenon_L1132_); trivial. % 22.56/22.64 apply (zenon_L2344_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.64 apply (zenon_L264_); trivial. % 22.56/22.64 apply (zenon_L92_); trivial. % 22.56/22.64 apply (zenon_L1353_); trivial. % 22.56/22.64 apply (zenon_L1876_); trivial. % 22.56/22.64 (* end of lemma zenon_L2345_ *) % 22.56/22.64 assert (zenon_L2346_ : (((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)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H139 zenon_H2c zenon_H65 zenon_H173 zenon_Ha5 zenon_Ha0 zenon_H1a2 zenon_Ha9 zenon_H14c zenon_Hac zenon_H1cd zenon_He3 zenon_H1ec zenon_H4e zenon_H1d4 zenon_H159 zenon_H156 zenon_H40 zenon_H158 zenon_H186 zenon_H13b zenon_H155 zenon_H77. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.64 apply (zenon_L180_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.64 apply (zenon_L306_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.64 apply (zenon_L2337_); trivial. % 22.56/22.64 apply (zenon_L98_); trivial. % 22.56/22.64 (* end of lemma zenon_L2346_ *) % 22.56/22.64 assert (zenon_L2347_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((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) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H169 zenon_H11a zenon_H236 zenon_H55 zenon_H1fb zenon_Hf5 zenon_H1d8 zenon_H117 zenon_H195 zenon_He2 zenon_Heb zenon_H40 zenon_H48 zenon_H68 zenon_H65 zenon_H15d zenon_H2c zenon_Ha9 zenon_Hac zenon_H77 zenon_H139 zenon_H179 zenon_He3 zenon_H1a2 zenon_H1cd zenon_Hb1 zenon_H14c zenon_Ha0 zenon_Hb6 zenon_Ha5 zenon_H13b zenon_H3c zenon_H24 zenon_H1fe zenon_H1f zenon_H158 zenon_H173 zenon_H4e zenon_H156 zenon_H186 zenon_H1ec zenon_H15c. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.64 apply (zenon_L250_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.64 apply (zenon_L27_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.64 apply (zenon_L1475_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.64 apply (zenon_L65_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.64 apply (zenon_L2330_); trivial. % 22.56/22.64 apply (zenon_L2331_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.64 apply (zenon_L2334_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.64 apply (zenon_L25_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.64 apply (zenon_L1594_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.64 apply (zenon_L1475_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.64 apply (zenon_L2336_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.64 apply (zenon_L2330_); trivial. % 22.56/22.64 apply (zenon_L246_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.64 exact (zenon_H1f zenon_H1e). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.64 apply (zenon_L25_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.64 apply (zenon_L27_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.64 apply (zenon_L1475_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.64 apply (zenon_L65_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.64 apply (zenon_L2330_); trivial. % 22.56/22.64 apply (zenon_L2346_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.64 apply (zenon_L2334_); trivial. % 22.56/22.64 apply (zenon_L2338_); trivial. % 22.56/22.64 apply (zenon_L373_); trivial. % 22.56/22.64 (* end of lemma zenon_L2347_ *) % 22.56/22.64 assert (zenon_L2348_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H173 zenon_Hf0 zenon_H6d zenon_H158 zenon_H28 zenon_H48 zenon_H40 zenon_H131 zenon_H105 zenon_Heb. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.56/22.64 apply (zenon_L392_); trivial. % 22.56/22.64 (* end of lemma zenon_L2348_ *) % 22.56/22.64 assert (zenon_L2349_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> False). % 22.56/22.64 do 0 intro. intros zenon_H2f zenon_H105 zenon_H6d. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.56/22.64 apply (zenon_L466_); trivial. % 22.56/22.64 (* end of lemma zenon_L2349_ *) % 22.56/22.64 assert (zenon_L2350_ : (((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 (e2) (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 (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H15d zenon_H4c zenon_H120 zenon_H104 zenon_H192 zenon_H34 zenon_H12e zenon_H105 zenon_H111 zenon_H38 zenon_H48. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.64 exact (zenon_H4c zenon_H47). % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.64 apply (zenon_L1650_); trivial. % 22.56/22.64 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.64 apply (zenon_L148_); trivial. % 22.56/22.64 apply (zenon_L246_); trivial. % 22.56/22.64 (* end of lemma zenon_L2350_ *) % 22.56/22.64 assert (zenon_L2351_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((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))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> False). % 22.56/22.64 do 0 intro. intros zenon_H36 zenon_H15d zenon_H4c zenon_H120 zenon_H104 zenon_H192 zenon_H12e zenon_H105 zenon_H111 zenon_H48. % 22.56/22.64 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.56/22.65 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.56/22.65 apply (zenon_L2350_); trivial. % 22.56/22.65 (* end of lemma zenon_L2351_ *) % 22.56/22.65 assert (zenon_L2352_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((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)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (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)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (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)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)))) -> (((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)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (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 (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H290 zenon_H234 zenon_H105 zenon_H230 zenon_Heb zenon_H131 zenon_H48 zenon_H158 zenon_Hf0 zenon_H2a zenon_H173 zenon_H1d8 zenon_H1fb zenon_H77 zenon_H1fe zenon_H104 zenon_H179 zenon_H140 zenon_H183 zenon_H1b4 zenon_H163 zenon_H129 zenon_H20b zenon_H190 zenon_H19a zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1bb zenon_H20f zenon_H1c3 zenon_H1cf zenon_H19d zenon_H15d zenon_Hf5 zenon_H111 zenon_H192 zenon_H6f zenon_H13a zenon_H13b zenon_H1a2 zenon_H1ef zenon_H68 zenon_H73 zenon_Hfa zenon_H196 zenon_H117 zenon_H121 zenon_H177 zenon_H11a zenon_Ha9 zenon_H1c6 zenon_Ha0 zenon_Hb6 zenon_H139 zenon_H125 zenon_H164 zenon_H55 zenon_H1cb zenon_He4 zenon_H156 zenon_H94 zenon_H22d zenon_H109 zenon_H100 zenon_Hb2 zenon_H4e zenon_H82 zenon_H189 zenon_H1a8 zenon_H186 zenon_H13c zenon_H5d zenon_Hcc zenon_H264. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1bf | zenon_intro zenon_H6d ]. % 22.56/22.65 exact (zenon_H1bf zenon_H105). % 22.56/22.65 apply (zenon_L468_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1bf | zenon_intro zenon_H6d ]. % 22.56/22.65 exact (zenon_H1bf zenon_H105). % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.56/22.65 apply (zenon_L2_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.56/22.65 apply (zenon_L482_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.56/22.65 apply (zenon_L315_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.56/22.65 apply (zenon_L317_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.56/22.65 apply (zenon_L318_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.56/22.65 apply (zenon_L11_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.56/22.65 apply (zenon_L483_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.56/22.65 apply (zenon_L485_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.56/22.65 apply (zenon_L435_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.56/22.65 apply (zenon_L522_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.56/22.65 apply (zenon_L37_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.56/22.65 apply (zenon_L458_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.56/22.65 apply (zenon_L460_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.56/22.65 apply (zenon_L531_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.56/22.65 apply (zenon_L467_); trivial. % 22.56/22.65 apply (zenon_L51_); trivial. % 22.56/22.65 (* end of lemma zenon_L2352_ *) % 22.56/22.65 assert (zenon_L2353_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (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)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (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)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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) (e3)))) -> (((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)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (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 (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H23b zenon_H290 zenon_H234 zenon_H105 zenon_H230 zenon_Heb zenon_H131 zenon_H158 zenon_Hf0 zenon_H173 zenon_H1d8 zenon_H1fb zenon_H77 zenon_H1fe zenon_H104 zenon_H179 zenon_H140 zenon_H183 zenon_H1b4 zenon_H163 zenon_H129 zenon_H20b zenon_H190 zenon_H19a zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1bb zenon_H20f zenon_H1c3 zenon_H1cf zenon_H19d zenon_H15d zenon_Hf5 zenon_H111 zenon_H192 zenon_H6f zenon_H13a zenon_H13b zenon_H1a2 zenon_H1ef zenon_H68 zenon_H73 zenon_Hfa zenon_H196 zenon_H117 zenon_H121 zenon_H177 zenon_H11a zenon_Ha9 zenon_H1c6 zenon_Ha0 zenon_Hb6 zenon_H139 zenon_H125 zenon_H164 zenon_H55 zenon_H1cb zenon_He4 zenon_H156 zenon_H94 zenon_H22d zenon_H109 zenon_H100 zenon_Hb2 zenon_H4e zenon_H82 zenon_H189 zenon_H1a8 zenon_H186 zenon_H13c zenon_H5d zenon_Hcc zenon_H264 zenon_H1f zenon_H48 zenon_H3d zenon_H237 zenon_H236. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.56/22.65 apply (zenon_L487_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.65 exact (zenon_H1f zenon_H1e). % 22.56/22.65 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.65 apply (zenon_L2352_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.65 exact (zenon_H237 zenon_H31). % 22.56/22.65 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.65 apply (zenon_L1841_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.65 apply (zenon_L214_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.65 apply (zenon_L488_); trivial. % 22.56/22.65 apply (zenon_L165_); trivial. % 22.56/22.65 (* end of lemma zenon_L2353_ *) % 22.56/22.65 assert (zenon_L2354_ : (((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 (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H12e zenon_H77 zenon_H102 zenon_H3d zenon_H192 zenon_H105 zenon_H104 zenon_H120. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.56/22.65 apply (zenon_L71_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.56/22.65 apply (zenon_L146_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.56/22.65 apply (zenon_L72_); trivial. % 22.56/22.65 exact (zenon_H120 zenon_H11f). % 22.56/22.65 (* end of lemma zenon_L2354_ *) % 22.56/22.65 assert (zenon_L2355_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((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) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((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)) = (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) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((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 (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (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) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H240 zenon_H3c zenon_H120 zenon_H12e zenon_H6d zenon_H236 zenon_H3d zenon_H48 zenon_H1f zenon_H264 zenon_Hcc zenon_H5d zenon_H13c zenon_H186 zenon_H1a8 zenon_H189 zenon_H82 zenon_H4e zenon_Hb2 zenon_H100 zenon_H109 zenon_H22d zenon_H94 zenon_H156 zenon_He4 zenon_H1cb zenon_H55 zenon_H164 zenon_H125 zenon_H139 zenon_Hb6 zenon_Ha0 zenon_H1c6 zenon_Ha9 zenon_H11a zenon_H177 zenon_H121 zenon_H117 zenon_H196 zenon_Hfa zenon_H73 zenon_H68 zenon_H1ef zenon_H1a2 zenon_H13b zenon_H13a zenon_H6f zenon_H192 zenon_H111 zenon_Hf5 zenon_H15d zenon_H19d zenon_H1cf zenon_H1c3 zenon_H20f zenon_H1bb zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H19a zenon_H190 zenon_H20b zenon_H129 zenon_H163 zenon_H1b4 zenon_H183 zenon_H140 zenon_H179 zenon_H104 zenon_H1fe zenon_H77 zenon_H1fb zenon_H1d8 zenon_H173 zenon_Hf0 zenon_H158 zenon_H131 zenon_Heb zenon_H230 zenon_H105 zenon_H234 zenon_H290 zenon_H23b. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.65 apply (zenon_L2353_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.65 exact (zenon_H1f zenon_H1e). % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.65 apply (zenon_L25_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.56/22.65 exact (zenon_H6c zenon_H67). % 22.56/22.65 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.56/22.65 apply (zenon_L24_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.56/22.65 apply (zenon_L27_); trivial. % 22.56/22.65 apply (zenon_L2354_); trivial. % 22.56/22.65 apply (zenon_L1847_); trivial. % 22.56/22.65 (* end of lemma zenon_L2355_ *) % 22.56/22.65 assert (zenon_L2356_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H61 zenon_H15d zenon_H4c zenon_H192 zenon_H105 zenon_H111 zenon_Hf5. % 22.56/22.65 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.56/22.65 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.65 exact (zenon_H4c zenon_H47). % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.65 apply (zenon_L146_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.65 apply (zenon_L148_); trivial. % 22.56/22.65 apply (zenon_L192_); trivial. % 22.56/22.65 (* end of lemma zenon_L2356_ *) % 22.56/22.65 assert (zenon_L2357_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> False). % 22.56/22.65 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_H105 zenon_H131 zenon_Hec. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.65 exact (zenon_H7a zenon_H3c). % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.65 exact (zenon_H40 zenon_H3f). % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.65 apply (zenon_L128_); trivial. % 22.56/22.65 exact (zenon_Hec zenon_H5c). % 22.56/22.65 (* end of lemma zenon_L2357_ *) % 22.56/22.65 assert (zenon_L2358_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 22.56/22.65 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_H77 zenon_H87 zenon_H11f zenon_H20f. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.65 exact (zenon_H7a zenon_H3c). % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.65 exact (zenon_H40 zenon_H3f). % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.65 apply (zenon_L343_); trivial. % 22.56/22.65 apply (zenon_L412_); trivial. % 22.56/22.65 (* end of lemma zenon_L2358_ *) % 22.56/22.65 assert (zenon_L2359_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((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))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H15d zenon_H4c zenon_H20f zenon_H104 zenon_H192 zenon_H12e zenon_H55 zenon_H6d zenon_H72 zenon_H4e zenon_H1e zenon_H68 zenon_H125 zenon_H105 zenon_H111 zenon_Heb zenon_H7a zenon_H40 zenon_H77 zenon_H87 zenon_Hf5. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.65 exact (zenon_H4c zenon_H47). % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.56/22.65 apply (zenon_L20_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.56/22.65 apply (zenon_L83_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.56/22.65 apply (zenon_L34_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.56/22.65 apply (zenon_L71_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.56/22.65 apply (zenon_L146_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.56/22.65 apply (zenon_L72_); trivial. % 22.56/22.65 apply (zenon_L2358_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.65 apply (zenon_L148_); trivial. % 22.56/22.65 apply (zenon_L1082_); trivial. % 22.56/22.65 (* end of lemma zenon_L2359_ *) % 22.56/22.65 assert (zenon_L2360_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.56/22.65 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_H105 zenon_H131 zenon_H155 zenon_Hf5. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.65 exact (zenon_H7a zenon_H3c). % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.65 exact (zenon_H40 zenon_H3f). % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.65 apply (zenon_L128_); trivial. % 22.56/22.65 apply (zenon_L192_); trivial. % 22.56/22.65 (* end of lemma zenon_L2360_ *) % 22.56/22.65 assert (zenon_L2361_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (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 (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H15d zenon_H4c zenon_H1cd zenon_H6d zenon_Ha9 zenon_H159 zenon_Hb6 zenon_H1c6 zenon_H72 zenon_H31 zenon_Ha0 zenon_H1a2 zenon_H111 zenon_Heb zenon_H7a zenon_H40 zenon_H105 zenon_H131 zenon_Hf5. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.65 exact (zenon_H4c zenon_H47). % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.56/22.65 apply (zenon_L68_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.56/22.65 apply (zenon_L436_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.56/22.65 apply (zenon_L400_); trivial. % 22.56/22.65 apply (zenon_L1111_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.65 apply (zenon_L148_); trivial. % 22.56/22.65 apply (zenon_L2360_); trivial. % 22.56/22.65 (* end of lemma zenon_L2361_ *) % 22.56/22.65 assert (zenon_L2362_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H1a2 zenon_H67 zenon_H105 zenon_H72 zenon_H14c zenon_Ha0 zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_Ha9 zenon_H6d zenon_H1cd. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.56/22.65 apply (zenon_L446_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.56/22.65 apply (zenon_L436_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.56/22.65 apply (zenon_L278_); trivial. % 22.56/22.65 apply (zenon_L1111_); trivial. % 22.56/22.65 (* end of lemma zenon_L2362_ *) % 22.56/22.65 assert (zenon_L2363_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (((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))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H15d zenon_H4c zenon_H68 zenon_H38 zenon_H72 zenon_H73 zenon_H77 zenon_H140 zenon_H26d zenon_H1cd zenon_H6d zenon_H159 zenon_H1c6 zenon_H1a2 zenon_Ha9 zenon_Hb6 zenon_Ha0 zenon_H139 zenon_H111 zenon_Heb zenon_H7a zenon_H40 zenon_H105 zenon_H131 zenon_Hf5. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.65 exact (zenon_H4c zenon_H47). % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.56/22.65 apply (zenon_L756_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.56/22.65 apply (zenon_L62_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.56/22.65 apply (zenon_L2362_); trivial. % 22.56/22.65 apply (zenon_L726_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.65 apply (zenon_L214_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.65 apply (zenon_L22_); trivial. % 22.56/22.65 apply (zenon_L165_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.65 apply (zenon_L148_); trivial. % 22.56/22.65 apply (zenon_L2360_); trivial. % 22.56/22.65 (* end of lemma zenon_L2363_ *) % 22.56/22.65 assert (zenon_L2364_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (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)) = (op (e0) (e1)))) -> (~((op (e0) (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)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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 (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) (e3)))) -> (((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)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H15c zenon_H15d zenon_Hf5 zenon_H111 zenon_H68 zenon_H4e zenon_H72 zenon_H55 zenon_H6d zenon_H12e zenon_H87 zenon_H20f zenon_H104 zenon_H192 zenon_H77 zenon_H125 zenon_H4c zenon_H290 zenon_H234 zenon_H230 zenon_H48 zenon_H158 zenon_Hf0 zenon_H173 zenon_H1d8 zenon_H1fb zenon_H1fe zenon_H179 zenon_H140 zenon_H183 zenon_H1b4 zenon_H163 zenon_H129 zenon_H20b zenon_H190 zenon_H19a zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1bb zenon_H1c3 zenon_H1cf zenon_H19d zenon_H6f zenon_H13a zenon_H13b zenon_H1a2 zenon_H1ef zenon_H73 zenon_Hfa zenon_H196 zenon_H117 zenon_H121 zenon_H177 zenon_H11a zenon_Ha9 zenon_H1c6 zenon_Ha0 zenon_Hb6 zenon_H139 zenon_H164 zenon_H1cb zenon_He4 zenon_H156 zenon_H94 zenon_H22d zenon_H109 zenon_H100 zenon_Hb2 zenon_H82 zenon_H189 zenon_H1a8 zenon_H186 zenon_H13c zenon_H5d zenon_Hcc zenon_H264 zenon_H1cd zenon_H26d zenon_H236 zenon_H7a zenon_H40 zenon_H131 zenon_H105 zenon_Heb. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.56/22.65 apply (zenon_L2357_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.65 apply (zenon_L2359_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.65 apply (zenon_L2352_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.65 apply (zenon_L2361_); trivial. % 22.56/22.65 apply (zenon_L2363_); trivial. % 22.56/22.65 (* end of lemma zenon_L2364_ *) % 22.56/22.65 assert (zenon_L2365_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e2) (e0)) = (op (e2) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (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 (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H15d zenon_H87 zenon_H55 zenon_H4e zenon_H125 zenon_Heb zenon_H100 zenon_H40 zenon_Hec zenon_H12e zenon_H192 zenon_H104 zenon_H120 zenon_H4c zenon_H82 zenon_H105 zenon_H111 zenon_H139 zenon_H68 zenon_H1e zenon_H6f zenon_H6d zenon_H73 zenon_H72 zenon_H77. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.65 exact (zenon_H4c zenon_H47). % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.65 exact (zenon_H4c zenon_H47). % 22.56/22.65 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.56/22.65 apply (zenon_L20_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.56/22.65 apply (zenon_L24_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.56/22.65 apply (zenon_L34_); trivial. % 22.56/22.65 apply (zenon_L2354_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.65 apply (zenon_L70_); trivial. % 22.56/22.65 apply (zenon_L84_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.65 apply (zenon_L148_); trivial. % 22.56/22.65 apply (zenon_L99_); trivial. % 22.56/22.65 (* end of lemma zenon_L2365_ *) % 22.56/22.65 assert (zenon_L2366_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 22.56/22.65 do 0 intro. intros zenon_Hb2 zenon_H155 zenon_H17c zenon_Hb6 zenon_H3c zenon_H94 zenon_Hb9 zenon_Hbb zenon_Hbc. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.56/22.65 apply (zenon_L444_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.56/22.65 apply (zenon_L46_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.56/22.65 apply (zenon_L47_); trivial. % 22.56/22.65 apply (zenon_L48_); trivial. % 22.56/22.65 (* end of lemma zenon_L2366_ *) % 22.56/22.65 assert (zenon_L2367_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H1bb zenon_H195 zenon_H10c zenon_Hec zenon_H20f zenon_H25b zenon_H120 zenon_Hbc zenon_Hb9 zenon_H94 zenon_H3c zenon_Hb6 zenon_H155 zenon_Hb2 zenon_Hbb zenon_H1cb. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 22.56/22.65 apply (zenon_L2318_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 22.56/22.65 exact (zenon_H120 zenon_H11f). % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 22.56/22.65 apply (zenon_L2366_); trivial. % 22.56/22.65 apply (zenon_L622_); trivial. % 22.56/22.65 (* end of lemma zenon_L2367_ *) % 22.56/22.65 assert (zenon_L2368_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 22.56/22.65 do 0 intro. intros zenon_H13b zenon_H48 zenon_He3 zenon_H68 zenon_Heb zenon_Ha0 zenon_H72 zenon_Ha9 zenon_H1a2 zenon_H31 zenon_H105 zenon_H18d zenon_H1cb zenon_Hb2 zenon_H94 zenon_Hbc zenon_H25b zenon_H20f zenon_H195 zenon_H1bb zenon_Hb6 zenon_H104 zenon_H6d zenon_H2d zenon_H117 zenon_H120 zenon_H13c zenon_H40 zenon_H77 zenon_H87 zenon_Hec. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.56/22.65 apply (zenon_L60_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.56/22.65 exact (zenon_He3 zenon_He7). % 22.56/22.65 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.56/22.65 apply (zenon_L62_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.56/22.65 apply (zenon_L46_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.56/22.65 apply (zenon_L67_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.56/22.65 apply (zenon_L289_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.56/22.65 apply (zenon_L400_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.56/22.65 apply (zenon_L68_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.56/22.65 apply (zenon_L436_); trivial. % 22.56/22.65 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.56/22.66 apply (zenon_L400_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.56/22.66 apply (zenon_L2367_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.56/22.66 exact (zenon_Hec zenon_H5c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.56/22.66 apply (zenon_L1101_); trivial. % 22.56/22.66 exact (zenon_H120 zenon_H11f). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.56/22.66 apply (zenon_L436_); trivial. % 22.56/22.66 apply (zenon_L90_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.66 exact (zenon_H40 zenon_H3f). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.66 apply (zenon_L343_); trivial. % 22.56/22.66 exact (zenon_Hec zenon_H5c). % 22.56/22.66 (* end of lemma zenon_L2368_ *) % 22.56/22.66 assert (zenon_L2369_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.56/22.66 do 0 intro. intros zenon_H13b zenon_Hec zenon_H77 zenon_H40 zenon_H48 zenon_Heb zenon_He3 zenon_H72 zenon_H68 zenon_Hf5 zenon_H38. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.56/22.66 apply (zenon_L60_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.56/22.66 exact (zenon_He3 zenon_He7). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.56/22.66 apply (zenon_L62_); trivial. % 22.56/22.66 apply (zenon_L663_); trivial. % 22.56/22.66 (* end of lemma zenon_L2369_ *) % 22.56/22.66 assert (zenon_L2370_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 22.56/22.66 do 0 intro. intros zenon_H13a zenon_H1e zenon_Hb6 zenon_H3d zenon_Ha0 zenon_H31 zenon_Ha9 zenon_Hf6. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.66 apply (zenon_L41_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.66 apply (zenon_L55_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.66 apply (zenon_L68_); trivial. % 22.56/22.66 apply (zenon_L92_); trivial. % 22.56/22.66 (* end of lemma zenon_L2370_ *) % 22.56/22.66 assert (zenon_L2371_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H240 zenon_H33 zenon_H9d zenon_H23d zenon_H1f zenon_H15d zenon_H9e zenon_Hb6 zenon_H105 zenon_H111 zenon_H48 zenon_H4c zenon_Ha0 zenon_H236. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.66 exact (zenon_H1f zenon_H1e). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.66 apply (zenon_L459_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.66 exact (zenon_H237 zenon_H31). % 22.56/22.66 apply (zenon_L156_); trivial. % 22.56/22.66 apply (zenon_L611_); trivial. % 22.56/22.66 (* end of lemma zenon_L2371_ *) % 22.56/22.66 assert (zenon_L2372_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (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) (e0)) = (op (e3) (e0)))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H9b zenon_H236 zenon_Ha0 zenon_H4c zenon_H48 zenon_H111 zenon_H105 zenon_Hb6 zenon_H15d zenon_H23d zenon_H33. % 22.56/22.66 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.56/22.66 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.56/22.66 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.56/22.66 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.56/22.66 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.56/22.66 apply (zenon_L2371_); trivial. % 22.56/22.66 apply (zenon_L2371_); trivial. % 22.56/22.66 (* end of lemma zenon_L2372_ *) % 22.56/22.66 assert (zenon_L2373_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 22.56/22.66 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_H1d4 zenon_H11f zenon_H20f. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.66 exact (zenon_H40 zenon_H3f). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.66 exact (zenon_H1d4 zenon_H4d). % 22.56/22.66 apply (zenon_L412_); trivial. % 22.56/22.66 (* end of lemma zenon_L2373_ *) % 22.56/22.66 assert (zenon_L2374_ : (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H1bb zenon_H129 zenon_H115 zenon_H20f zenon_H1d4 zenon_H40 zenon_H7a zenon_Heb zenon_H1cb zenon_H160 zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_Ha9 zenon_H6d zenon_H1b7. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 22.56/22.66 apply (zenon_L298_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 22.56/22.66 apply (zenon_L2373_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 22.56/22.66 apply (zenon_L236_); trivial. % 22.56/22.66 apply (zenon_L1195_); trivial. % 22.56/22.66 (* end of lemma zenon_L2374_ *) % 22.56/22.66 assert (zenon_L2375_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((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) = (e2))) -> (~((e0) = (e1))) -> (((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 (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H82 zenon_H4c zenon_H7a zenon_H105 zenon_Ha9 zenon_H117 zenon_H195 zenon_H68 zenon_H48 zenon_H141 zenon_H13a zenon_H1e zenon_H7d zenon_H77 zenon_H6d zenon_H40 zenon_Hb6 zenon_He4 zenon_Ha0 zenon_H31 zenon_Ha5 zenon_Hf5. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.66 apply (zenon_L1609_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.66 apply (zenon_L41_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.66 apply (zenon_L1083_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.66 apply (zenon_L68_); trivial. % 22.56/22.66 apply (zenon_L262_); trivial. % 22.56/22.66 (* end of lemma zenon_L2375_ *) % 22.56/22.66 assert (zenon_L2376_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> False). % 22.56/22.66 do 0 intro. intros zenon_H117 zenon_H1cd zenon_H159 zenon_H3d zenon_H1c6 zenon_H1ef zenon_H72 zenon_H67 zenon_H1a2 zenon_Ha9 zenon_H6d zenon_Hb6 zenon_H105 zenon_Ha0 zenon_H115. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.56/22.66 apply (zenon_L1783_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.56/22.66 apply (zenon_L289_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.56/22.66 apply (zenon_L400_); trivial. % 22.56/22.66 apply (zenon_L77_); trivial. % 22.56/22.66 (* end of lemma zenon_L2376_ *) % 22.56/22.66 assert (zenon_L2377_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e3))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H141 zenon_H68 zenon_H195 zenon_Ha5 zenon_H117 zenon_H1cd zenon_H159 zenon_H3d zenon_H1c6 zenon_H1ef zenon_H72 zenon_H67 zenon_H1a2 zenon_Ha9 zenon_H6d zenon_Hb6 zenon_H105 zenon_Ha0. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.56/22.66 apply (zenon_L1394_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.56/22.66 apply (zenon_L54_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.56/22.66 apply (zenon_L1784_); trivial. % 22.56/22.66 apply (zenon_L2376_); trivial. % 22.56/22.66 (* end of lemma zenon_L2377_ *) % 22.56/22.66 assert (zenon_L2378_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H82 zenon_H4c zenon_H7a zenon_Ha0 zenon_H105 zenon_Hb6 zenon_H6d zenon_Ha9 zenon_H117 zenon_Ha5 zenon_H195 zenon_H68 zenon_H109 zenon_H141 zenon_H34 zenon_H48. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.66 apply (zenon_L1588_); trivial. % 22.56/22.66 apply (zenon_L456_); trivial. % 22.56/22.66 (* end of lemma zenon_L2378_ *) % 22.56/22.66 assert (zenon_L2379_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H82 zenon_H4c zenon_H7a zenon_H196 zenon_H117 zenon_Ha5 zenon_H195 zenon_H48 zenon_H141 zenon_H139 zenon_H6f zenon_Ha0 zenon_Ha9 zenon_He4 zenon_Hb6 zenon_H40 zenon_H6d zenon_H77 zenon_H7d zenon_H1e zenon_H13a zenon_H38 zenon_H68. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.66 apply (zenon_L1393_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.66 apply (zenon_L20_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.66 apply (zenon_L21_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.66 apply (zenon_L41_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.66 apply (zenon_L1083_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.66 apply (zenon_L193_); trivial. % 22.56/22.66 apply (zenon_L156_); trivial. % 22.56/22.66 apply (zenon_L165_); trivial. % 22.56/22.66 (* end of lemma zenon_L2379_ *) % 22.56/22.66 assert (zenon_L2380_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 22.56/22.66 do 0 intro. intros zenon_H141 zenon_H68 zenon_H195 zenon_Ha5 zenon_Ha0 zenon_H6d zenon_Ha9 zenon_H1a2 zenon_H67 zenon_H105 zenon_H72 zenon_H1ef zenon_H1c6 zenon_Hb6 zenon_H3d zenon_H159 zenon_H1cd zenon_H117 zenon_H196 zenon_H38. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.56/22.66 apply (zenon_L1394_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.56/22.66 apply (zenon_L54_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.56/22.66 apply (zenon_L1784_); trivial. % 22.56/22.66 apply (zenon_L1162_); trivial. % 22.56/22.66 (* end of lemma zenon_L2380_ *) % 22.56/22.66 assert (zenon_L2381_ : (((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)) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H125 zenon_H1d5 zenon_H66 zenon_H68 zenon_H25 zenon_H6d zenon_H55 zenon_H7e zenon_H77. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.56/22.66 apply (zenon_L252_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.56/22.66 apply (zenon_L171_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.56/22.66 apply (zenon_L34_); trivial. % 22.56/22.66 apply (zenon_L71_); trivial. % 22.56/22.66 (* end of lemma zenon_L2381_ *) % 22.56/22.66 assert (zenon_L2382_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H82 zenon_H4c zenon_H7a zenon_H7d zenon_Hac zenon_Hb6 zenon_Ha5 zenon_H5d zenon_H1a8 zenon_H3d zenon_H1b3 zenon_H68 zenon_H189 zenon_H1c3 zenon_H77 zenon_Ha0 zenon_H19a zenon_Ha9 zenon_Hb2 zenon_H11f zenon_H18a. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.56/22.66 apply (zenon_L928_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.56/22.66 apply (zenon_L42_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.56/22.66 apply (zenon_L151_); trivial. % 22.56/22.66 apply (zenon_L44_); trivial. % 22.56/22.66 apply (zenon_L140_); trivial. % 22.56/22.66 (* end of lemma zenon_L2382_ *) % 22.56/22.66 assert (zenon_L2383_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H1bb zenon_H129 zenon_H115 zenon_H18a zenon_Hb2 zenon_Ha9 zenon_H19a zenon_Ha0 zenon_H77 zenon_H1c3 zenon_H189 zenon_H68 zenon_H1b3 zenon_H3d zenon_H1a8 zenon_H5d zenon_Ha5 zenon_Hb6 zenon_Hac zenon_H7d zenon_H7a zenon_H4c zenon_H82 zenon_H1cb zenon_H160 zenon_Hb1 zenon_H20f. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H167 | zenon_intro zenon_H1bc ]. % 22.56/22.66 apply (zenon_L298_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H11f | zenon_intro zenon_H1bd ]. % 22.56/22.66 apply (zenon_L2382_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H17c | zenon_intro zenon_Hc3 ]. % 22.56/22.66 apply (zenon_L236_); trivial. % 22.56/22.66 apply (zenon_L1203_); trivial. % 22.56/22.66 (* end of lemma zenon_L2383_ *) % 22.56/22.66 assert (zenon_L2384_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (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)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H1cf zenon_Hfe zenon_H4e zenon_H76 zenon_H190 zenon_H6d zenon_H27e zenon_H20f zenon_Hb1 zenon_H1cb zenon_H82 zenon_H4c zenon_H7a zenon_H7d zenon_Hac zenon_Hb6 zenon_H5d zenon_H68 zenon_H1c3 zenon_Ha0 zenon_H19a zenon_Ha9 zenon_Hb2 zenon_H18a zenon_H129 zenon_H1bb zenon_H5c zenon_H1cd zenon_H189 zenon_H1b3 zenon_H3d zenon_H77 zenon_H1a8 zenon_Ha5 zenon_H195. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.56/22.66 apply (zenon_L193_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.56/22.66 apply (zenon_L83_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.56/22.66 apply (zenon_L366_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H115 | zenon_intro zenon_H27f ]. % 22.56/22.66 apply (zenon_L2383_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H128 | zenon_intro zenon_H280 ]. % 22.56/22.66 apply (zenon_L149_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H93 | zenon_intro zenon_Hb9 ]. % 22.56/22.66 apply (zenon_L1115_); trivial. % 22.56/22.66 apply (zenon_L172_); trivial. % 22.56/22.66 (* end of lemma zenon_L2384_ *) % 22.56/22.66 assert (zenon_L2385_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e2)) = (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)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (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)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.66 do 0 intro. intros zenon_Heb zenon_H40 zenon_H105 zenon_H131 zenon_H1cf zenon_Hfe zenon_H4e zenon_H76 zenon_H190 zenon_H6d zenon_H27e zenon_H20f zenon_Hb1 zenon_H1cb zenon_H82 zenon_H4c zenon_H7a zenon_H7d zenon_Hac zenon_Hb6 zenon_H5d zenon_H68 zenon_H1c3 zenon_Ha0 zenon_H19a zenon_Ha9 zenon_Hb2 zenon_H18a zenon_H129 zenon_H1bb zenon_H1cd zenon_H189 zenon_H1b3 zenon_H3d zenon_H77 zenon_H1a8 zenon_Ha5 zenon_H195. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.66 exact (zenon_H40 zenon_H3f). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.66 apply (zenon_L128_); trivial. % 22.56/22.66 apply (zenon_L2384_); trivial. % 22.56/22.66 (* end of lemma zenon_L2385_ *) % 22.56/22.66 assert (zenon_L2386_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((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) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H1fe zenon_H31 zenon_He4 zenon_H7d zenon_H13a zenon_Hf5 zenon_H131 zenon_H40 zenon_Heb zenon_H111 zenon_H139 zenon_H1d5 zenon_H125 zenon_H1cd zenon_H159 zenon_H1c6 zenon_H1ef zenon_H1a2 zenon_H1b3 zenon_Hfa zenon_H55 zenon_H77 zenon_H15d zenon_H82 zenon_H4c zenon_H7a zenon_Ha0 zenon_H105 zenon_Hb6 zenon_H6d zenon_Ha9 zenon_H117 zenon_Ha5 zenon_H195 zenon_H68 zenon_H109 zenon_H141 zenon_H48. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.66 apply (zenon_L2375_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.66 apply (zenon_L1609_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.66 apply (zenon_L171_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.66 exact (zenon_H1b3 zenon_Hef). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.66 apply (zenon_L2377_); trivial. % 22.56/22.66 apply (zenon_L299_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.66 apply (zenon_L214_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.66 apply (zenon_L2381_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.66 apply (zenon_L171_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.66 exact (zenon_H1b3 zenon_Hef). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.66 apply (zenon_L2377_); trivial. % 22.56/22.66 apply (zenon_L63_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.56/22.66 apply (zenon_L171_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.56/22.66 apply (zenon_L34_); trivial. % 22.56/22.66 apply (zenon_L71_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.66 apply (zenon_L148_); trivial. % 22.56/22.66 apply (zenon_L2360_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.66 apply (zenon_L1394_); trivial. % 22.56/22.66 apply (zenon_L2378_); trivial. % 22.56/22.66 (* end of lemma zenon_L2386_ *) % 22.56/22.66 assert (zenon_L2387_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((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 (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H82 zenon_H4c zenon_H7a zenon_H38 zenon_H196 zenon_H117 zenon_Hb6 zenon_Ha9 zenon_H6d zenon_Ha0 zenon_Ha5 zenon_H195 zenon_H68 zenon_H141 zenon_H34 zenon_H48. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.66 apply (zenon_L1393_); trivial. % 22.56/22.66 apply (zenon_L456_); trivial. % 22.56/22.66 (* end of lemma zenon_L2387_ *) % 22.56/22.66 assert (zenon_L2388_ : ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((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 (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (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) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H44 zenon_H11a zenon_H15d zenon_H111 zenon_Hb2 zenon_H7d zenon_Hb1 zenon_Hb6 zenon_Ha5 zenon_H5d zenon_Ha0 zenon_H125 zenon_H55 zenon_H1cf zenon_H1bb zenon_H1b7 zenon_H1c6 zenon_H1cb zenon_H20f zenon_H129 zenon_H195 zenon_H139 zenon_H196 zenon_H177 zenon_H77 zenon_H94 zenon_H27e zenon_H6d zenon_H190 zenon_H4e zenon_Ha9 zenon_Hf5 zenon_H13a zenon_H68 zenon_H82 zenon_H4c zenon_H15c zenon_Hf0 zenon_H158 zenon_H48 zenon_Hac zenon_H13b zenon_H173 zenon_H179 zenon_H1fe zenon_H109 zenon_H1a2 zenon_H1cd zenon_H1ef zenon_Hfa zenon_H141 zenon_H117 zenon_He4 zenon_H1d5 zenon_H6f zenon_H236 zenon_H40 zenon_H131 zenon_H105 zenon_Heb zenon_H18a zenon_H1a8 zenon_H1c3 zenon_H189 zenon_H19a zenon_H169. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.56/22.66 apply (zenon_L2357_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.66 apply (zenon_L2078_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.56/22.66 apply (zenon_L20_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.66 apply (zenon_L41_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.66 apply (zenon_L55_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.56/22.66 apply (zenon_L41_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.56/22.66 apply (zenon_L42_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.66 exact (zenon_H40 zenon_H3f). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.66 exact (zenon_H1d4 zenon_H4d). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.56/22.66 apply (zenon_L193_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.56/22.66 apply (zenon_L83_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.56/22.66 apply (zenon_L366_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H115 | zenon_intro zenon_H27f ]. % 22.56/22.66 apply (zenon_L2374_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H128 | zenon_intro zenon_H280 ]. % 22.56/22.66 apply (zenon_L149_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H93 | zenon_intro zenon_Hb9 ]. % 22.56/22.66 apply (zenon_L215_); trivial. % 22.56/22.66 apply (zenon_L47_); trivial. % 22.56/22.66 apply (zenon_L221_); trivial. % 22.56/22.66 apply (zenon_L262_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.56/22.66 apply (zenon_L34_); trivial. % 22.56/22.66 apply (zenon_L71_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.66 apply (zenon_L148_); trivial. % 22.56/22.66 apply (zenon_L461_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.66 apply (zenon_L464_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.66 apply (zenon_L2375_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.66 apply (zenon_L1609_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.66 exact (zenon_H40 zenon_H3f). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.66 exact (zenon_H1d4 zenon_H4d). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.66 apply (zenon_L171_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.66 apply (zenon_L61_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.66 apply (zenon_L2377_); trivial. % 22.56/22.66 apply (zenon_L206_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.56/22.66 apply (zenon_L171_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.56/22.66 apply (zenon_L34_); trivial. % 22.56/22.66 apply (zenon_L71_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.66 apply (zenon_L239_); trivial. % 22.56/22.66 apply (zenon_L2360_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.66 apply (zenon_L1394_); trivial. % 22.56/22.66 apply (zenon_L2378_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.66 apply (zenon_L2379_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.66 apply (zenon_L1393_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.66 apply (zenon_L171_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.66 apply (zenon_L61_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.66 apply (zenon_L2380_); trivial. % 22.56/22.66 apply (zenon_L299_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.66 apply (zenon_L214_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.66 apply (zenon_L2381_); trivial. % 22.56/22.66 apply (zenon_L165_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.66 apply (zenon_L148_); trivial. % 22.56/22.66 apply (zenon_L461_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.66 apply (zenon_L1394_); trivial. % 22.56/22.66 apply (zenon_L2378_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.56/22.66 apply (zenon_L2357_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.66 apply (zenon_L2078_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.56/22.66 apply (zenon_L20_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.66 apply (zenon_L41_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.66 apply (zenon_L55_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.66 apply (zenon_L2385_); trivial. % 22.56/22.66 apply (zenon_L262_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.56/22.66 apply (zenon_L34_); trivial. % 22.56/22.66 apply (zenon_L71_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.66 apply (zenon_L148_); trivial. % 22.56/22.66 apply (zenon_L2360_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.66 apply (zenon_L304_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.66 apply (zenon_L2386_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.66 apply (zenon_L2379_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.66 exact (zenon_H4c zenon_H47). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.66 exact (zenon_H7a zenon_H3c). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.66 apply (zenon_L1393_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.66 apply (zenon_L171_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.66 exact (zenon_H1b3 zenon_Hef). % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.66 apply (zenon_L2380_); trivial. % 22.56/22.66 apply (zenon_L299_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.66 apply (zenon_L214_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.66 apply (zenon_L2381_); trivial. % 22.56/22.66 apply (zenon_L165_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.66 apply (zenon_L148_); trivial. % 22.56/22.66 apply (zenon_L246_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.66 apply (zenon_L1394_); trivial. % 22.56/22.66 apply (zenon_L2387_); trivial. % 22.56/22.66 apply (zenon_L385_); trivial. % 22.56/22.66 (* end of lemma zenon_L2388_ *) % 22.56/22.66 assert (zenon_L2389_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((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 (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.56/22.66 do 0 intro. intros zenon_H36 zenon_H4c zenon_H12e zenon_H105 zenon_H104 zenon_H192 zenon_H48 zenon_H111 zenon_H15d zenon_Hac. % 22.56/22.66 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.56/22.66 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.56/22.66 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.56/22.66 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.56/22.66 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.56/22.66 exact (zenon_H1c7 zenon_Hac). % 22.56/22.66 apply (zenon_L2350_); trivial. % 22.56/22.66 (* end of lemma zenon_L2389_ *) % 22.56/22.66 assert (zenon_L2390_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((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) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((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)) = (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) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((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 (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (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) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.56/22.66 do 0 intro. intros zenon_H240 zenon_H3c zenon_H195 zenon_Hac zenon_H6d zenon_H3a zenon_H23d zenon_H4c zenon_H236 zenon_H3d zenon_H48 zenon_H1f zenon_H264 zenon_Hcc zenon_H5d zenon_H13c zenon_H186 zenon_H1a8 zenon_H189 zenon_H82 zenon_H4e zenon_Hb2 zenon_H100 zenon_H109 zenon_H22d zenon_H94 zenon_H156 zenon_He4 zenon_H1cb zenon_H55 zenon_H164 zenon_H125 zenon_H139 zenon_Hb6 zenon_Ha0 zenon_H1c6 zenon_Ha9 zenon_H11a zenon_H177 zenon_H121 zenon_H117 zenon_H196 zenon_Hfa zenon_H73 zenon_H68 zenon_H1ef zenon_H1a2 zenon_H13b zenon_H13a zenon_H6f zenon_H192 zenon_H111 zenon_Hf5 zenon_H15d zenon_H19d zenon_H1cf zenon_H1c3 zenon_H20f zenon_H1bb zenon_H212 zenon_Hbc zenon_H7d zenon_H18a zenon_H19a zenon_H190 zenon_H20b zenon_H129 zenon_H163 zenon_H1b4 zenon_H183 zenon_H140 zenon_H179 zenon_H104 zenon_H1fe zenon_H77 zenon_H1fb zenon_H1d8 zenon_H173 zenon_Hf0 zenon_H158 zenon_H131 zenon_Heb zenon_H230 zenon_H105 zenon_H234 zenon_H290 zenon_H23b. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.66 apply (zenon_L2353_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.66 exact (zenon_H1f zenon_H1e). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.66 apply (zenon_L318_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.66 exact (zenon_H1f zenon_H1e). % 22.56/22.66 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.66 apply (zenon_L25_); trivial. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.66 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.66 exact (zenon_H6c zenon_H67). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_L21_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_L264_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.56/22.67 apply (zenon_L24_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.56/22.67 apply (zenon_L61_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.56/22.67 apply (zenon_L46_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.56/22.67 apply (zenon_L79_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.56/22.67 apply (zenon_L436_); trivial. % 22.56/22.67 apply (zenon_L1394_); trivial. % 22.56/22.67 apply (zenon_L63_); trivial. % 22.56/22.67 apply (zenon_L1847_); trivial. % 22.56/22.67 exact (zenon_H238 zenon_H38). % 22.56/22.67 apply (zenon_L1861_); trivial. % 22.56/22.67 (* end of lemma zenon_L2390_ *) % 22.56/22.67 assert (zenon_L2391_ : (((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)) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H125 zenon_H1d5 zenon_H66 zenon_H68 zenon_H94 zenon_H93 zenon_Hb2 zenon_Ha4 zenon_Ha0 zenon_H25 zenon_H1ef zenon_H110 zenon_Ha9. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.56/22.67 apply (zenon_L252_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.56/22.67 apply (zenon_L171_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.56/22.67 apply (zenon_L38_); trivial. % 22.56/22.67 apply (zenon_L597_); trivial. % 22.56/22.67 (* end of lemma zenon_L2391_ *) % 22.56/22.67 assert (zenon_L2392_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H139 zenon_H77 zenon_H47 zenon_H2a zenon_Ha9 zenon_H110 zenon_H1ef zenon_H25 zenon_Ha0 zenon_Ha4 zenon_Hb2 zenon_H94 zenon_H68 zenon_H1d5 zenon_H125 zenon_H93 zenon_H196. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 apply (zenon_L251_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_L147_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_L2391_); trivial. % 22.56/22.67 apply (zenon_L167_); trivial. % 22.56/22.67 (* end of lemma zenon_L2392_ *) % 22.56/22.67 assert (zenon_L2393_ : (((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 (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H13c zenon_H179 zenon_H9d zenon_H159 zenon_H131 zenon_H110 zenon_H9e zenon_Hf5. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.56/22.67 apply (zenon_L123_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.56/22.67 exact (zenon_H159 zenon_H10c). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.56/22.67 apply (zenon_L259_); trivial. % 22.56/22.67 apply (zenon_L262_); trivial. % 22.56/22.67 (* end of lemma zenon_L2393_ *) % 22.56/22.67 assert (zenon_L2394_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((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 (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H13a zenon_H2a zenon_Hb6 zenon_H153 zenon_Hb2 zenon_Ha4 zenon_Ha0 zenon_H25 zenon_H1ef zenon_H13c zenon_H179 zenon_H159 zenon_H131 zenon_H110 zenon_Hf5. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.67 apply (zenon_L53_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.67 apply (zenon_L95_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.56/22.67 apply (zenon_L116_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.56/22.67 apply (zenon_L282_); trivial. % 22.56/22.67 apply (zenon_L2393_); trivial. % 22.56/22.67 (* end of lemma zenon_L2394_ *) % 22.56/22.67 assert (zenon_L2395_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> False). % 22.56/22.67 do 0 intro. intros zenon_H92 zenon_H110 zenon_H93. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.56/22.67 exact (zenon_H16b zenon_H93). % 22.56/22.67 exact (zenon_H191 zenon_H110). % 22.56/22.67 (* end of lemma zenon_L2395_ *) % 22.56/22.67 assert (zenon_L2396_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> False). % 22.56/22.67 do 0 intro. intros zenon_H2f zenon_H110 zenon_H93. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.56/22.67 apply (zenon_L2395_); trivial. % 22.56/22.67 (* end of lemma zenon_L2396_ *) % 22.56/22.67 assert (zenon_L2397_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H36 zenon_H48 zenon_H18d zenon_H1b7 zenon_H77 zenon_H1b4 zenon_H20f zenon_H129 zenon_H93 zenon_Hc4 zenon_H1bb zenon_H1cb zenon_H231 zenon_H110 zenon_H104 zenon_H18a zenon_H24e zenon_H1cd zenon_H7d zenon_H12e zenon_Hbc. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.56/22.67 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.56/22.67 apply (zenon_L1514_); trivial. % 22.56/22.67 (* end of lemma zenon_L2397_ *) % 22.56/22.67 assert (zenon_L2398_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H236 zenon_H1f zenon_H48 zenon_H237 zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_H111 zenon_H110 zenon_Ha0. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.67 exact (zenon_H1f zenon_H1e). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.67 apply (zenon_L65_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.67 exact (zenon_H237 zenon_H31). % 22.56/22.67 apply (zenon_L1842_); trivial. % 22.56/22.67 (* end of lemma zenon_L2398_ *) % 22.56/22.67 assert (zenon_L2399_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H204 zenon_H23d zenon_H236 zenon_Ha4 zenon_Hb6 zenon_H111 zenon_H110 zenon_Ha0 zenon_H13a zenon_H3d zenon_H48 zenon_H1f zenon_Ha9 zenon_H77 zenon_H68 zenon_H196 zenon_H93 zenon_H139 zenon_H240. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.67 apply (zenon_L2398_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.67 exact (zenon_H1f zenon_H1e). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.67 exact (zenon_H205 zenon_H2a). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 exact (zenon_H6c zenon_H67). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_L214_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_L264_); trivial. % 22.56/22.67 apply (zenon_L167_); trivial. % 22.56/22.67 apply (zenon_L1857_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.56/22.67 apply (zenon_L2398_); trivial. % 22.56/22.67 apply (zenon_L1861_); trivial. % 22.56/22.67 (* end of lemma zenon_L2399_ *) % 22.56/22.67 assert (zenon_L2400_ : ((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H1d zenon_H240 zenon_H139 zenon_H93 zenon_H196 zenon_H68 zenon_H77 zenon_Ha9 zenon_H48 zenon_H3d zenon_H13a zenon_Ha0 zenon_H110 zenon_H111 zenon_Hb6 zenon_Ha4 zenon_H236 zenon_H23d zenon_H204. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.56/22.67 apply (zenon_L2399_); trivial. % 22.56/22.67 apply (zenon_L2399_); trivial. % 22.56/22.67 (* end of lemma zenon_L2400_ *) % 22.56/22.67 assert (zenon_L2401_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> False). % 22.56/22.67 do 0 intro. intros zenon_H5a zenon_H110 zenon_H93. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.56/22.67 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.56/22.67 apply (zenon_L2395_); trivial. % 22.56/22.67 (* end of lemma zenon_L2401_ *) % 22.56/22.67 assert (zenon_L2402_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H140 zenon_H162 zenon_H177 zenon_H26d zenon_H1b7 zenon_H179 zenon_H164 zenon_H25 zenon_H4e zenon_H110 zenon_H19a zenon_Ha0 zenon_H9e zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H1cb. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.56/22.67 apply (zenon_L2168_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.56/22.67 apply (zenon_L274_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.56/22.67 apply (zenon_L278_); trivial. % 22.56/22.67 apply (zenon_L267_); trivial. % 22.56/22.67 (* end of lemma zenon_L2402_ *) % 22.56/22.67 assert (zenon_L2403_ : (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H2a zenon_Hb6 zenon_H153 zenon_H140 zenon_H162 zenon_H177 zenon_H26d zenon_H1b7 zenon_H179 zenon_H164 zenon_H25 zenon_H4e zenon_H110 zenon_H19a zenon_Ha0 zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H1cb. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.67 apply (zenon_L53_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.67 apply (zenon_L95_); trivial. % 22.56/22.67 apply (zenon_L2402_); trivial. % 22.56/22.67 (* end of lemma zenon_L2403_ *) % 22.56/22.67 assert (zenon_L2404_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (((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 (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H153 zenon_H164 zenon_H2d zenon_H109 zenon_H2a zenon_H192 zenon_H1cb zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_Ha0 zenon_H19a zenon_H162. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.67 apply (zenon_L53_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.67 apply (zenon_L95_); trivial. % 22.56/22.67 apply (zenon_L2164_); trivial. % 22.56/22.67 (* end of lemma zenon_L2404_ *) % 22.56/22.67 assert (zenon_L2405_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (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)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H1fe zenon_H140 zenon_H177 zenon_H26d zenon_H179 zenon_H4e zenon_Hf5 zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H164 zenon_H109 zenon_H2a zenon_H192 zenon_H1cb zenon_Ha0 zenon_H162 zenon_H139 zenon_H195 zenon_H266 zenon_H55 zenon_H6f zenon_H110 zenon_H190 zenon_H1f1 zenon_H13f zenon_Ha9 zenon_H196 zenon_H15d zenon_H19a zenon_H1b7 zenon_H7f zenon_H77 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_H18a. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.67 apply (zenon_L2161_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 apply (zenon_L251_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_L147_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.67 apply (zenon_L53_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.67 apply (zenon_L193_); trivial. % 22.56/22.67 apply (zenon_L2402_); trivial. % 22.56/22.67 apply (zenon_L167_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.67 apply (zenon_L146_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.67 apply (zenon_L2403_); trivial. % 22.56/22.67 apply (zenon_L192_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 apply (zenon_L251_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_L2131_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_L2165_); trivial. % 22.56/22.67 apply (zenon_L167_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.67 apply (zenon_L65_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.67 apply (zenon_L2404_); trivial. % 22.56/22.67 apply (zenon_L192_); trivial. % 22.56/22.67 apply (zenon_L1343_); trivial. % 22.56/22.67 (* end of lemma zenon_L2405_ *) % 22.56/22.67 assert (zenon_L2406_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (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 (e1) (e3)) = (e1)) -> (((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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((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) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (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) (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))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.56/22.67 do 0 intro. intros zenon_Hc8 zenon_H109 zenon_H179 zenon_H26d zenon_H68 zenon_H1fe zenon_H18d zenon_H1b7 zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H1bb zenon_H18a zenon_H19a zenon_H139 zenon_H93 zenon_H196 zenon_H1f1 zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H195 zenon_H13f zenon_H77 zenon_Ha0 zenon_H1ef zenon_H110 zenon_Hb2 zenon_Hf5 zenon_H5c zenon_H15d zenon_Hfa zenon_H173 zenon_H4e zenon_H13a zenon_H234 zenon_H141 zenon_H2c zenon_H164 zenon_H7d zenon_Hbc zenon_H212 zenon_H1cb zenon_H33 zenon_He4 zenon_H177 zenon_H1cf zenon_H140 zenon_Hb6 zenon_Ha9 zenon_Ha4 zenon_H7f zenon_H192 zenon_H48 zenon_Hf0 zenon_H189 zenon_H1a8 zenon_H61 zenon_H236. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.56/22.67 apply (zenon_L2140_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.67 apply (zenon_L2161_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.67 apply (zenon_L2405_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.67 apply (zenon_L2170_); trivial. % 22.56/22.67 apply (zenon_L1717_); trivial. % 22.56/22.67 (* end of lemma zenon_L2406_ *) % 22.56/22.67 assert (zenon_L2407_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 22.56/22.67 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H6e zenon_H111 zenon_H110 zenon_Hb6 zenon_H155. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.67 apply (zenon_L110_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.67 apply (zenon_L75_); trivial. % 22.56/22.67 apply (zenon_L115_); trivial. % 22.56/22.67 (* end of lemma zenon_L2407_ *) % 22.56/22.67 assert (zenon_L2408_ : (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (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 (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (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) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H77 zenon_Hb2 zenon_Hf5 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H19a zenon_Ha0 zenon_H48 zenon_H1cb zenon_H1b7 zenon_H33 zenon_H164 zenon_H141 zenon_H2c zenon_H234 zenon_He4 zenon_H15d zenon_H73 zenon_H18d zenon_H120 zenon_Heb zenon_H1ef zenon_H209 zenon_H139 zenon_H68 zenon_H1e zenon_Hb6 zenon_H110 zenon_H111 zenon_Ha9 zenon_Ha4 zenon_H13a zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.67 apply (zenon_L13_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.67 apply (zenon_L215_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 apply (zenon_L20_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.67 apply (zenon_L110_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.67 apply (zenon_L75_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.67 apply (zenon_L46_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.67 apply (zenon_L540_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.67 apply (zenon_L184_); trivial. % 22.56/22.67 apply (zenon_L2133_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.56/22.67 apply (zenon_L282_); trivial. % 22.56/22.67 exact (zenon_H209 zenon_H9d). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_L94_); trivial. % 22.56/22.67 apply (zenon_L167_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 apply (zenon_L20_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_L2407_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_L122_); trivial. % 22.56/22.67 apply (zenon_L167_); trivial. % 22.56/22.67 (* end of lemma zenon_L2408_ *) % 22.56/22.67 assert (zenon_L2409_ : (((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)) -> (~((op (e3) (e0)) = (e3))) -> False). % 22.56/22.67 do 0 intro. intros zenon_Hb2 zenon_Ha4 zenon_Hb6 zenon_H3c zenon_H1ef zenon_H110 zenon_H209. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.56/22.67 apply (zenon_L46_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.56/22.67 apply (zenon_L282_); trivial. % 22.56/22.67 exact (zenon_H209 zenon_H9d). % 22.56/22.67 (* end of lemma zenon_L2409_ *) % 22.56/22.67 assert (zenon_L2410_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 22.56/22.67 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H6e zenon_Ha0 zenon_H31 zenon_Hb6 zenon_H155. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.67 apply (zenon_L110_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.67 apply (zenon_L68_); trivial. % 22.56/22.67 apply (zenon_L115_); trivial. % 22.56/22.67 (* end of lemma zenon_L2410_ *) % 22.56/22.67 assert (zenon_L2411_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H15d zenon_H177 zenon_H160 zenon_H77 zenon_H48 zenon_H139 zenon_H1e zenon_Hb6 zenon_Ha0 zenon_Ha9 zenon_Ha4 zenon_H13a zenon_H68 zenon_H31 zenon_H93 zenon_H196. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.67 apply (zenon_L13_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.67 apply (zenon_L215_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.67 apply (zenon_L239_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 apply (zenon_L20_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_L2410_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_L264_); trivial. % 22.56/22.67 apply (zenon_L167_); trivial. % 22.56/22.67 (* end of lemma zenon_L2411_ *) % 22.56/22.67 assert (zenon_L2412_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H139 zenon_H47 zenon_H77 zenon_H266 zenon_H2d zenon_H55 zenon_H6f zenon_H110 zenon_H190 zenon_H5c zenon_H186 zenon_H31 zenon_H48 zenon_H201 zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 apply (zenon_L251_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_L2180_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_L122_); trivial. % 22.56/22.67 apply (zenon_L167_); trivial. % 22.56/22.67 (* end of lemma zenon_L2412_ *) % 22.56/22.67 assert (zenon_L2413_ : (~((op (e3) (e0)) = (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)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((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 (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H209 zenon_H110 zenon_H1ef zenon_Heb zenon_Hf0 zenon_H13f zenon_H120 zenon_Hb6 zenon_H18d zenon_H139 zenon_H47 zenon_H77 zenon_H266 zenon_H2d zenon_H55 zenon_H6f zenon_H190 zenon_H186 zenon_H31 zenon_H48 zenon_H201 zenon_Ha4 zenon_Hb2 zenon_H111 zenon_Ha9 zenon_H13a zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 apply (zenon_L251_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.67 apply (zenon_L110_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.67 apply (zenon_L75_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.67 apply (zenon_L46_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.56/22.67 apply (zenon_L217_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.56/22.67 apply (zenon_L118_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.56/22.67 apply (zenon_L2130_); trivial. % 22.56/22.67 apply (zenon_L218_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.67 apply (zenon_L302_); trivial. % 22.56/22.67 apply (zenon_L2412_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.56/22.67 apply (zenon_L282_); trivial. % 22.56/22.67 exact (zenon_H209 zenon_H9d). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_L122_); trivial. % 22.56/22.67 apply (zenon_L167_); trivial. % 22.56/22.67 (* end of lemma zenon_L2413_ *) % 22.56/22.67 assert (zenon_L2414_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H139 zenon_H77 zenon_H47 zenon_H155 zenon_Hb6 zenon_H31 zenon_Ha0 zenon_Ha9 zenon_Ha4 zenon_H13a zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 apply (zenon_L251_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_L2410_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_L122_); trivial. % 22.56/22.67 apply (zenon_L167_); trivial. % 22.56/22.67 (* end of lemma zenon_L2414_ *) % 22.56/22.67 assert (zenon_L2415_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((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)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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)) = (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))))) -> (~((e0) = (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) (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e0)) = (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)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H236 zenon_H19a zenon_H1cb zenon_H192 zenon_Hf5 zenon_H1b7 zenon_H33 zenon_H141 zenon_H2c zenon_H234 zenon_He4 zenon_H73 zenon_H160 zenon_H209 zenon_Hbc zenon_H7d zenon_H18a zenon_H212 zenon_H12e zenon_H15d zenon_H68 zenon_Heb zenon_Hf0 zenon_H13f zenon_H266 zenon_H55 zenon_H6f zenon_H190 zenon_H186 zenon_H201 zenon_H82 zenon_H1ef zenon_Hb2 zenon_H139 zenon_H121 zenon_Ha0 zenon_H1a3 zenon_H164 zenon_Hb6 zenon_H110 zenon_H111 zenon_Ha9 zenon_Ha4 zenon_H13a zenon_H177 zenon_H196 zenon_H1fe zenon_H18d zenon_H48 zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H93 zenon_H77 zenon_H120. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.56/22.67 apply (zenon_L2408_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.67 apply (zenon_L2408_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.67 apply (zenon_L2129_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.67 apply (zenon_L352_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.67 apply (zenon_L65_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.67 apply (zenon_L352_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.67 apply (zenon_L2409_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.67 apply (zenon_L217_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.67 apply (zenon_L53_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.67 apply (zenon_L95_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.56/22.67 apply (zenon_L46_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.56/22.67 apply (zenon_L219_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.56/22.67 apply (zenon_L302_); trivial. % 22.56/22.67 apply (zenon_L2152_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.56/22.67 apply (zenon_L282_); trivial. % 22.56/22.67 exact (zenon_H209 zenon_H9d). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_L147_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_L94_); trivial. % 22.56/22.67 apply (zenon_L167_); trivial. % 22.56/22.67 apply (zenon_L596_); trivial. % 22.56/22.67 apply (zenon_L528_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.56/22.67 apply (zenon_L2411_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.56/22.67 apply (zenon_L2129_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.56/22.67 apply (zenon_L2413_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.67 apply (zenon_L2413_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.67 apply (zenon_L2409_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.67 apply (zenon_L217_); trivial. % 22.56/22.67 apply (zenon_L1931_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.56/22.67 apply (zenon_L239_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.56/22.67 apply (zenon_L2414_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.56/22.67 apply (zenon_L2409_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.56/22.67 apply (zenon_L217_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 apply (zenon_L548_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.56/22.67 apply (zenon_L2407_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.56/22.67 apply (zenon_L122_); trivial. % 22.56/22.67 apply (zenon_L167_); trivial. % 22.56/22.67 apply (zenon_L528_); trivial. % 22.56/22.67 apply (zenon_L555_); trivial. % 22.56/22.67 (* end of lemma zenon_L2415_ *) % 22.56/22.67 assert (zenon_L2416_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H19a zenon_Ha0 zenon_H9e zenon_Hc4 zenon_H181 zenon_H120 zenon_H20f zenon_H1bb zenon_H93 zenon_H68 zenon_H34 zenon_H18a. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.56/22.67 apply (zenon_L156_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.56/22.67 apply (zenon_L422_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.56/22.67 apply (zenon_L158_); trivial. % 22.56/22.67 apply (zenon_L416_); trivial. % 22.56/22.67 (* end of lemma zenon_L2416_ *) % 22.56/22.67 assert (zenon_L2417_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_H111 zenon_H110 zenon_H19a zenon_Ha0 zenon_Hc4 zenon_H181 zenon_H120 zenon_H20f zenon_H1bb zenon_H93 zenon_H68 zenon_H34 zenon_H18a. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.67 apply (zenon_L55_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.56/22.67 apply (zenon_L75_); trivial. % 22.56/22.67 apply (zenon_L2416_); trivial. % 22.56/22.67 (* end of lemma zenon_L2417_ *) % 22.56/22.67 assert (zenon_L2418_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H19a zenon_H48 zenon_H155 zenon_Hc4 zenon_H181 zenon_H120 zenon_H20f zenon_H1bb zenon_H93 zenon_H68 zenon_H34 zenon_H18a. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.56/22.67 apply (zenon_L246_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.56/22.67 apply (zenon_L422_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.56/22.67 apply (zenon_L158_); trivial. % 22.56/22.67 apply (zenon_L416_); trivial. % 22.56/22.67 (* end of lemma zenon_L2418_ *) % 22.56/22.67 assert (zenon_L2419_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((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))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H1a8 zenon_Ha9 zenon_Hdb zenon_H7e zenon_H67 zenon_H177 zenon_H31 zenon_H19a zenon_H77 zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H120 zenon_H20f zenon_H1bb zenon_H93 zenon_H68 zenon_H164 zenon_H189 zenon_H99 zenon_H160 zenon_H1cd. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.56/22.67 apply (zenon_L110_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.56/22.67 apply (zenon_L864_); trivial. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.56/22.67 apply (zenon_L458_); trivial. % 22.56/22.67 apply (zenon_L240_); trivial. % 22.56/22.67 (* end of lemma zenon_L2419_ *) % 22.56/22.67 assert (zenon_L2420_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.56/22.67 do 0 intro. intros zenon_H139 zenon_H110 zenon_H111 zenon_H1a8 zenon_H7e zenon_H19a zenon_H77 zenon_H1b4 zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H181 zenon_H120 zenon_H20f zenon_H1bb zenon_H68 zenon_H164 zenon_H189 zenon_H99 zenon_H1cd zenon_H155 zenon_Hb6 zenon_H31 zenon_Ha0 zenon_Ha9 zenon_Ha4 zenon_H13a zenon_H160 zenon_H177 zenon_H93 zenon_H196. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.56/22.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.56/22.67 exact (zenon_Ha4 zenon_H9f). % 22.56/22.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.56/22.67 apply (zenon_L2419_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.67 apply (zenon_L75_); trivial. % 22.64/22.67 apply (zenon_L115_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.67 apply (zenon_L2410_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.67 apply (zenon_L122_); trivial. % 22.64/22.67 apply (zenon_L167_); trivial. % 22.64/22.67 (* end of lemma zenon_L2420_ *) % 22.64/22.67 assert (zenon_L2421_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H1c6 zenon_Ha9 zenon_H6e zenon_H159 zenon_H190 zenon_H110 zenon_H1c7. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.67 apply (zenon_L110_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.67 exact (zenon_H159 zenon_H10c). % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.67 apply (zenon_L163_); trivial. % 22.64/22.67 exact (zenon_H1c7 zenon_Hac). % 22.64/22.67 (* end of lemma zenon_L2421_ *) % 22.64/22.67 assert (zenon_L2422_ : (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H13c zenon_H179 zenon_H9d zenon_H159 zenon_H131 zenon_H110 zenon_H19a zenon_H48 zenon_H155 zenon_Ha0 zenon_H93 zenon_H68 zenon_H162. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.67 apply (zenon_L123_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.67 exact (zenon_H159 zenon_H10c). % 22.64/22.67 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.67 apply (zenon_L259_); trivial. % 22.64/22.67 apply (zenon_L247_); trivial. % 22.64/22.67 (* end of lemma zenon_L2422_ *) % 22.64/22.67 assert (zenon_L2423_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (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 (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H121 zenon_H162 zenon_H68 zenon_H93 zenon_Ha0 zenon_H155 zenon_H48 zenon_H19a zenon_H131 zenon_H159 zenon_H179 zenon_H13c zenon_H1c7 zenon_H104 zenon_H110 zenon_Hc4. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H9d | zenon_intro zenon_H122 ]. % 22.64/22.67 apply (zenon_L2422_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hac | zenon_intro zenon_H123 ]. % 22.64/22.67 exact (zenon_H1c7 zenon_Hac). % 22.64/22.67 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc3 ]. % 22.64/22.67 apply (zenon_L129_); trivial. % 22.64/22.67 exact (zenon_Hc4 zenon_Hc3). % 22.64/22.67 (* end of lemma zenon_L2423_ *) % 22.64/22.67 assert (zenon_L2424_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H139 zenon_Ha0 zenon_H110 zenon_H111 zenon_Ha9 zenon_H47 zenon_Hb6 zenon_H13a zenon_H153 zenon_H77 zenon_H38 zenon_H68. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.67 apply (zenon_L251_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.67 apply (zenon_L2017_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.67 apply (zenon_L94_); trivial. % 22.64/22.67 apply (zenon_L165_); trivial. % 22.64/22.67 (* end of lemma zenon_L2424_ *) % 22.64/22.67 assert (zenon_L2425_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e2)) = (e3)) -> False). % 22.64/22.67 do 0 intro. intros zenon_H1bb zenon_H129 zenon_H5c zenon_H20f zenon_H38 zenon_H1b4 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H110. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H191 | zenon_intro zenon_H93 ]. % 22.64/22.67 exact (zenon_H191 zenon_H110). % 22.64/22.67 apply (zenon_L1236_); trivial. % 22.64/22.67 (* end of lemma zenon_L2425_ *) % 22.64/22.67 assert (zenon_L2426_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H177 zenon_Hb6 zenon_H110 zenon_H1ef zenon_H25 zenon_Ha0 zenon_H121 zenon_H33 zenon_H1c7 zenon_H104 zenon_Hc4 zenon_Hb2 zenon_H100 zenon_H160 zenon_H26a zenon_H93 zenon_H159 zenon_H179 zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H111 zenon_H82 zenon_H38 zenon_H48. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.67 apply (zenon_L2018_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.67 apply (zenon_L1300_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.67 apply (zenon_L2424_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.67 apply (zenon_L25_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.67 apply (zenon_L819_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.67 apply (zenon_L116_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.67 apply (zenon_L282_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.67 apply (zenon_L69_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.67 apply (zenon_L123_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.67 exact (zenon_H159 zenon_H10c). % 22.64/22.67 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.64/22.67 apply (zenon_L246_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.64/22.67 apply (zenon_L2425_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.64/22.67 apply (zenon_L218_); trivial. % 22.64/22.67 apply (zenon_L1699_); trivial. % 22.64/22.67 apply (zenon_L525_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.67 apply (zenon_L184_); trivial. % 22.64/22.67 apply (zenon_L2425_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.67 apply (zenon_L819_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.67 apply (zenon_L116_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.67 apply (zenon_L282_); trivial. % 22.64/22.67 apply (zenon_L134_); trivial. % 22.64/22.67 apply (zenon_L246_); trivial. % 22.64/22.67 (* end of lemma zenon_L2426_ *) % 22.64/22.67 assert (zenon_L2427_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (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 (e1) (e2)) = (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 (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 (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (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 (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e2)) = (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 (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (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))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (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)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H1fe zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H94 zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_H117 zenon_H236 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H196 zenon_H13c zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H131 zenon_H4e zenon_H1cf zenon_H283 zenon_H179 zenon_H159 zenon_H26a zenon_H100 zenon_H1ef zenon_H82 zenon_H68 zenon_Ha9 zenon_H139 zenon_He4 zenon_H195 zenon_H163 zenon_H189 zenon_H5d zenon_Hfa zenon_H13a zenon_Hb2 zenon_H110 zenon_H104 zenon_H33 zenon_H121 zenon_H73 zenon_H13f zenon_Hf0 zenon_H111 zenon_Heb zenon_Ha0 zenon_Hb6 zenon_H177 zenon_H15d zenon_H12e zenon_H77 zenon_H93 zenon_H38 zenon_H1b4 zenon_H20f zenon_H129 zenon_H48 zenon_H18d zenon_Hc4 zenon_H1cb zenon_H18a zenon_H1bb zenon_H24e zenon_H7d zenon_H1b7 zenon_H1cd zenon_H160 zenon_H1c7. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.67 apply (zenon_L2018_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.67 apply (zenon_L1300_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.67 apply (zenon_L20_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.67 apply (zenon_L2257_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.67 apply (zenon_L94_); trivial. % 22.64/22.67 apply (zenon_L167_); trivial. % 22.64/22.67 apply (zenon_L246_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.67 apply (zenon_L2426_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.67 apply (zenon_L2018_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.67 apply (zenon_L1300_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.67 apply (zenon_L2424_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.67 apply (zenon_L819_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.67 apply (zenon_L1911_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.67 apply (zenon_L95_); trivial. % 22.64/22.67 apply (zenon_L156_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.67 apply (zenon_L217_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.67 apply (zenon_L819_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.67 apply (zenon_L46_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.67 apply (zenon_L219_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.67 apply (zenon_L184_); trivial. % 22.64/22.67 apply (zenon_L413_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.67 apply (zenon_L67_); trivial. % 22.64/22.67 apply (zenon_L134_); trivial. % 22.64/22.67 apply (zenon_L246_); trivial. % 22.64/22.67 apply (zenon_L1510_); trivial. % 22.64/22.67 (* end of lemma zenon_L2427_ *) % 22.64/22.67 assert (zenon_L2428_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 22.64/22.67 do 0 intro. intros zenon_Hc0 zenon_H110 zenon_H104. % 22.64/22.67 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.64/22.67 apply (zenon_L129_); trivial. % 22.64/22.67 (* end of lemma zenon_L2428_ *) % 22.64/22.67 assert (zenon_L2429_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (~((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) (e2)) = (op (e2) (e2)))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H1ec zenon_H25 zenon_H4e zenon_H186 zenon_H5c zenon_H167 zenon_H68 zenon_H163 zenon_H7f zenon_H77 zenon_Ha9 zenon_H9d zenon_H183 zenon_H110 zenon_H131. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H1ed ]. % 22.64/22.67 apply (zenon_L274_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H4d | zenon_intro zenon_H1ee ]. % 22.64/22.67 apply (zenon_L138_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H72 | zenon_intro zenon_H133 ]. % 22.64/22.67 apply (zenon_L1815_); trivial. % 22.64/22.67 apply (zenon_L259_); trivial. % 22.64/22.67 (* end of lemma zenon_L2429_ *) % 22.64/22.67 assert (zenon_L2430_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (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 (e2) (e3)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (~((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) (e2)) = (op (e2) (e2)))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H19a zenon_H1b7 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H48 zenon_H93 zenon_H1ec zenon_H25 zenon_H4e zenon_H186 zenon_H5c zenon_H68 zenon_H163 zenon_H7f zenon_H77 zenon_Ha9 zenon_H9d zenon_H183 zenon_H110 zenon_H131. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.64/22.67 apply (zenon_L1276_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.64/22.67 apply (zenon_L157_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.64/22.67 apply (zenon_L158_); trivial. % 22.64/22.67 apply (zenon_L2429_); trivial. % 22.64/22.67 (* end of lemma zenon_L2430_ *) % 22.64/22.67 assert (zenon_L2431_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H82 zenon_H28 zenon_H131 zenon_H110 zenon_H183 zenon_Ha9 zenon_H163 zenon_H186 zenon_H4e zenon_H25 zenon_H1ec zenon_H18d zenon_Hc4 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H1b7 zenon_H55 zenon_H40 zenon_H1d8 zenon_He4 zenon_H1ef zenon_Hb2 zenon_H139 zenon_H19a zenon_Ha0 zenon_H5c zenon_H48 zenon_H1cb zenon_H192 zenon_H18a zenon_H164 zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H68 zenon_H2a zenon_H153 zenon_H77 zenon_H93 zenon_H196. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.67 apply (zenon_L2150_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.67 apply (zenon_L26_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.67 exact (zenon_Ha4 zenon_H9f). % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.67 apply (zenon_L116_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.67 apply (zenon_L282_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.64/22.67 apply (zenon_L738_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.64/22.67 exact (zenon_H40 zenon_H3f). % 22.64/22.67 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.64/22.67 apply (zenon_L15_); trivial. % 22.64/22.67 apply (zenon_L2430_); trivial. % 22.64/22.67 apply (zenon_L2153_); trivial. % 22.64/22.67 (* end of lemma zenon_L2431_ *) % 22.64/22.67 assert (zenon_L2432_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((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). % 22.64/22.67 do 0 intro. intros zenon_H15d zenon_H125 zenon_H1d5 zenon_H94 zenon_H196 zenon_H93 zenon_H77 zenon_H2a zenon_H68 zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H164 zenon_H18a zenon_H192 zenon_H1cb zenon_H48 zenon_Ha0 zenon_H19a zenon_H139 zenon_Hb2 zenon_H1ef zenon_He4 zenon_H1d8 zenon_H40 zenon_H55 zenon_H1b7 zenon_H1bb zenon_H1b4 zenon_H20f zenon_H129 zenon_Hc4 zenon_H18d zenon_H1ec zenon_H25 zenon_H4e zenon_H186 zenon_H163 zenon_Ha9 zenon_H183 zenon_H110 zenon_H131 zenon_H28 zenon_H82 zenon_H5c zenon_Hf5. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.67 apply (zenon_L2392_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.67 apply (zenon_L65_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.67 apply (zenon_L2431_); trivial. % 22.64/22.67 apply (zenon_L192_); trivial. % 22.64/22.67 (* end of lemma zenon_L2432_ *) % 22.64/22.67 assert (zenon_L2433_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H1fe zenon_H209 zenon_H110 zenon_H1ef zenon_Hb2 zenon_H82 zenon_H5d zenon_H164 zenon_H15d zenon_H196 zenon_H177 zenon_H77 zenon_H139 zenon_H20f zenon_H1bb zenon_H1cb zenon_H160 zenon_Hc4 zenon_H192 zenon_H12e zenon_H18a zenon_H68 zenon_H93 zenon_H48 zenon_Ha0 zenon_H19a zenon_Hb6 zenon_H2a zenon_Ha4 zenon_H13a zenon_H5c zenon_Hf5. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.67 apply (zenon_L2173_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.67 apply (zenon_L2129_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.67 apply (zenon_L2174_); trivial. % 22.64/22.67 apply (zenon_L2177_); trivial. % 22.64/22.67 (* end of lemma zenon_L2433_ *) % 22.64/22.67 assert (zenon_L2434_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> False). % 22.64/22.67 do 0 intro. intros zenon_H201 zenon_H48 zenon_H31 zenon_H186 zenon_H5c zenon_H190 zenon_H110 zenon_Hef zenon_Hf0 zenon_H55 zenon_H2d zenon_H266 zenon_H77 zenon_H160. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.67 apply (zenon_L239_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.67 apply (zenon_L138_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.67 apply (zenon_L1896_); trivial. % 22.64/22.67 apply (zenon_L367_); trivial. % 22.64/22.67 (* end of lemma zenon_L2434_ *) % 22.64/22.67 assert (zenon_L2435_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H1a8 zenon_H3d zenon_H77 zenon_H266 zenon_H2d zenon_H55 zenon_Hf0 zenon_H110 zenon_H190 zenon_H5c zenon_H186 zenon_H31 zenon_H48 zenon_H201 zenon_H189 zenon_H99 zenon_H160 zenon_H1cd. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.67 apply (zenon_L214_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.67 apply (zenon_L2434_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.67 apply (zenon_L458_); trivial. % 22.64/22.67 apply (zenon_L240_); trivial. % 22.64/22.67 (* end of lemma zenon_L2435_ *) % 22.64/22.67 assert (zenon_L2436_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((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 (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H1fe zenon_H209 zenon_H1ef zenon_Hb2 zenon_H1a8 zenon_H266 zenon_H55 zenon_Hf0 zenon_H110 zenon_H190 zenon_H186 zenon_H201 zenon_H189 zenon_H99 zenon_H1cd zenon_H6f zenon_H15d zenon_H196 zenon_H93 zenon_H177 zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H19a zenon_Ha0 zenon_H68 zenon_H77 zenon_H139 zenon_H20f zenon_H1bb zenon_H18a zenon_H1cb zenon_H160 zenon_Hc4 zenon_H192 zenon_H12e zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.67 apply (zenon_L2179_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.67 apply (zenon_L2129_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.67 apply (zenon_L2412_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.67 apply (zenon_L2435_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.67 apply (zenon_L239_); trivial. % 22.64/22.67 apply (zenon_L192_); trivial. % 22.64/22.67 apply (zenon_L2186_); trivial. % 22.64/22.67 (* end of lemma zenon_L2436_ *) % 22.64/22.67 assert (zenon_L2437_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H15d zenon_H196 zenon_H177 zenon_H160 zenon_H77 zenon_H139 zenon_H162 zenon_H19a zenon_Ha0 zenon_H48 zenon_H93 zenon_H68 zenon_H1cb zenon_H192 zenon_H2a zenon_H109 zenon_H2d zenon_H164 zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H5c zenon_Hf5. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.67 apply (zenon_L352_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.67 apply (zenon_L65_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.67 apply (zenon_L2404_); trivial. % 22.64/22.67 apply (zenon_L192_); trivial. % 22.64/22.67 (* end of lemma zenon_L2437_ *) % 22.64/22.67 assert (zenon_L2438_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (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 (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.67 do 0 intro. intros zenon_H1fe zenon_H140 zenon_H26d zenon_H1b7 zenon_H179 zenon_H4e zenon_H110 zenon_H164 zenon_H109 zenon_H162 zenon_H15d zenon_H196 zenon_H177 zenon_H77 zenon_H139 zenon_H20f zenon_H1bb zenon_H1cb zenon_H160 zenon_Hc4 zenon_H192 zenon_H12e zenon_H18a zenon_H68 zenon_H93 zenon_H48 zenon_Ha0 zenon_H19a zenon_Hb6 zenon_H2a zenon_Ha4 zenon_H13a zenon_H5c zenon_Hf5. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.67 apply (zenon_L2173_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.67 apply (zenon_L352_); trivial. % 22.64/22.67 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.68 apply (zenon_L65_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.68 apply (zenon_L2403_); trivial. % 22.64/22.68 apply (zenon_L192_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.68 apply (zenon_L2437_); trivial. % 22.64/22.68 apply (zenon_L2177_); trivial. % 22.64/22.68 (* end of lemma zenon_L2438_ *) % 22.64/22.68 assert (zenon_L2439_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 22.64/22.68 do 0 intro. intros zenon_Hb2 zenon_Hb6 zenon_H47 zenon_H5d zenon_Ha5 zenon_H1ef zenon_H110 zenon_Ha9 zenon_H102. % 22.64/22.68 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.68 apply (zenon_L253_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.68 apply (zenon_L42_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.68 apply (zenon_L282_); trivial. % 22.64/22.68 apply (zenon_L91_); trivial. % 22.64/22.68 (* end of lemma zenon_L2439_ *) % 22.64/22.68 assert (zenon_L2440_ : (((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)) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 22.64/22.68 do 0 intro. intros zenon_H125 zenon_H1d5 zenon_H66 zenon_H68 zenon_H25 zenon_H94 zenon_H93 zenon_Hb2 zenon_Hb6 zenon_H47 zenon_H5d zenon_Ha5 zenon_H1ef zenon_H110 zenon_Ha9. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.68 apply (zenon_L252_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.68 apply (zenon_L171_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.68 apply (zenon_L38_); trivial. % 22.64/22.68 apply (zenon_L2439_); trivial. % 22.64/22.68 (* end of lemma zenon_L2440_ *) % 22.64/22.68 assert (zenon_L2441_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.64/22.68 do 0 intro. intros zenon_H139 zenon_H77 zenon_Ha0 zenon_H110 zenon_H111 zenon_H47 zenon_Hb6 zenon_H13a zenon_H129 zenon_H93 zenon_H177 zenon_Ha9 zenon_Hac zenon_H34 zenon_H183 zenon_H38 zenon_H68. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.68 apply (zenon_L251_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.68 apply (zenon_L2017_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.68 apply (zenon_L1596_); trivial. % 22.64/22.68 apply (zenon_L165_); trivial. % 22.64/22.68 (* end of lemma zenon_L2441_ *) % 22.64/22.68 assert (zenon_L2442_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.64/22.68 do 0 intro. intros zenon_H1fe zenon_H1ef zenon_H94 zenon_H1d5 zenon_H125 zenon_Hb2 zenon_H5d zenon_Ha5 zenon_H7d zenon_H15d zenon_H68 zenon_H183 zenon_H177 zenon_H13a zenon_Hb6 zenon_H111 zenon_H110 zenon_Ha0 zenon_H139 zenon_Hac zenon_Ha9 zenon_H189 zenon_H1b3 zenon_H77 zenon_H1a8 zenon_Hc4 zenon_H93 zenon_H129 zenon_H20f zenon_H1b4 zenon_H1bb zenon_H73 zenon_H40 zenon_H7a zenon_Heb zenon_H38 zenon_H48. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.68 apply (zenon_L13_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.68 apply (zenon_L1735_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.68 apply (zenon_L1736_); trivial. % 22.64/22.68 apply (zenon_L246_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.68 apply (zenon_L251_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.68 apply (zenon_L2017_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.68 apply (zenon_L2440_); trivial. % 22.64/22.68 apply (zenon_L165_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.68 apply (zenon_L1735_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.68 apply (zenon_L1736_); trivial. % 22.64/22.68 apply (zenon_L246_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.68 apply (zenon_L355_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.68 apply (zenon_L1735_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.68 apply (zenon_L1736_); trivial. % 22.64/22.68 apply (zenon_L246_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.68 apply (zenon_L2441_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.68 apply (zenon_L1735_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.68 apply (zenon_L1736_); trivial. % 22.64/22.68 apply (zenon_L246_); trivial. % 22.64/22.68 (* end of lemma zenon_L2442_ *) % 22.64/22.68 assert (zenon_L2443_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 22.64/22.68 do 0 intro. intros zenon_H169 zenon_H15d zenon_H73 zenon_H77 zenon_H189 zenon_Ha9 zenon_Hac zenon_H1a8 zenon_H48 zenon_H13a zenon_Ha0 zenon_H110 zenon_H111 zenon_Hb6 zenon_H125 zenon_H5d zenon_Ha5 zenon_H1ef zenon_Hb2 zenon_H94 zenon_H68 zenon_H1d5 zenon_H139 zenon_H7d zenon_H183 zenon_H177 zenon_H1fe zenon_H7a zenon_H40 zenon_H1bb zenon_Hc4 zenon_H93 zenon_H129 zenon_H20f zenon_H38 zenon_H1b4 zenon_Heb. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.68 apply (zenon_L1589_); trivial. % 22.64/22.68 apply (zenon_L2442_); trivial. % 22.64/22.68 (* end of lemma zenon_L2443_ *) % 22.64/22.68 assert (zenon_L2444_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 22.64/22.68 do 0 intro. intros zenon_He2 zenon_H11f zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha5 zenon_Hf5 zenon_Ha9 zenon_H9f zenon_H1c3 zenon_He3 zenon_H2d zenon_H55 zenon_Ha0 zenon_Hac. % 22.64/22.68 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.68 apply (zenon_L1517_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.68 exact (zenon_He3 zenon_He7). % 22.64/22.68 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.68 apply (zenon_L702_); trivial. % 22.64/22.68 apply (zenon_L107_); trivial. % 22.64/22.68 (* end of lemma zenon_L2444_ *) % 22.64/22.68 assert (zenon_L2445_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 22.64/22.68 do 0 intro. intros zenon_H22d zenon_Hac zenon_Ha0 zenon_H55 zenon_He3 zenon_H1c3 zenon_H9f zenon_Ha9 zenon_Hf5 zenon_Ha5 zenon_H196 zenon_H1b4 zenon_H1fb zenon_H25e zenon_H77 zenon_H11f zenon_He2 zenon_H3c zenon_H100 zenon_H94 zenon_H93 zenon_H110 zenon_H1ef. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H2d | zenon_intro zenon_H22e ]. % 22.64/22.68 apply (zenon_L2444_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H54 | zenon_intro zenon_H22f ]. % 22.64/22.68 apply (zenon_L69_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H65 | zenon_intro zenon_Ha8 ]. % 22.64/22.68 apply (zenon_L38_); trivial. % 22.64/22.68 apply (zenon_L282_); trivial. % 22.64/22.68 (* end of lemma zenon_L2445_ *) % 22.64/22.68 assert (zenon_L2446_ : ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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))))) -> (~((e2) = (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e2)) = (e3)) -> False). % 22.64/22.68 do 0 intro. intros zenon_H54 zenon_H100 zenon_H40 zenon_H1d4 zenon_H1bb zenon_H129 zenon_H20f zenon_H38 zenon_H1b4 zenon_H283 zenon_Ha0 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_Ha9 zenon_H13a zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H1ef zenon_Hb6 zenon_H13c zenon_H139 zenon_H77 zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1b7 zenon_H1c6 zenon_H68 zenon_H25b zenon_H186 zenon_Hf5 zenon_H48 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H236 zenon_H117 zenon_Heb zenon_H15d zenon_H282 zenon_Hcc zenon_H1c3 zenon_H26d zenon_H1fb zenon_H5d zenon_H94 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H110. % 22.64/22.68 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.68 apply (zenon_L69_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.68 exact (zenon_H40 zenon_H3f). % 22.64/22.68 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.68 exact (zenon_H1d4 zenon_H4d). % 22.64/22.68 apply (zenon_L2425_); trivial. % 22.64/22.68 (* end of lemma zenon_L2446_ *) % 22.64/22.68 assert (zenon_L2447_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (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) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.64/22.68 do 0 intro. intros zenon_H139 zenon_H1e zenon_H159 zenon_H173 zenon_H40 zenon_He3 zenon_H158 zenon_H129 zenon_H93 zenon_H177 zenon_Ha9 zenon_Hac zenon_H7e zenon_H77 zenon_H183 zenon_H38 zenon_H68. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.68 apply (zenon_L20_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.68 apply (zenon_L306_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.68 apply (zenon_L1575_); trivial. % 22.64/22.68 apply (zenon_L165_); trivial. % 22.64/22.68 (* end of lemma zenon_L2447_ *) % 22.64/22.68 assert (zenon_L2448_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.68 do 0 intro. intros zenon_H139 zenon_H68 zenon_H1e zenon_H159 zenon_H173 zenon_H40 zenon_He3 zenon_H158 zenon_H153 zenon_H77 zenon_H93 zenon_H196. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.68 apply (zenon_L20_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.68 apply (zenon_L306_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.68 apply (zenon_L94_); trivial. % 22.64/22.68 apply (zenon_L167_); trivial. % 22.64/22.68 (* end of lemma zenon_L2448_ *) % 22.64/22.68 assert (zenon_L2449_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 22.64/22.68 do 0 intro. intros zenon_H20b zenon_H26d zenon_Ha0 zenon_H38 zenon_Hb6 zenon_He2 zenon_He3 zenon_H1b7 zenon_H11f zenon_H48 zenon_H40 zenon_H1d8 zenon_He4 zenon_Hac zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha5 zenon_Hf5 zenon_Ha9 zenon_H1c3 zenon_H13a zenon_H160 zenon_H177 zenon_H110 zenon_H111. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H31 | zenon_intro zenon_H20c ]. % 22.64/22.68 apply (zenon_L756_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H153 | zenon_intro zenon_H20d ]. % 22.64/22.68 apply (zenon_L1603_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H66 | zenon_intro zenon_Hfe ]. % 22.64/22.68 apply (zenon_L122_); trivial. % 22.64/22.68 apply (zenon_L75_); trivial. % 22.64/22.68 (* end of lemma zenon_L2449_ *) % 22.64/22.68 assert (zenon_L2450_ : (((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.68 do 0 intro. intros zenon_H12e zenon_H3d zenon_H192 zenon_H1bb zenon_H18a zenon_H1cb zenon_Hc4 zenon_H183 zenon_H68 zenon_H34 zenon_H111 zenon_H110 zenon_H177 zenon_H13a zenon_H1c3 zenon_Ha9 zenon_Hf5 zenon_Ha5 zenon_H196 zenon_H1b4 zenon_H1fb zenon_H25e zenon_H77 zenon_Hac zenon_He4 zenon_H1d8 zenon_H40 zenon_H48 zenon_H1b7 zenon_He3 zenon_He2 zenon_Hb6 zenon_H38 zenon_Ha0 zenon_H26d zenon_H20b zenon_H93 zenon_H129. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.64/22.68 apply (zenon_L456_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.64/22.68 apply (zenon_L146_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.64/22.68 apply (zenon_L1598_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.64/22.68 apply (zenon_L291_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.64/22.68 apply (zenon_L371_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.64/22.68 apply (zenon_L2449_); trivial. % 22.64/22.68 apply (zenon_L126_); trivial. % 22.64/22.68 (* end of lemma zenon_L2450_ *) % 22.64/22.68 assert (zenon_L2451_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (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)) = (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 (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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (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) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (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)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.64/22.68 do 0 intro. intros zenon_H1fe zenon_H82 zenon_H22d zenon_H284 zenon_H19a zenon_H281 zenon_H94 zenon_H5d zenon_Hcc zenon_H282 zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H189 zenon_H27e zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H13c zenon_H1ef zenon_H266 zenon_H6f zenon_H190 zenon_H13e zenon_H73 zenon_H131 zenon_H163 zenon_H1cf zenon_H283 zenon_H20f zenon_H100 zenon_H186 zenon_H156 zenon_H1d4 zenon_H4e zenon_H1ec zenon_H55 zenon_H15d zenon_H158 zenon_H173 zenon_H159 zenon_H139 zenon_H20b zenon_H26d zenon_H177 zenon_H110 zenon_H111 zenon_H192 zenon_H12e zenon_H129 zenon_H93 zenon_H1bb zenon_H18a zenon_Ha0 zenon_Hb6 zenon_He2 zenon_He3 zenon_H1b7 zenon_H40 zenon_H1d8 zenon_He4 zenon_Hac zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha5 zenon_Hf5 zenon_Ha9 zenon_H1c3 zenon_H13a zenon_H1cb zenon_Hc4 zenon_H68 zenon_H183 zenon_H38 zenon_H48. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.68 apply (zenon_L13_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.68 apply (zenon_L13_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.68 apply (zenon_L20_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.68 apply (zenon_L214_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.64/22.68 apply (zenon_L246_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.64/22.68 apply (zenon_L17_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.64/22.68 apply (zenon_L218_); trivial. % 22.64/22.68 apply (zenon_L2445_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.68 apply (zenon_L55_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.68 apply (zenon_L193_); trivial. % 22.64/22.68 apply (zenon_L262_); trivial. % 22.64/22.68 apply (zenon_L167_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.68 apply (zenon_L2446_); trivial. % 22.64/22.68 apply (zenon_L2447_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.68 apply (zenon_L2448_); trivial. % 22.64/22.68 apply (zenon_L246_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.68 apply (zenon_L309_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.68 apply (zenon_L1594_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.68 apply (zenon_L1597_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.68 apply (zenon_L2450_); trivial. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.68 apply (zenon_L1605_); trivial. % 22.64/22.68 apply (zenon_L246_); trivial. % 22.64/22.68 (* end of lemma zenon_L2451_ *) % 22.64/22.68 assert (zenon_L2452_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (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) (e2)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((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) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 22.64/22.68 do 0 intro. intros zenon_H169 zenon_H139 zenon_H18d zenon_He2 zenon_Hac zenon_Ha0 zenon_H55 zenon_He3 zenon_Ha9 zenon_Ha5 zenon_H25e zenon_Hf5 zenon_H196 zenon_H1b4 zenon_H1fb zenon_H1c3 zenon_H100 zenon_H94 zenon_H1ef zenon_H110 zenon_H22d zenon_H93 zenon_H5d zenon_H38 zenon_Hb6 zenon_H13a zenon_H77 zenon_H68 zenon_H284 zenon_H19a zenon_H281 zenon_H26d zenon_Hcc zenon_H282 zenon_H15d zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H189 zenon_H27e zenon_H186 zenon_H25b zenon_H1c6 zenon_H1b7 zenon_H1a2 zenon_H1cb zenon_H16a zenon_H13c zenon_H266 zenon_H6f zenon_H190 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H20f zenon_H129 zenon_H1bb zenon_H40 zenon_H177 zenon_H183 zenon_H159 zenon_H82 zenon_H48 zenon_H192 zenon_H18a zenon_Hc4 zenon_He4 zenon_H1d8 zenon_H111 zenon_H20b zenon_H12e zenon_H1fe. % 22.64/22.68 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.68 apply (zenon_L2451_); trivial. % 22.64/22.68 apply (zenon_L1113_); trivial. % 22.64/22.68 (* end of lemma zenon_L2452_ *) % 22.64/22.68 assert (zenon_L2453_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((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 (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((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)) = (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) (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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((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) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 22.64/22.69 do 0 intro. intros zenon_He2 zenon_H22d zenon_H192 zenon_H1d8 zenon_H20b zenon_H1a8 zenon_H125 zenon_H1d5 zenon_H183 zenon_H15d zenon_H196 zenon_H121 zenon_H33 zenon_Ha9 zenon_H177 zenon_H68 zenon_H139 zenon_Hb2 zenon_H100 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H131 zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H13c zenon_H16a zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_Hf5 zenon_H27e zenon_H195 zenon_H236 zenon_H117 zenon_Heb zenon_H282 zenon_Hcc zenon_H1c3 zenon_H5d zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H26a zenon_H159 zenon_H179 zenon_H1ef zenon_H82 zenon_H13f zenon_Hf0 zenon_Hfa zenon_He4 zenon_H1fe zenon_H189 zenon_H94 zenon_Hb6 zenon_H111 zenon_Ha0 zenon_H13a zenon_H48 zenon_H18d zenon_H1b7 zenon_H77 zenon_H1b4 zenon_H20f zenon_H129 zenon_H1bb zenon_H1cb zenon_H231 zenon_H104 zenon_H18a zenon_H24e zenon_H1cd zenon_H7d zenon_H12e zenon_Hbc zenon_H26d zenon_H1fb zenon_H38 zenon_H110. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H191 | zenon_intro zenon_H93 ]. % 22.64/22.69 exact (zenon_H191 zenon_H110). % 22.64/22.69 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.69 apply (zenon_L2_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.69 apply (zenon_L1146_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.69 apply (zenon_L1147_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.69 apply (zenon_L1515_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.69 apply (zenon_L1843_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.69 apply (zenon_L11_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.69 apply (zenon_L2401_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.69 apply (zenon_L1717_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.69 apply (zenon_L1208_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.69 apply (zenon_L1209_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.69 apply (zenon_L37_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.69 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.69 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.69 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.69 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.69 apply (zenon_L2427_); trivial. % 22.64/22.69 apply (zenon_L555_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.69 apply (zenon_L1353_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.69 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.69 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.69 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.69 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.69 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.69 apply (zenon_L2443_); trivial. % 22.64/22.69 apply (zenon_L2443_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.69 apply (zenon_L2452_); trivial. % 22.64/22.69 apply (zenon_L2452_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.69 apply (zenon_L2428_); trivial. % 22.64/22.69 apply (zenon_L51_); trivial. % 22.64/22.69 apply (zenon_L1213_); trivial. % 22.64/22.69 (* end of lemma zenon_L2453_ *) % 22.64/22.69 assert (zenon_L2454_ : ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((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 (e1) (e2)) = (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 (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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (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 (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H110 zenon_H38 zenon_H1fb zenon_H26d zenon_Hbc zenon_H12e zenon_H7d zenon_H1cd zenon_H24e zenon_H18a zenon_H104 zenon_H231 zenon_H1cb zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H77 zenon_H1b7 zenon_H18d zenon_H48 zenon_H13a zenon_Ha0 zenon_H111 zenon_Hb6 zenon_H94 zenon_H189 zenon_H1fe zenon_He4 zenon_Hfa zenon_Hf0 zenon_H13f zenon_H82 zenon_H1ef zenon_H179 zenon_H26a zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H5d zenon_H1c3 zenon_Hcc zenon_H282 zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H27e zenon_Hf5 zenon_H186 zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H13c zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H100 zenon_Hb2 zenon_H139 zenon_H68 zenon_H177 zenon_Ha9 zenon_H33 zenon_H121 zenon_H196 zenon_H15d zenon_H183 zenon_H1d5 zenon_H125 zenon_H1a8 zenon_H20b zenon_H1d8 zenon_H192 zenon_H22d zenon_He2. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H159 | zenon_intro zenon_H5c ]. % 22.64/22.69 apply (zenon_L2453_); trivial. % 22.64/22.69 apply (zenon_L2425_); trivial. % 22.64/22.69 (* end of lemma zenon_L2454_ *) % 22.64/22.69 assert (zenon_L2455_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((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)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (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 (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (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) (e3)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (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 (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 (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 (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) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_Hc8 zenon_H109 zenon_H179 zenon_H140 zenon_H24e zenon_H104 zenon_H231 zenon_H111 zenon_Hfa zenon_H13f zenon_H26a zenon_H100 zenon_H121 zenon_H183 zenon_H1d5 zenon_H125 zenon_H20b zenon_H1d8 zenon_H22d zenon_He2 zenon_H15d zenon_Hf5 zenon_H13a zenon_H234 zenon_H5c zenon_H141 zenon_H110 zenon_Ha0 zenon_H2c zenon_H164 zenon_H18a zenon_H7d zenon_Hbc zenon_H212 zenon_H1cb zenon_H1b7 zenon_H19a zenon_H33 zenon_He4 zenon_Hb6 zenon_Ha9 zenon_Ha4 zenon_H68 zenon_H77 zenon_H177 zenon_H160 zenon_H196 zenon_H93 zenon_H139 zenon_H48 zenon_H1fe zenon_H12e zenon_H20f zenon_Hc4 zenon_H1bb zenon_H82 zenon_H192 zenon_H5d zenon_H1ef zenon_Hb2 zenon_H186 zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H201 zenon_H1a8 zenon_H1cd zenon_H189 zenon_H99 zenon_Hf0 zenon_H284 zenon_H25e zenon_H281 zenon_H94 zenon_H1fb zenon_H26d zenon_H1c3 zenon_Hcc zenon_H282 zenon_Heb zenon_H117 zenon_H236 zenon_H18d zenon_H195 zenon_H27e zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H13c zenon_H13e zenon_H158 zenon_H156 zenon_H173 zenon_H1ec zenon_H73 zenon_H131 zenon_H4e zenon_H163 zenon_H1cf zenon_H283 zenon_H1b4 zenon_H129. % 22.64/22.69 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.69 apply (zenon_L2133_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.69 apply (zenon_L2433_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.69 apply (zenon_L2436_); trivial. % 22.64/22.69 apply (zenon_L1236_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.69 apply (zenon_L2193_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.69 apply (zenon_L2438_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.69 apply (zenon_L2194_); trivial. % 22.64/22.69 apply (zenon_L2454_); trivial. % 22.64/22.69 (* end of lemma zenon_L2455_ *) % 22.64/22.69 assert (zenon_L2456_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H19a zenon_H177 zenon_H160 zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha9 zenon_H111 zenon_H110 zenon_Ha0 zenon_H77 zenon_H139 zenon_H5c zenon_H48 zenon_H93 zenon_H68 zenon_He0 zenon_H1b7. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.64/22.69 apply (zenon_L2018_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.64/22.69 apply (zenon_L157_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.64/22.69 apply (zenon_L158_); trivial. % 22.64/22.69 apply (zenon_L556_); trivial. % 22.64/22.69 (* end of lemma zenon_L2456_ *) % 22.64/22.69 assert (zenon_L2457_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H24e zenon_H1b7 zenon_H68 zenon_H93 zenon_H48 zenon_H5c zenon_H139 zenon_H77 zenon_Ha0 zenon_H110 zenon_H111 zenon_Ha9 zenon_H47 zenon_Hb6 zenon_H13a zenon_H177 zenon_H19a zenon_H53 zenon_H1f1 zenon_H1cd zenon_H160 zenon_H10c zenon_H11a. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_He0 | zenon_intro zenon_H24f ]. % 22.64/22.69 apply (zenon_L2456_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H7f | zenon_intro zenon_H250 ]. % 22.64/22.69 apply (zenon_L284_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H171 | zenon_intro zenon_Hac ]. % 22.64/22.69 apply (zenon_L240_); trivial. % 22.64/22.69 apply (zenon_L79_); trivial. % 22.64/22.69 (* end of lemma zenon_L2457_ *) % 22.64/22.69 assert (zenon_L2458_ : (((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) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H164 zenon_H2d zenon_H109 zenon_H26d zenon_H31 zenon_H183 zenon_H9d zenon_H6e zenon_H192 zenon_H11a zenon_H10c zenon_H1cd zenon_H1f1 zenon_H53 zenon_H19a zenon_H177 zenon_H13a zenon_Hb6 zenon_H47 zenon_Ha9 zenon_H111 zenon_H110 zenon_Ha0 zenon_H77 zenon_H139 zenon_H5c zenon_H48 zenon_H93 zenon_H1b7 zenon_H24e zenon_H68. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.64/22.69 apply (zenon_L359_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.64/22.69 apply (zenon_L821_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.64/22.69 apply (zenon_L406_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H102 | zenon_intro zenon_H184 ]. % 22.64/22.69 apply (zenon_L91_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H171 | zenon_intro zenon_H185 ]. % 22.64/22.69 apply (zenon_L1128_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H160 | zenon_intro zenon_H17c ]. % 22.64/22.69 apply (zenon_L2457_); trivial. % 22.64/22.69 apply (zenon_L295_); trivial. % 22.64/22.69 (* end of lemma zenon_L2458_ *) % 22.64/22.69 assert (zenon_L2459_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (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 (e3) (e2)) = (op (e3) (e3)))) -> (((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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((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) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (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))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((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)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H204 zenon_H82 zenon_H140 zenon_H23d zenon_H33 zenon_H236 zenon_H9e zenon_Ha0 zenon_H1f zenon_H1bb zenon_H129 zenon_H20f zenon_H1b4 zenon_H283 zenon_H1cf zenon_H163 zenon_H4e zenon_H73 zenon_H1ec zenon_H173 zenon_H156 zenon_H158 zenon_H13e zenon_H1ef zenon_H196 zenon_H16a zenon_H1cb zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H186 zenon_H27e zenon_H189 zenon_H195 zenon_H18d zenon_H117 zenon_Heb zenon_H282 zenon_Hcc zenon_H1c3 zenon_H1fb zenon_H5d zenon_H281 zenon_H25e zenon_H284 zenon_H125 zenon_H9d zenon_Ha9 zenon_H93 zenon_H94 zenon_H68 zenon_H15d zenon_H13c zenon_Hf5 zenon_H131 zenon_H48 zenon_H164 zenon_H192 zenon_H24e zenon_H11a zenon_H1cd zenon_H1f1 zenon_H139 zenon_Hb6 zenon_H111 zenon_H110 zenon_H13a zenon_H77 zenon_H183 zenon_H177 zenon_H26d zenon_H5c zenon_H1b7 zenon_H19a zenon_H109 zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13f zenon_H179 zenon_H18a zenon_H1fe zenon_H240. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.69 apply (zenon_L1873_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.69 exact (zenon_H1f zenon_H1e). % 22.64/22.69 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.69 exact (zenon_H205 zenon_H2a). % 22.64/22.69 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.69 exact (zenon_H1f zenon_H1e). % 22.64/22.69 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.69 apply (zenon_L2196_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.69 exact (zenon_H6c zenon_H67). % 22.64/22.69 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.69 apply (zenon_L123_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.69 apply (zenon_L217_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.69 apply (zenon_L2458_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.69 apply (zenon_L2130_); trivial. % 22.64/22.69 apply (zenon_L218_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.69 apply (zenon_L259_); trivial. % 22.64/22.69 apply (zenon_L262_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.69 apply (zenon_L264_); trivial. % 22.64/22.69 apply (zenon_L92_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.69 apply (zenon_L1853_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.69 apply (zenon_L239_); trivial. % 22.64/22.69 apply (zenon_L192_); trivial. % 22.64/22.69 apply (zenon_L851_); trivial. % 22.64/22.69 apply (zenon_L1236_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.69 apply (zenon_L2198_); trivial. % 22.64/22.69 apply (zenon_L611_); trivial. % 22.64/22.69 (* end of lemma zenon_L2459_ *) % 22.64/22.69 assert (zenon_L2460_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_Ha9 zenon_H66 zenon_Ha5 zenon_Hf5. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.69 exact (zenon_Ha4 zenon_H9f). % 22.64/22.69 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.69 apply (zenon_L55_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.69 apply (zenon_L193_); trivial. % 22.64/22.69 apply (zenon_L262_); trivial. % 22.64/22.69 (* end of lemma zenon_L2460_ *) % 22.64/22.69 assert (zenon_L2461_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H6e zenon_Hb6 zenon_H153 zenon_Ha5 zenon_Hf5. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.69 exact (zenon_Ha4 zenon_H9f). % 22.64/22.69 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.69 apply (zenon_L110_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.69 apply (zenon_L95_); trivial. % 22.64/22.69 apply (zenon_L262_); trivial. % 22.64/22.69 (* end of lemma zenon_L2461_ *) % 22.64/22.69 assert (zenon_L2462_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H139 zenon_H68 zenon_H1e zenon_Hf5 zenon_Ha5 zenon_Hb6 zenon_Ha9 zenon_Ha4 zenon_H13a zenon_H153 zenon_H77 zenon_H93 zenon_H196. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.69 apply (zenon_L20_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.69 apply (zenon_L2461_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.69 apply (zenon_L94_); trivial. % 22.64/22.69 apply (zenon_L167_); trivial. % 22.64/22.69 (* end of lemma zenon_L2462_ *) % 22.64/22.69 assert (zenon_L2463_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H15d zenon_H1e zenon_H48 zenon_Ha5 zenon_Hb6 zenon_H2a zenon_Ha0 zenon_Ha4 zenon_H13a zenon_H5c zenon_Hf5. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.69 apply (zenon_L13_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.69 apply (zenon_L65_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.69 apply (zenon_L600_); trivial. % 22.64/22.69 apply (zenon_L192_); trivial. % 22.64/22.69 (* end of lemma zenon_L2463_ *) % 22.64/22.69 assert (zenon_L2464_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H15d zenon_H7d zenon_Hac zenon_H2d zenon_H5d zenon_Hb2 zenon_H48 zenon_Ha5 zenon_Hb6 zenon_H2a zenon_Ha0 zenon_Ha4 zenon_H13a zenon_H5c zenon_Hf5. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.69 apply (zenon_L355_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.69 apply (zenon_L65_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.69 apply (zenon_L600_); trivial. % 22.64/22.69 apply (zenon_L192_); trivial. % 22.64/22.69 (* end of lemma zenon_L2464_ *) % 22.64/22.69 assert (zenon_L2465_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Hb6 zenon_H3d zenon_Ha0 zenon_H31 zenon_Ha5 zenon_Hf5. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.69 exact (zenon_Ha4 zenon_H9f). % 22.64/22.69 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.69 apply (zenon_L55_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.69 apply (zenon_L68_); trivial. % 22.64/22.69 apply (zenon_L262_); trivial. % 22.64/22.69 (* end of lemma zenon_L2465_ *) % 22.64/22.69 assert (zenon_L2466_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H15d zenon_H1e zenon_Ha5 zenon_Ha0 zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.69 apply (zenon_L13_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.69 apply (zenon_L2465_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.69 apply (zenon_L239_); trivial. % 22.64/22.69 apply (zenon_L192_); trivial. % 22.64/22.69 (* end of lemma zenon_L2466_ *) % 22.64/22.69 assert (zenon_L2467_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_Ha9 zenon_H6e zenon_Ha0 zenon_H31 zenon_Ha5 zenon_Hf5. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.69 exact (zenon_Ha4 zenon_H9f). % 22.64/22.69 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.69 apply (zenon_L110_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.69 apply (zenon_L68_); trivial. % 22.64/22.69 apply (zenon_L262_); trivial. % 22.64/22.69 (* end of lemma zenon_L2467_ *) % 22.64/22.69 assert (zenon_L2468_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H139 zenon_H77 zenon_Hf5 zenon_H31 zenon_Ha0 zenon_Ha4 zenon_H13a zenon_Ha9 zenon_H110 zenon_H1ef zenon_Ha5 zenon_H5d zenon_H47 zenon_Hb6 zenon_Hb2 zenon_H94 zenon_H25 zenon_H68 zenon_H1d5 zenon_H125 zenon_H93 zenon_H196. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.69 apply (zenon_L251_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.69 apply (zenon_L2467_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.69 apply (zenon_L2440_); trivial. % 22.64/22.69 apply (zenon_L167_); trivial. % 22.64/22.69 (* end of lemma zenon_L2468_ *) % 22.64/22.69 assert (zenon_L2469_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H15d zenon_H7d zenon_Hac zenon_H2d zenon_H5d zenon_Hb2 zenon_Ha5 zenon_Ha0 zenon_Hb6 zenon_Ha4 zenon_H13a zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.69 apply (zenon_L355_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.69 apply (zenon_L2465_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.69 apply (zenon_L239_); trivial. % 22.64/22.69 apply (zenon_L192_); trivial. % 22.64/22.69 (* end of lemma zenon_L2469_ *) % 22.64/22.69 assert (zenon_L2470_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (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 (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H15d zenon_H196 zenon_H177 zenon_H13a zenon_Ha4 zenon_Ha0 zenon_Ha5 zenon_H77 zenon_H139 zenon_H20f zenon_H183 zenon_H68 zenon_Hac zenon_Ha9 zenon_Hc4 zenon_H1cb zenon_H34 zenon_H18a zenon_H1bb zenon_H93 zenon_H129 zenon_H192 zenon_H12e zenon_H48 zenon_H31 zenon_H5c zenon_Hf5. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.69 apply (zenon_L251_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.69 apply (zenon_L2467_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.69 apply (zenon_L1596_); trivial. % 22.64/22.69 apply (zenon_L167_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.69 apply (zenon_L1599_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.69 apply (zenon_L239_); trivial. % 22.64/22.69 apply (zenon_L192_); trivial. % 22.64/22.69 (* end of lemma zenon_L2470_ *) % 22.64/22.69 assert (zenon_L2471_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (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) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.64/22.69 do 0 intro. intros zenon_H169 zenon_H189 zenon_H1a8 zenon_H15c zenon_H111 zenon_H73 zenon_H15d zenon_H5c zenon_H68 zenon_H77 zenon_H13a zenon_Ha5 zenon_Hf5 zenon_Ha9 zenon_Hb6 zenon_Ha4 zenon_H196 zenon_H93 zenon_H139 zenon_H48 zenon_H1fe zenon_H177 zenon_H129 zenon_H183 zenon_H12e zenon_H20f zenon_H1bb zenon_Hc4 zenon_H1cb zenon_H18a zenon_H192 zenon_H7d zenon_H1d5 zenon_H94 zenon_Hb2 zenon_H110 zenon_H1ef zenon_H5d zenon_H125 zenon_H173 zenon_H40 zenon_H11a zenon_Hac zenon_H158 zenon_Ha0 zenon_Heb zenon_H1b4 zenon_H7a zenon_H236. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.69 apply (zenon_L13_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.69 apply (zenon_L20_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.69 apply (zenon_L214_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.69 apply (zenon_L2460_); trivial. % 22.64/22.69 apply (zenon_L167_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.69 apply (zenon_L2462_); trivial. % 22.64/22.69 apply (zenon_L192_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.69 apply (zenon_L2463_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.69 apply (zenon_L251_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.69 apply (zenon_L358_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.69 apply (zenon_L2440_); trivial. % 22.64/22.69 apply (zenon_L167_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.69 apply (zenon_L65_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.69 apply (zenon_L600_); trivial. % 22.64/22.69 apply (zenon_L192_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.69 apply (zenon_L2464_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.69 apply (zenon_L251_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.69 apply (zenon_L147_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.69 apply (zenon_L1596_); trivial. % 22.64/22.69 apply (zenon_L167_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.69 apply (zenon_L1599_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.69 apply (zenon_L600_); trivial. % 22.64/22.69 apply (zenon_L192_); trivial. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.69 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.70 apply (zenon_L2466_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.70 apply (zenon_L2468_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.70 apply (zenon_L2465_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.70 apply (zenon_L239_); trivial. % 22.64/22.70 apply (zenon_L192_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.70 apply (zenon_L2469_); trivial. % 22.64/22.70 apply (zenon_L2470_); trivial. % 22.64/22.70 apply (zenon_L1589_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.70 apply (zenon_L13_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.70 apply (zenon_L1735_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.70 apply (zenon_L2462_); trivial. % 22.64/22.70 apply (zenon_L192_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.70 apply (zenon_L1224_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.70 apply (zenon_L2466_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.70 apply (zenon_L2468_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.70 apply (zenon_L1735_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.70 apply (zenon_L239_); trivial. % 22.64/22.70 apply (zenon_L192_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.70 apply (zenon_L2469_); trivial. % 22.64/22.70 apply (zenon_L2470_); trivial. % 22.64/22.70 apply (zenon_L2442_); trivial. % 22.64/22.70 (* end of lemma zenon_L2471_ *) % 22.64/22.70 assert (zenon_L2472_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (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)) = (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) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((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 (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (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 (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 (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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((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 (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H169 zenon_H5c zenon_H110 zenon_H1fb zenon_H26d zenon_Hbc zenon_H1cd zenon_H24e zenon_H104 zenon_H231 zenon_H1b4 zenon_H1b7 zenon_H18d zenon_H111 zenon_H94 zenon_H189 zenon_He4 zenon_Hfa zenon_Hf0 zenon_H13f zenon_H82 zenon_H1ef zenon_H179 zenon_H26a zenon_H284 zenon_H25e zenon_H19a zenon_H281 zenon_H1c3 zenon_Hcc zenon_H282 zenon_Heb zenon_H117 zenon_H236 zenon_H195 zenon_H27e zenon_H25b zenon_H1c6 zenon_H1a2 zenon_H16a zenon_H13c zenon_H266 zenon_H6f zenon_H190 zenon_H55 zenon_H13e zenon_H73 zenon_H131 zenon_H163 zenon_H1cf zenon_H283 zenon_H100 zenon_H33 zenon_H121 zenon_H1d5 zenon_H125 zenon_H1a8 zenon_H20b zenon_H1d8 zenon_H22d zenon_He2 zenon_Ha0 zenon_H1ec zenon_H186 zenon_H156 zenon_H4e zenon_H5d zenon_H7d zenon_Hac zenon_Hb2 zenon_H192 zenon_H18a zenon_H1cb zenon_Hc4 zenon_H1bb zenon_H20f zenon_H12e zenon_H183 zenon_H129 zenon_H177 zenon_H1fe zenon_H48 zenon_H139 zenon_H93 zenon_H196 zenon_Ha4 zenon_Hb6 zenon_Ha9 zenon_Hf5 zenon_Ha5 zenon_H13a zenon_He3 zenon_H40 zenon_H173 zenon_H158 zenon_H68 zenon_H77 zenon_H15d zenon_H15c. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.64/22.70 exact (zenon_Hec zenon_H5c). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.70 apply (zenon_L13_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.70 apply (zenon_L20_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.70 apply (zenon_L306_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.70 apply (zenon_L2460_); trivial. % 22.64/22.70 apply (zenon_L167_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.70 apply (zenon_L2448_); trivial. % 22.64/22.70 apply (zenon_L192_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.70 apply (zenon_L2463_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.70 apply (zenon_L309_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.70 apply (zenon_L2464_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.70 apply (zenon_L1597_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.70 apply (zenon_L1599_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.70 apply (zenon_L600_); trivial. % 22.64/22.70 apply (zenon_L192_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.70 apply (zenon_L13_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.70 apply (zenon_L2465_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.70 apply (zenon_L2448_); trivial. % 22.64/22.70 apply (zenon_L192_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.70 apply (zenon_L309_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.70 apply (zenon_L2469_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.70 apply (zenon_L1597_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.70 apply (zenon_L1599_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.70 apply (zenon_L239_); trivial. % 22.64/22.70 apply (zenon_L192_); trivial. % 22.64/22.70 apply (zenon_L2453_); trivial. % 22.64/22.70 apply (zenon_L1614_); trivial. % 22.64/22.70 (* end of lemma zenon_L2472_ *) % 22.64/22.70 assert (zenon_L2473_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((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)) = (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) (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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e2) (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) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 22.64/22.70 do 0 intro. intros zenon_H201 zenon_H212 zenon_H2c zenon_H141 zenon_H234 zenon_H140 zenon_H23d zenon_H164 zenon_H1f1 zenon_H109 zenon_H236 zenon_H1b4 zenon_Heb zenon_Ha0 zenon_H158 zenon_H11a zenon_H173 zenon_H125 zenon_H5d zenon_H1ef zenon_Hb2 zenon_H94 zenon_H1d5 zenon_H7d zenon_H192 zenon_H18a zenon_H1cb zenon_Hc4 zenon_H1bb zenon_H20f zenon_H12e zenon_H183 zenon_H129 zenon_H177 zenon_H1fe zenon_H48 zenon_H139 zenon_H93 zenon_H196 zenon_Ha4 zenon_Hb6 zenon_Ha9 zenon_Hf5 zenon_H13a zenon_H77 zenon_H68 zenon_H5c zenon_H15d zenon_H73 zenon_H111 zenon_H1a8 zenon_H189 zenon_H4e zenon_H156 zenon_H186 zenon_H1ec zenon_He2 zenon_H22d zenon_H1d8 zenon_H20b zenon_H121 zenon_H33 zenon_H100 zenon_H283 zenon_H1cf zenon_H163 zenon_H131 zenon_H13e zenon_H55 zenon_H190 zenon_H6f zenon_H266 zenon_H13c zenon_H16a zenon_H1a2 zenon_H1c6 zenon_H25b zenon_H27e zenon_H195 zenon_H117 zenon_H282 zenon_Hcc zenon_H1c3 zenon_H281 zenon_H19a zenon_H25e zenon_H284 zenon_H26a zenon_H179 zenon_H82 zenon_H13f zenon_Hf0 zenon_Hfa zenon_He4 zenon_H18d zenon_H1b7 zenon_H231 zenon_H24e zenon_H1cd zenon_Hbc zenon_H26d zenon_H1fb zenon_H104 zenon_H110. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.70 apply (zenon_L2_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.70 apply (zenon_L2432_); trivial. % 22.64/22.70 apply (zenon_L2432_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.70 apply (zenon_L2396_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.70 apply (zenon_L2397_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.70 apply (zenon_L1206_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.70 apply (zenon_L11_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.70 apply (zenon_L1207_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.70 apply (zenon_L2406_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.70 apply (zenon_L1208_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.70 apply (zenon_L1209_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.70 apply (zenon_L37_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.70 apply (zenon_L2455_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.70 apply (zenon_L2459_); trivial. % 22.64/22.70 apply (zenon_L2459_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.70 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.70 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.70 apply (zenon_L2471_); trivial. % 22.64/22.70 apply (zenon_L2471_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.70 apply (zenon_L2472_); trivial. % 22.64/22.70 apply (zenon_L2472_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.70 apply (zenon_L2428_); trivial. % 22.64/22.70 apply (zenon_L51_); trivial. % 22.64/22.70 (* end of lemma zenon_L2473_ *) % 22.64/22.70 assert (zenon_L2474_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_Heb zenon_H48 zenon_H25 zenon_H40 zenon_H1d4 zenon_H11f zenon_H20f. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.70 apply (zenon_L25_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.70 exact (zenon_H40 zenon_H3f). % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.70 exact (zenon_H1d4 zenon_H4d). % 22.64/22.70 apply (zenon_L412_); trivial. % 22.64/22.70 (* end of lemma zenon_L2474_ *) % 22.64/22.70 assert (zenon_L2475_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H169 zenon_H173 zenon_H2a zenon_H11a zenon_Hac zenon_H158 zenon_H48 zenon_H25 zenon_H40 zenon_H20f zenon_H11f zenon_Heb. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.70 apply (zenon_L2474_); trivial. % 22.64/22.70 apply (zenon_L372_); trivial. % 22.64/22.70 (* end of lemma zenon_L2475_ *) % 22.64/22.70 assert (zenon_L2476_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H28 zenon_H173 zenon_H11a zenon_Hac zenon_H158 zenon_H48 zenon_H40 zenon_H20f zenon_H11f zenon_Heb. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.70 apply (zenon_L2475_); trivial. % 22.64/22.70 (* end of lemma zenon_L2476_ *) % 22.64/22.70 assert (zenon_L2477_ : (((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 (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> False). % 22.64/22.70 do 0 intro. intros zenon_H164 zenon_H2d zenon_H109 zenon_Hac zenon_Ha0 zenon_H31 zenon_H177 zenon_H48 zenon_H11f. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.64/22.70 apply (zenon_L359_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.64/22.70 apply (zenon_L107_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.64/22.70 apply (zenon_L406_); trivial. % 22.64/22.70 apply (zenon_L1803_); trivial. % 22.64/22.70 (* end of lemma zenon_L2477_ *) % 22.64/22.70 assert (zenon_L2478_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (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 (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> False). % 22.64/22.70 do 0 intro. intros zenon_H2f zenon_H164 zenon_H109 zenon_Hac zenon_Ha0 zenon_H177 zenon_H48 zenon_H11f. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.64/22.70 apply (zenon_L2477_); trivial. % 22.64/22.70 (* end of lemma zenon_L2478_ *) % 22.64/22.70 assert (zenon_L2479_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> False). % 22.64/22.70 do 0 intro. intros zenon_Hca zenon_H11f zenon_Hac. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.70 exact (zenon_H1c7 zenon_Hac). % 22.64/22.70 exact (zenon_H120 zenon_H11f). % 22.64/22.70 (* end of lemma zenon_L2479_ *) % 22.64/22.70 assert (zenon_L2480_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> False). % 22.64/22.70 do 0 intro. intros zenon_H36 zenon_H11f zenon_Hac. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.70 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.70 apply (zenon_L2479_); trivial. % 22.64/22.70 (* end of lemma zenon_L2480_ *) % 22.64/22.70 assert (zenon_L2481_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H92 zenon_H139 zenon_H196 zenon_Ha9 zenon_Hb6 zenon_H4d zenon_H1cd zenon_H1a2 zenon_H173 zenon_H2a zenon_H40 zenon_H11a zenon_Hac zenon_H158 zenon_H48 zenon_H73 zenon_H1b4 zenon_H11f zenon_H15d zenon_H7b zenon_H77 zenon_H53 zenon_H8b zenon_H16a. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.64/22.70 apply (zenon_L378_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.70 apply (zenon_L380_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.70 apply (zenon_L65_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.70 apply (zenon_L184_); trivial. % 22.64/22.70 apply (zenon_L187_); trivial. % 22.64/22.70 (* end of lemma zenon_L2481_ *) % 22.64/22.70 assert (zenon_L2482_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H92 zenon_H1bf zenon_H13e zenon_H15d zenon_H11f zenon_H1b4 zenon_H4d zenon_H73 zenon_H2a zenon_H48 zenon_Hb6 zenon_Ha0 zenon_H16a zenon_H8b zenon_H53 zenon_H77 zenon_Ha9 zenon_H7d zenon_Hac zenon_Hb2 zenon_H68 zenon_H140 zenon_Hbc zenon_H13d zenon_H1d8 zenon_H1fe. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.70 apply (zenon_L13_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.70 apply (zenon_L65_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.70 apply (zenon_L184_); trivial. % 22.64/22.70 apply (zenon_L187_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.70 apply (zenon_L323_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.70 apply (zenon_L65_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.70 apply (zenon_L184_); trivial. % 22.64/22.70 apply (zenon_L187_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.70 apply (zenon_L327_); trivial. % 22.64/22.70 apply (zenon_L329_); trivial. % 22.64/22.70 apply (zenon_L382_); trivial. % 22.64/22.70 (* end of lemma zenon_L2482_ *) % 22.64/22.70 assert (zenon_L2483_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> False). % 22.64/22.70 do 0 intro. intros zenon_H61 zenon_H11f zenon_Hac. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.70 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.70 apply (zenon_L2479_); trivial. % 22.64/22.70 (* end of lemma zenon_L2483_ *) % 22.64/22.70 assert (zenon_L2484_ : (((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)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H15d zenon_H4c zenon_H48 zenon_H2a zenon_H66 zenon_H77 zenon_H11f zenon_H1b4. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.70 exact (zenon_H4c zenon_H47). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.70 apply (zenon_L65_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.70 apply (zenon_L94_); trivial. % 22.64/22.70 apply (zenon_L187_); trivial. % 22.64/22.70 (* end of lemma zenon_L2484_ *) % 22.64/22.70 assert (zenon_L2485_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> False). % 22.64/22.70 do 0 intro. intros zenon_H63 zenon_H48 zenon_H77 zenon_H1b4 zenon_H11f zenon_H15d zenon_H2a. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.64/22.70 exact (zenon_H205 zenon_H2a). % 22.64/22.70 apply (zenon_L2484_); trivial. % 22.64/22.70 (* end of lemma zenon_L2485_ *) % 22.64/22.70 assert (zenon_L2486_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_He4 zenon_H48 zenon_H2a zenon_H40 zenon_H6d zenon_H77 zenon_H11f zenon_H1b7. % 22.64/22.70 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.64/22.70 apply (zenon_L65_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.64/22.70 exact (zenon_H40 zenon_H3f). % 22.64/22.70 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.64/22.70 apply (zenon_L56_); trivial. % 22.64/22.70 apply (zenon_L780_); trivial. % 22.64/22.70 (* end of lemma zenon_L2486_ *) % 22.64/22.70 assert (zenon_L2487_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3))))))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> False). % 22.64/22.70 do 0 intro. intros zenon_H99 zenon_H11f zenon_Hac. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.70 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.70 apply (zenon_L2479_); trivial. % 22.64/22.70 (* end of lemma zenon_L2487_ *) % 22.64/22.70 assert (zenon_L2488_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H201 zenon_Hb6 zenon_Hfe zenon_H1d4 zenon_H1bf zenon_H11f zenon_H1cb. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.70 apply (zenon_L95_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.70 exact (zenon_H1d4 zenon_H4d). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.70 exact (zenon_H1bf zenon_H105). % 22.64/22.70 apply (zenon_L846_); trivial. % 22.64/22.70 (* end of lemma zenon_L2488_ *) % 22.64/22.70 assert (zenon_L2489_ : (((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) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H15d zenon_H201 zenon_H1d4 zenon_H1bf zenon_H1cb zenon_H48 zenon_Hf5 zenon_Ha5 zenon_Hb6 zenon_H2a zenon_Ha0 zenon_H1c3 zenon_Ha9 zenon_H196 zenon_H1fb zenon_H25e zenon_H77 zenon_H13a zenon_H11f zenon_H1b4. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.70 apply (zenon_L253_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.70 apply (zenon_L53_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.70 apply (zenon_L2488_); trivial. % 22.64/22.70 apply (zenon_L262_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.70 apply (zenon_L65_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.70 apply (zenon_L1518_); trivial. % 22.64/22.70 apply (zenon_L187_); trivial. % 22.64/22.70 (* end of lemma zenon_L2489_ *) % 22.64/22.70 assert (zenon_L2490_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (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) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e2)) = (op (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)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((op (e3) (e3)) = (e1)) -> False). % 22.64/22.70 do 0 intro. intros zenon_H230 zenon_Heb zenon_H20f zenon_H40 zenon_H48 zenon_H158 zenon_H11a zenon_H2a zenon_H173 zenon_H1d8 zenon_H16a zenon_H77 zenon_H15d zenon_H1b4 zenon_H73 zenon_H1a2 zenon_H1cd zenon_Hb6 zenon_Ha9 zenon_H196 zenon_H139 zenon_H1fe zenon_Hbc zenon_H140 zenon_H68 zenon_Hb2 zenon_H7d zenon_Ha0 zenon_H13e zenon_H1bf zenon_H1b7 zenon_He4 zenon_H1c3 zenon_H1fb zenon_H25e zenon_H201 zenon_H1cb zenon_Hf5 zenon_H13a zenon_Hcc zenon_H11f. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 22.64/22.70 exact (zenon_H120 zenon_H11f). % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.70 apply (zenon_L2_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.70 apply (zenon_L2475_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.70 apply (zenon_L315_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.70 apply (zenon_L2480_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.70 apply (zenon_L318_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.70 apply (zenon_L11_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.70 apply (zenon_L2481_); trivial. % 22.64/22.70 apply (zenon_L2481_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.70 apply (zenon_L2482_); trivial. % 22.64/22.70 apply (zenon_L2482_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.70 apply (zenon_L2483_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.70 apply (zenon_L2485_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.64/22.70 apply (zenon_L2486_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.70 apply (zenon_L37_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.70 apply (zenon_L2487_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.70 apply (zenon_L387_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.70 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.70 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.70 apply (zenon_L2489_); trivial. % 22.64/22.70 apply (zenon_L372_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.70 apply (zenon_L388_); trivial. % 22.64/22.70 apply (zenon_L51_); trivial. % 22.64/22.70 (* end of lemma zenon_L2490_ *) % 22.64/22.70 assert (zenon_L2491_ : (((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 (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H82 zenon_H4c zenon_H4e zenon_H4d zenon_H55 zenon_H53 zenon_H11f zenon_H18a. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.70 exact (zenon_H4c zenon_H47). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.70 apply (zenon_L14_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.70 apply (zenon_L15_); trivial. % 22.64/22.70 apply (zenon_L140_); trivial. % 22.64/22.70 (* end of lemma zenon_L2491_ *) % 22.64/22.70 assert (zenon_L2492_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (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) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H240 zenon_H23d zenon_H3a zenon_H236 zenon_H3d zenon_H48 zenon_H1f zenon_Hac zenon_H4c zenon_H4e zenon_H55 zenon_H18a zenon_H82 zenon_H129 zenon_H13f zenon_H3c zenon_H11f zenon_Hcc zenon_H13a zenon_Hf5 zenon_H1cb zenon_H201 zenon_H25e zenon_H1fb zenon_H1c3 zenon_He4 zenon_H1b7 zenon_H1bf zenon_H13e zenon_Ha0 zenon_H7d zenon_Hb2 zenon_H68 zenon_H140 zenon_Hbc zenon_H1fe zenon_H139 zenon_H196 zenon_Ha9 zenon_Hb6 zenon_H1cd zenon_H1a2 zenon_H73 zenon_H1b4 zenon_H15d zenon_H77 zenon_H16a zenon_H1d8 zenon_H173 zenon_H11a zenon_H158 zenon_H40 zenon_H20f zenon_Heb zenon_H230 zenon_H23b. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.70 apply (zenon_L487_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.70 exact (zenon_H1f zenon_H1e). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.70 apply (zenon_L2490_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.70 exact (zenon_H237 zenon_H31). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.70 exact (zenon_Ha4 zenon_H9f). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.70 apply (zenon_L55_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.70 exact (zenon_Ha4 zenon_H9f). % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.70 apply (zenon_L46_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.70 apply (zenon_L151_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.70 apply (zenon_L95_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.70 apply (zenon_L2491_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.70 exact (zenon_H1bf zenon_H105). % 22.64/22.70 apply (zenon_L846_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.70 exact (zenon_H1bf zenon_H105). % 22.64/22.70 apply (zenon_L85_); trivial. % 22.64/22.70 apply (zenon_L44_); trivial. % 22.64/22.70 apply (zenon_L156_); trivial. % 22.64/22.70 apply (zenon_L1862_); trivial. % 22.64/22.70 (* end of lemma zenon_L2492_ *) % 22.64/22.70 assert (zenon_L2493_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e3)) = (e0))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H236 zenon_H1f zenon_H1b4 zenon_H11f zenon_H77 zenon_H48 zenon_H4c zenon_H15d zenon_H68 zenon_H66 zenon_H238. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.70 exact (zenon_H1f zenon_H1e). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.70 apply (zenon_L2484_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.70 apply (zenon_L264_); trivial. % 22.64/22.70 exact (zenon_H238 zenon_H38). % 22.64/22.70 (* end of lemma zenon_L2493_ *) % 22.64/22.70 assert (zenon_L2494_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((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)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H23b zenon_H1d5 zenon_H23d zenon_H1f zenon_H15d zenon_H11f zenon_H1b4 zenon_H66 zenon_H77 zenon_H48 zenon_H4c zenon_H68 zenon_H236. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.70 apply (zenon_L2493_); trivial. % 22.64/22.70 apply (zenon_L601_); trivial. % 22.64/22.70 (* end of lemma zenon_L2494_ *) % 22.64/22.70 assert (zenon_L2495_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((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) (e0)) = (op (e0) (e2)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H63 zenon_H236 zenon_H68 zenon_H4c zenon_H48 zenon_H77 zenon_H1b4 zenon_H11f zenon_H15d zenon_H23d zenon_H1d5. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.70 apply (zenon_L2494_); trivial. % 22.64/22.70 apply (zenon_L2494_); trivial. % 22.64/22.70 (* end of lemma zenon_L2495_ *) % 22.64/22.70 assert (zenon_L2496_ : ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H44 zenon_Hf0 zenon_H6d zenon_H11a zenon_Hac zenon_H158 zenon_H40 zenon_H87 zenon_H77 zenon_H20f zenon_H11f zenon_Heb. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.70 apply (zenon_L2358_); trivial. % 22.64/22.70 apply (zenon_L385_); trivial. % 22.64/22.70 (* end of lemma zenon_L2496_ *) % 22.64/22.70 assert (zenon_L2497_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_Heb zenon_H7a zenon_H40 zenon_H73 zenon_H153 zenon_H11f zenon_H20f. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.70 exact (zenon_H7a zenon_H3c). % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.70 exact (zenon_H40 zenon_H3f). % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.70 apply (zenon_L184_); trivial. % 22.64/22.70 apply (zenon_L412_); trivial. % 22.64/22.70 (* end of lemma zenon_L2497_ *) % 22.64/22.70 assert (zenon_L2498_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H201 zenon_H66 zenon_H77 zenon_H1d4 zenon_H1bf zenon_H11f zenon_H1cb. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.70 apply (zenon_L94_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.70 exact (zenon_H1d4 zenon_H4d). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.70 exact (zenon_H1bf zenon_H105). % 22.64/22.70 apply (zenon_L846_); trivial. % 22.64/22.70 (* end of lemma zenon_L2498_ *) % 22.64/22.70 assert (zenon_L2499_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H13a zenon_Hf6 zenon_H3d zenon_H1cb zenon_H11f zenon_H1bf zenon_H1d4 zenon_Hb6 zenon_H201 zenon_Ha5 zenon_Hf5. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.70 apply (zenon_L673_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.70 apply (zenon_L55_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.70 apply (zenon_L2488_); trivial. % 22.64/22.70 apply (zenon_L262_); trivial. % 22.64/22.70 (* end of lemma zenon_L2499_ *) % 22.64/22.70 assert (zenon_L2500_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H13a zenon_Hf6 zenon_H11f zenon_Hb6 zenon_H3d zenon_Ha0 zenon_H31 zenon_Ha5 zenon_Hf5. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.70 apply (zenon_L673_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.70 apply (zenon_L55_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.70 apply (zenon_L68_); trivial. % 22.64/22.70 apply (zenon_L262_); trivial. % 22.64/22.70 (* end of lemma zenon_L2500_ *) % 22.64/22.70 assert (zenon_L2501_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H169 zenon_He3 zenon_H11a zenon_Hac zenon_H158 zenon_H48 zenon_H25 zenon_H40 zenon_H20f zenon_H11f zenon_Heb. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.70 apply (zenon_L2474_); trivial. % 22.64/22.70 apply (zenon_L373_); trivial. % 22.64/22.70 (* end of lemma zenon_L2501_ *) % 22.64/22.70 assert (zenon_L2502_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H201 zenon_H1b7 zenon_H48 zenon_Hdd zenon_H40 zenon_H1d8 zenon_He4 zenon_H1d4 zenon_H1bf zenon_H11f zenon_H1cb. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.70 apply (zenon_L1600_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.70 exact (zenon_H1d4 zenon_H4d). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.70 exact (zenon_H1bf zenon_H105). % 22.64/22.70 apply (zenon_L846_); trivial. % 22.64/22.70 (* end of lemma zenon_L2502_ *) % 22.64/22.70 assert (zenon_L2503_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H13a zenon_H34 zenon_H7d zenon_H1b7 zenon_H48 zenon_H40 zenon_H1d8 zenon_He4 zenon_He3 zenon_H1c3 zenon_Ha9 zenon_H196 zenon_H1b4 zenon_H1fb zenon_H25e zenon_H77 zenon_He2 zenon_H3d zenon_H1cb zenon_H11f zenon_H1bf zenon_H1d4 zenon_Hb6 zenon_H201 zenon_Ha5 zenon_Hf5. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.70 apply (zenon_L1517_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.70 exact (zenon_He3 zenon_He7). % 22.64/22.70 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.70 apply (zenon_L2502_); trivial. % 22.64/22.70 apply (zenon_L802_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.70 apply (zenon_L55_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.70 apply (zenon_L2488_); trivial. % 22.64/22.70 apply (zenon_L262_); trivial. % 22.64/22.70 (* end of lemma zenon_L2503_ *) % 22.64/22.70 assert (zenon_L2504_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H13a zenon_Hac zenon_He4 zenon_H77 zenon_H40 zenon_H48 zenon_H1b7 zenon_He3 zenon_H1c3 zenon_Hf5 zenon_Ha5 zenon_H196 zenon_H1b4 zenon_H1fb zenon_H25e zenon_He2 zenon_Ha9 zenon_H6e zenon_H1cb zenon_H11f zenon_H1bf zenon_H1d4 zenon_Hb6 zenon_H201 zenon_H38 zenon_Ha0. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.70 apply (zenon_L1517_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.70 exact (zenon_He3 zenon_He7). % 22.64/22.70 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.64/22.70 apply (zenon_L214_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.64/22.70 exact (zenon_H40 zenon_H3f). % 22.64/22.70 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.64/22.70 apply (zenon_L111_); trivial. % 22.64/22.70 apply (zenon_L780_); trivial. % 22.64/22.70 apply (zenon_L107_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.70 apply (zenon_L110_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.70 apply (zenon_L2488_); trivial. % 22.64/22.70 apply (zenon_L156_); trivial. % 22.64/22.70 (* end of lemma zenon_L2504_ *) % 22.64/22.70 assert (zenon_L2505_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 22.64/22.70 do 0 intro. intros zenon_He2 zenon_H77 zenon_H25e zenon_H1fb zenon_H1b4 zenon_H196 zenon_Ha5 zenon_Hf5 zenon_Ha9 zenon_H9f zenon_H1c3 zenon_He3 zenon_H1b7 zenon_H11f zenon_H48 zenon_H40 zenon_H153 zenon_H1d8 zenon_He4 zenon_H7d zenon_H34. % 22.64/22.70 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.70 apply (zenon_L1517_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.70 exact (zenon_He3 zenon_He7). % 22.64/22.70 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.70 apply (zenon_L1600_); trivial. % 22.64/22.70 apply (zenon_L802_); trivial. % 22.64/22.70 (* end of lemma zenon_L2505_ *) % 22.64/22.70 assert (zenon_L2506_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (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) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e2)) = (op (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)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((op (e3) (e3)) = (e1)) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H290 zenon_Hf0 zenon_H230 zenon_Heb zenon_H20f zenon_H48 zenon_H158 zenon_H11a zenon_H2a zenon_H173 zenon_H1d8 zenon_H16a zenon_H77 zenon_H15d zenon_H1b4 zenon_H73 zenon_H1a2 zenon_H1cd zenon_Hb6 zenon_Ha9 zenon_H196 zenon_H139 zenon_H1fe zenon_Hbc zenon_H140 zenon_H68 zenon_Hb2 zenon_H7d zenon_Ha0 zenon_H13e zenon_H1b7 zenon_He4 zenon_H1c3 zenon_H1fb zenon_H25e zenon_H201 zenon_H1cb zenon_Hf5 zenon_H13a zenon_Hcc zenon_H11f zenon_H264. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1bf | zenon_intro zenon_H6d ]. % 22.64/22.70 apply (zenon_L2490_); trivial. % 22.64/22.70 apply (zenon_L2486_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 22.64/22.70 exact (zenon_H120 zenon_H11f). % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.70 apply (zenon_L2_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.70 apply (zenon_L482_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.70 apply (zenon_L315_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.70 apply (zenon_L2480_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.70 apply (zenon_L318_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.70 apply (zenon_L11_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.70 apply (zenon_L483_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.70 apply (zenon_L2483_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.70 apply (zenon_L2485_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.70 apply (zenon_L522_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.70 apply (zenon_L37_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.70 apply (zenon_L2487_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.70 apply (zenon_L387_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.70 apply (zenon_L531_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.70 apply (zenon_L388_); trivial. % 22.64/22.70 apply (zenon_L51_); trivial. % 22.64/22.70 (* end of lemma zenon_L2506_ *) % 22.64/22.70 assert (zenon_L2507_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H13a zenon_Ha4 zenon_H3d zenon_H11f zenon_H77 zenon_H6d zenon_H189 zenon_Ha9 zenon_H68 zenon_H1c3 zenon_H73 zenon_Hac zenon_H11a zenon_H3c zenon_Hb6 zenon_H13c zenon_H38 zenon_Ha0. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.70 exact (zenon_Ha4 zenon_H9f). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.70 apply (zenon_L55_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.70 apply (zenon_L46_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.70 apply (zenon_L79_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.70 apply (zenon_L89_); trivial. % 22.64/22.70 apply (zenon_L925_); trivial. % 22.64/22.70 apply (zenon_L156_); trivial. % 22.64/22.70 (* end of lemma zenon_L2507_ *) % 22.64/22.70 assert (zenon_L2508_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (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) (e1)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((op (e3) (e3)) = (e1)) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (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 (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H240 zenon_H6f zenon_H23d zenon_H4c zenon_H236 zenon_H3d zenon_H48 zenon_H1f zenon_H13c zenon_H189 zenon_H6d zenon_Hac zenon_H3c zenon_H264 zenon_H11f zenon_Hcc zenon_H13a zenon_Hf5 zenon_H1cb zenon_H201 zenon_H25e zenon_H1fb zenon_H1c3 zenon_He4 zenon_H1b7 zenon_H13e zenon_Ha0 zenon_H7d zenon_Hb2 zenon_H68 zenon_H140 zenon_Hbc zenon_H1fe zenon_H139 zenon_H196 zenon_Ha9 zenon_Hb6 zenon_H1cd zenon_H1a2 zenon_H73 zenon_H1b4 zenon_H15d zenon_H77 zenon_H16a zenon_H1d8 zenon_H173 zenon_H11a zenon_H158 zenon_H20f zenon_Heb zenon_H230 zenon_Hf0 zenon_H290 zenon_H23b. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.70 apply (zenon_L487_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.70 exact (zenon_H1f zenon_H1e). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.70 apply (zenon_L2506_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.70 exact (zenon_H237 zenon_H31). % 22.64/22.70 apply (zenon_L2507_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.70 exact (zenon_H1f zenon_H1e). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.70 apply (zenon_L65_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.70 exact (zenon_H6c zenon_H67). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.70 apply (zenon_L21_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.70 apply (zenon_L264_); trivial. % 22.64/22.70 apply (zenon_L1859_); trivial. % 22.64/22.70 exact (zenon_H238 zenon_H38). % 22.64/22.70 apply (zenon_L1861_); trivial. % 22.64/22.70 (* end of lemma zenon_L2508_ *) % 22.64/22.70 assert (zenon_L2509_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (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) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e2)) = (op (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)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((op (e3) (e3)) = (e1)) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H3a zenon_H290 zenon_Hf0 zenon_H230 zenon_Heb zenon_H20f zenon_H158 zenon_H11a zenon_H173 zenon_H1d8 zenon_H16a zenon_H77 zenon_H15d zenon_H1b4 zenon_H73 zenon_H1a2 zenon_H1cd zenon_Hb6 zenon_Ha9 zenon_H196 zenon_H139 zenon_H1fe zenon_Hbc zenon_H140 zenon_H68 zenon_Hb2 zenon_H7d zenon_Ha0 zenon_H13e zenon_H1b7 zenon_He4 zenon_H1c3 zenon_H1fb zenon_H25e zenon_H201 zenon_H1cb zenon_Hf5 zenon_H13a zenon_Hcc zenon_H11f zenon_H264 zenon_Hac zenon_H6d zenon_H189 zenon_H13c zenon_H48 zenon_H236 zenon_H4c zenon_H23d zenon_H6f. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.70 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.70 apply (zenon_L2508_); trivial. % 22.64/22.70 apply (zenon_L2508_); trivial. % 22.64/22.70 (* end of lemma zenon_L2509_ *) % 22.64/22.70 assert (zenon_L2510_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_Hdb zenon_H40 zenon_H55 zenon_H54 zenon_H11f zenon_H1b7. % 22.64/22.70 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.64/22.70 apply (zenon_L55_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.64/22.70 exact (zenon_H40 zenon_H3f). % 22.64/22.70 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.64/22.70 apply (zenon_L15_); trivial. % 22.64/22.70 apply (zenon_L780_); trivial. % 22.64/22.70 (* end of lemma zenon_L2510_ *) % 22.64/22.70 assert (zenon_L2511_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_Hb2 zenon_Hf6 zenon_H11f zenon_H5d zenon_Ha5 zenon_Hb6 zenon_H54 zenon_Hac zenon_H7d. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.70 apply (zenon_L673_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.70 apply (zenon_L42_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.70 apply (zenon_L151_); trivial. % 22.64/22.70 apply (zenon_L44_); trivial. % 22.64/22.70 (* end of lemma zenon_L2511_ *) % 22.64/22.70 assert (zenon_L2512_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (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))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.64/22.70 do 0 intro. intros zenon_H82 zenon_H4c zenon_H7a zenon_H7d zenon_Hac zenon_Hb6 zenon_Ha5 zenon_H5d zenon_Hb2 zenon_H13a zenon_H68 zenon_H6d zenon_H189 zenon_H1c3 zenon_H77 zenon_Ha0 zenon_H19a zenon_H1b7 zenon_H55 zenon_H40 zenon_He4 zenon_Ha9 zenon_Hf5 zenon_H6f zenon_H1e zenon_H139 zenon_H11f zenon_H18a. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.70 exact (zenon_H4c zenon_H47). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.70 exact (zenon_H7a zenon_H3c). % 22.64/22.70 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.70 apply (zenon_L20_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.70 apply (zenon_L21_); trivial. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.70 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.70 apply (zenon_L927_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.71 apply (zenon_L2510_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.71 apply (zenon_L193_); trivial. % 22.64/22.71 apply (zenon_L262_); trivial. % 22.64/22.71 apply (zenon_L2511_); trivial. % 22.64/22.71 apply (zenon_L140_); trivial. % 22.64/22.71 (* end of lemma zenon_L2512_ *) % 22.64/22.71 assert (zenon_L2513_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H15d zenon_H4c zenon_Hf5 zenon_Ha5 zenon_Ha0 zenon_Hb6 zenon_H19a zenon_H26d zenon_H77 zenon_H1c3 zenon_Ha9 zenon_H189 zenon_H6d zenon_H68 zenon_H13a zenon_H48 zenon_H31 zenon_H11f zenon_H1b4. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.71 exact (zenon_H4c zenon_H47). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.64/22.71 apply (zenon_L756_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.64/22.71 apply (zenon_L90_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.64/22.71 apply (zenon_L885_); trivial. % 22.64/22.71 apply (zenon_L926_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.71 apply (zenon_L55_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.71 apply (zenon_L68_); trivial. % 22.64/22.71 apply (zenon_L262_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.71 apply (zenon_L239_); trivial. % 22.64/22.71 apply (zenon_L187_); trivial. % 22.64/22.71 (* end of lemma zenon_L2513_ *) % 22.64/22.71 assert (zenon_L2514_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H201 zenon_H48 zenon_H31 zenon_H156 zenon_H3f zenon_H1bf zenon_H11f zenon_H1cb. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.71 apply (zenon_L239_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.71 apply (zenon_L486_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.71 exact (zenon_H1bf zenon_H105). % 22.64/22.71 apply (zenon_L846_); trivial. % 22.64/22.71 (* end of lemma zenon_L2514_ *) % 22.64/22.71 assert (zenon_L2515_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (e0))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H236 zenon_H1f zenon_H3d zenon_H1cb zenon_H11f zenon_H1bf zenon_H3f zenon_H156 zenon_H48 zenon_H201 zenon_H238. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.71 exact (zenon_H1f zenon_H1e). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.71 apply (zenon_L65_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.71 apply (zenon_L2514_); trivial. % 22.64/22.71 exact (zenon_H238 zenon_H38). % 22.64/22.71 (* end of lemma zenon_L2515_ *) % 22.64/22.71 assert (zenon_L2516_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (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 (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H240 zenon_H23d zenon_H4c zenon_H236 zenon_H156 zenon_H3f zenon_H1bf zenon_H1cb zenon_H11f zenon_H201 zenon_H3d zenon_H48 zenon_H1f zenon_H264 zenon_Hcc zenon_H13a zenon_Hf5 zenon_H25e zenon_H1fb zenon_H1c3 zenon_He4 zenon_H1b7 zenon_H13e zenon_Ha0 zenon_H7d zenon_Hb2 zenon_H68 zenon_H140 zenon_Hbc zenon_H1fe zenon_H139 zenon_H196 zenon_Ha9 zenon_Hb6 zenon_H1cd zenon_H1a2 zenon_H73 zenon_H1b4 zenon_H15d zenon_H77 zenon_H16a zenon_H1d8 zenon_H173 zenon_H11a zenon_H158 zenon_H20f zenon_Heb zenon_H230 zenon_Hf0 zenon_H290 zenon_H23b. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.71 apply (zenon_L2515_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.71 exact (zenon_H1f zenon_H1e). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.71 apply (zenon_L2506_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.71 exact (zenon_H237 zenon_H31). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.71 exact (zenon_Ha4 zenon_H9f). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.71 apply (zenon_L55_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.71 apply (zenon_L95_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.71 apply (zenon_L486_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.71 exact (zenon_H1bf zenon_H105). % 22.64/22.71 apply (zenon_L846_); trivial. % 22.64/22.71 apply (zenon_L156_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.71 apply (zenon_L2515_); trivial. % 22.64/22.71 apply (zenon_L1861_); trivial. % 22.64/22.71 (* end of lemma zenon_L2516_ *) % 22.64/22.71 assert (zenon_L2517_ : (((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 (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 22.64/22.71 do 0 intro. intros zenon_H164 zenon_H25 zenon_H179 zenon_H2a zenon_H192 zenon_Hbb zenon_Ha0 zenon_H68 zenon_H17c. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.64/22.71 apply (zenon_L297_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.64/22.71 apply (zenon_L292_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.64/22.71 apply (zenon_L80_); trivial. % 22.64/22.71 apply (zenon_L295_); trivial. % 22.64/22.71 (* end of lemma zenon_L2517_ *) % 22.64/22.71 assert (zenon_L2518_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 22.64/22.71 do 0 intro. intros zenon_H28 zenon_H164 zenon_H179 zenon_H192 zenon_Hbb zenon_Ha0 zenon_H68 zenon_H17c. % 22.64/22.71 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.64/22.71 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.64/22.71 apply (zenon_L2517_); trivial. % 22.64/22.71 (* end of lemma zenon_L2518_ *) % 22.64/22.71 assert (zenon_L2519_ : (((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)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H16a zenon_H68 zenon_H2d zenon_H1ba zenon_H8b zenon_H17c zenon_H129. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.64/22.71 apply (zenon_L27_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.64/22.71 exact (zenon_H1ba zenon_H6d). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.64/22.71 exact (zenon_H8b zenon_H8a). % 22.64/22.71 apply (zenon_L126_); trivial. % 22.64/22.71 (* end of lemma zenon_L2519_ *) % 22.64/22.71 assert (zenon_L2520_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H2f zenon_H48 zenon_H1cf zenon_H1cb zenon_H77 zenon_Hb6 zenon_Hbb zenon_H201 zenon_H68 zenon_H8b zenon_H129 zenon_H17c zenon_H16a. % 22.64/22.71 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.64/22.71 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.64/22.71 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.71 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.71 apply (zenon_L2519_); trivial. % 22.64/22.71 apply (zenon_L1916_); trivial. % 22.64/22.71 (* end of lemma zenon_L2520_ *) % 22.64/22.71 assert (zenon_L2521_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H2f zenon_H48 zenon_H1cf zenon_H1cb zenon_H77 zenon_Hb6 zenon_Hbb zenon_H201 zenon_H68 zenon_H8b zenon_H129 zenon_H17c zenon_H16a. % 22.64/22.71 apply (zenon_L2520_); trivial. % 22.64/22.71 (* end of lemma zenon_L2521_ *) % 22.64/22.71 assert (zenon_L2522_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H25e zenon_H115 zenon_H66 zenon_Ha9 zenon_H2a zenon_Ha0 zenon_H13a zenon_H1b4 zenon_H17c zenon_Hb9 zenon_H196. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H38 | zenon_intro zenon_H25f ]. % 22.64/22.71 apply (zenon_L1162_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H155 | zenon_intro zenon_H260 ]. % 22.64/22.71 apply (zenon_L494_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H9e ]. % 22.64/22.71 apply (zenon_L347_); trivial. % 22.64/22.71 apply (zenon_L154_); trivial. % 22.64/22.71 (* end of lemma zenon_L2522_ *) % 22.64/22.71 assert (zenon_L2523_ : ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H17c zenon_H68 zenon_H25e zenon_H13a zenon_H1b4 zenon_Hf5 zenon_H1fb zenon_H19a zenon_Ha0 zenon_H2a zenon_Ha9 zenon_H66 zenon_Hb9 zenon_H196. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.64/22.71 apply (zenon_L316_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.64/22.71 apply (zenon_L665_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.64/22.71 apply (zenon_L2522_); trivial. % 22.64/22.71 apply (zenon_L295_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.71 apply (zenon_L53_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.71 apply (zenon_L193_); trivial. % 22.64/22.71 apply (zenon_L154_); trivial. % 22.64/22.71 (* end of lemma zenon_L2523_ *) % 22.64/22.71 assert (zenon_L2524_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H1cf zenon_H196 zenon_Hb9 zenon_Ha9 zenon_H2a zenon_Ha0 zenon_H19a zenon_H1fb zenon_Hf5 zenon_H1b4 zenon_H13a zenon_H25e zenon_H68 zenon_H4e zenon_H76 zenon_H8b zenon_H17c zenon_H1cb. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.64/22.71 apply (zenon_L2523_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.64/22.71 apply (zenon_L83_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.64/22.71 exact (zenon_H8b zenon_H8a). % 22.64/22.71 apply (zenon_L236_); trivial. % 22.64/22.71 (* end of lemma zenon_L2524_ *) % 22.64/22.71 assert (zenon_L2525_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H13b zenon_H48 zenon_H3c zenon_H173 zenon_H20f zenon_H68 zenon_H1b3 zenon_H1cf zenon_Ha9 zenon_H2a zenon_Ha0 zenon_H19a zenon_H1fb zenon_H13a zenon_H4e zenon_H8b zenon_H1cb zenon_Hfa zenon_H25e zenon_Hf5 zenon_H9f zenon_H1b4 zenon_H17c zenon_Hb9 zenon_H196. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.71 apply (zenon_L25_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.71 apply (zenon_L272_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.71 apply (zenon_L2524_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.71 exact (zenon_H1b3 zenon_Hef). % 22.64/22.71 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.71 apply (zenon_L62_); trivial. % 22.64/22.71 apply (zenon_L570_); trivial. % 22.64/22.71 apply (zenon_L665_); trivial. % 22.64/22.71 (* end of lemma zenon_L2525_ *) % 22.64/22.71 assert (zenon_L2526_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H117 zenon_Ha0 zenon_H2d zenon_Ha9 zenon_H6d zenon_H104 zenon_Hbb zenon_H9e zenon_H196. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.64/22.71 apply (zenon_L67_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.64/22.71 apply (zenon_L289_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.64/22.71 apply (zenon_L129_); trivial. % 22.64/22.71 apply (zenon_L154_); trivial. % 22.64/22.71 (* end of lemma zenon_L2526_ *) % 22.64/22.71 assert (zenon_L2527_ : (((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))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 22.64/22.71 do 0 intro. intros zenon_H12e zenon_H48 zenon_H34 zenon_H3d zenon_H192 zenon_Hbb zenon_Hb6 zenon_H77 zenon_H17c. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H7e | zenon_intro zenon_H12f ]. % 22.64/22.71 apply (zenon_L456_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H7f | zenon_intro zenon_H130 ]. % 22.64/22.71 apply (zenon_L146_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H106 | zenon_intro zenon_H11f ]. % 22.64/22.71 apply (zenon_L363_); trivial. % 22.64/22.71 apply (zenon_L884_); trivial. % 22.64/22.71 (* end of lemma zenon_L2527_ *) % 22.64/22.71 assert (zenon_L2528_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> False). % 22.64/22.71 do 0 intro. intros zenon_H240 zenon_H77 zenon_H3d zenon_H68 zenon_H1b4 zenon_H17c zenon_H139 zenon_H31. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.71 exact (zenon_H237 zenon_H31). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.71 exact (zenon_H6c zenon_H67). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.71 apply (zenon_L214_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.71 apply (zenon_L264_); trivial. % 22.64/22.71 apply (zenon_L347_); trivial. % 22.64/22.71 (* end of lemma zenon_L2528_ *) % 22.64/22.71 assert (zenon_L2529_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((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) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e3)) = (e0))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H236 zenon_Hb6 zenon_Hbb zenon_H192 zenon_H48 zenon_H12e zenon_H13b zenon_H3c zenon_H173 zenon_H20f zenon_H1cf zenon_H19a zenon_H1fb zenon_H13a zenon_H4e zenon_H8b zenon_H1cb zenon_Hfa zenon_H25e zenon_Hf5 zenon_H177 zenon_H1a8 zenon_H1b3 zenon_H196 zenon_H104 zenon_Ha9 zenon_Ha0 zenon_H117 zenon_H1b7 zenon_H164 zenon_H179 zenon_H1f zenon_H1fe zenon_H139 zenon_H17c zenon_H1b4 zenon_H68 zenon_H3d zenon_H77 zenon_H240 zenon_H238. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.71 exact (zenon_H1f zenon_H1e). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.71 exact (zenon_H1f zenon_H1e). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.71 apply (zenon_L2517_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.71 apply (zenon_L214_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.71 exact (zenon_H1b3 zenon_Hef). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.64/22.71 apply (zenon_L67_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.64/22.71 apply (zenon_L289_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.64/22.71 apply (zenon_L129_); trivial. % 22.64/22.71 apply (zenon_L2525_); trivial. % 22.64/22.71 apply (zenon_L188_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.71 apply (zenon_L53_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.71 apply (zenon_L178_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.71 apply (zenon_L214_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.71 exact (zenon_H1b3 zenon_Hef). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.71 apply (zenon_L2526_); trivial. % 22.64/22.71 apply (zenon_L188_); trivial. % 22.64/22.71 apply (zenon_L2527_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.71 apply (zenon_L2528_); trivial. % 22.64/22.71 exact (zenon_H238 zenon_H38). % 22.64/22.71 (* end of lemma zenon_L2529_ *) % 22.64/22.71 assert (zenon_L2530_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H15d zenon_H1b4 zenon_H17c zenon_H68 zenon_H6f zenon_H139 zenon_H1cd zenon_Hbb zenon_H6d zenon_Ha9 zenon_H159 zenon_Hb6 zenon_H1c6 zenon_H48 zenon_H31 zenon_Heb zenon_H7a zenon_H40 zenon_H77 zenon_H87 zenon_Hf5. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.71 apply (zenon_L251_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.71 apply (zenon_L21_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.71 apply (zenon_L264_); trivial. % 22.64/22.71 apply (zenon_L347_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.71 apply (zenon_L1111_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.71 apply (zenon_L239_); trivial. % 22.64/22.71 apply (zenon_L1082_); trivial. % 22.64/22.71 (* end of lemma zenon_L2530_ *) % 22.64/22.71 assert (zenon_L2531_ : ((~((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 (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H15c zenon_H139 zenon_H17c zenon_H1b4 zenon_H31 zenon_H68 zenon_H6d zenon_H6f zenon_H1c6 zenon_Hbb zenon_H1cd zenon_Ha9 zenon_Hb6 zenon_H48 zenon_Hf5 zenon_H15d zenon_H7a zenon_H40 zenon_H87 zenon_H77 zenon_Heb. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.64/22.71 apply (zenon_L344_); trivial. % 22.64/22.71 apply (zenon_L2530_); trivial. % 22.64/22.71 (* end of lemma zenon_L2531_ *) % 22.64/22.71 assert (zenon_L2532_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_Hb2 zenon_H155 zenon_H17c zenon_Hec zenon_H72 zenon_H77 zenon_H40 zenon_Hb6 zenon_Heb zenon_Ha0 zenon_H2d zenon_Hbb zenon_Hbc. % 22.64/22.71 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.71 apply (zenon_L444_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.71 apply (zenon_L66_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.71 apply (zenon_L67_); trivial. % 22.64/22.71 apply (zenon_L48_); trivial. % 22.64/22.71 (* end of lemma zenon_L2532_ *) % 22.64/22.71 assert (zenon_L2533_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (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) (e3)) = (e1))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 22.64/22.71 do 0 intro. intros zenon_H19a zenon_H26d zenon_H31 zenon_H9f zenon_Hf5 zenon_H196 zenon_Hb9 zenon_H1b4 zenon_Hb2 zenon_Hec zenon_H72 zenon_H77 zenon_H40 zenon_Hb6 zenon_Heb zenon_Ha0 zenon_H2d zenon_Hbb zenon_Hbc zenon_H25e zenon_H68 zenon_H17c. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.64/22.71 apply (zenon_L756_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.64/22.71 apply (zenon_L665_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H38 | zenon_intro zenon_H25f ]. % 22.64/22.71 apply (zenon_L1162_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H155 | zenon_intro zenon_H260 ]. % 22.64/22.71 apply (zenon_L2532_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H9e ]. % 22.64/22.71 apply (zenon_L347_); trivial. % 22.64/22.71 apply (zenon_L154_); trivial. % 22.64/22.71 apply (zenon_L295_); trivial. % 22.64/22.71 (* end of lemma zenon_L2533_ *) % 22.64/22.71 assert (zenon_L2534_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (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) (e3)) = (e1))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 22.64/22.71 do 0 intro. intros zenon_H117 zenon_Ha9 zenon_H6d zenon_H104 zenon_H19a zenon_H26d zenon_H31 zenon_H9f zenon_Hf5 zenon_H196 zenon_H1b4 zenon_Hb2 zenon_Hec zenon_H72 zenon_H77 zenon_H40 zenon_Hb6 zenon_Heb zenon_Ha0 zenon_H2d zenon_Hbb zenon_Hbc zenon_H25e zenon_H68 zenon_H17c. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.64/22.71 apply (zenon_L67_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.64/22.71 apply (zenon_L289_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.64/22.71 apply (zenon_L129_); trivial. % 22.64/22.71 apply (zenon_L2533_); trivial. % 22.64/22.71 (* end of lemma zenon_L2534_ *) % 22.64/22.71 assert (zenon_L2535_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H1fe zenon_H6f zenon_H139 zenon_H48 zenon_Hbc zenon_Hbb zenon_Ha0 zenon_Heb zenon_Hb6 zenon_H40 zenon_H77 zenon_H72 zenon_Hec zenon_H117 zenon_Ha9 zenon_H104 zenon_H19a zenon_H26d zenon_Hf5 zenon_H196 zenon_H1b4 zenon_Hb2 zenon_H25e zenon_H17c zenon_He2 zenon_H1d8 zenon_H31 zenon_He3 zenon_H6d zenon_H68 zenon_H7d. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.71 apply (zenon_L20_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.71 apply (zenon_L21_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.71 apply (zenon_L264_); trivial. % 22.64/22.71 apply (zenon_L347_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.71 apply (zenon_L60_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.71 apply (zenon_L2534_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.71 apply (zenon_L66_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.71 apply (zenon_L67_); trivial. % 22.64/22.71 apply (zenon_L48_); trivial. % 22.64/22.71 apply (zenon_L1087_); trivial. % 22.64/22.71 (* end of lemma zenon_L2535_ *) % 22.64/22.71 assert (zenon_L2536_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H15c zenon_H158 zenon_H156 zenon_H3e zenon_H139 zenon_H17c zenon_H1b4 zenon_H31 zenon_H6d zenon_H6f zenon_H68 zenon_Heb zenon_H72 zenon_H77 zenon_H40 zenon_H48 zenon_Ha0 zenon_Ha9 zenon_H104 zenon_Hbb zenon_H19a zenon_Hb2 zenon_Hbc zenon_Hb6 zenon_Hf5 zenon_H196 zenon_H25e zenon_H26d zenon_H117 zenon_He2 zenon_H7d zenon_He3 zenon_H1d8 zenon_H1fe. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.64/22.71 apply (zenon_L2535_); trivial. % 22.64/22.71 apply (zenon_L102_); trivial. % 22.64/22.71 (* end of lemma zenon_L2536_ *) % 22.64/22.71 assert (zenon_L2537_ : ((~((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) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((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 (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H44 zenon_H158 zenon_H156 zenon_H72 zenon_Ha0 zenon_H104 zenon_H19a zenon_Hb2 zenon_Hbc zenon_H196 zenon_H25e zenon_H26d zenon_H117 zenon_He2 zenon_H7d zenon_H1d8 zenon_H1fe zenon_H15c zenon_H139 zenon_H17c zenon_H1b4 zenon_H31 zenon_H68 zenon_H6d zenon_H6f zenon_H1c6 zenon_Hbb zenon_H1cd zenon_Ha9 zenon_Hb6 zenon_H48 zenon_Hf5 zenon_H15d zenon_H87 zenon_H77 zenon_Heb zenon_H3e. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.71 apply (zenon_L2531_); trivial. % 22.64/22.71 apply (zenon_L2531_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.71 apply (zenon_L2536_); trivial. % 22.64/22.71 apply (zenon_L2536_); trivial. % 22.64/22.71 (* end of lemma zenon_L2537_ *) % 22.64/22.71 assert (zenon_L2538_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H13a zenon_H155 zenon_H17c zenon_Ha9 zenon_H6e zenon_Ha0 zenon_H31 zenon_Hb9 zenon_H196. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.71 apply (zenon_L444_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.71 apply (zenon_L110_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.71 apply (zenon_L68_); trivial. % 22.64/22.71 apply (zenon_L154_); trivial. % 22.64/22.71 (* end of lemma zenon_L2538_ *) % 22.64/22.71 assert (zenon_L2539_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H25e zenon_H136 zenon_Hf5 zenon_H31 zenon_Ha0 zenon_H6e zenon_Ha9 zenon_H13a zenon_H1b4 zenon_H17c zenon_Hb9 zenon_H196. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H38 | zenon_intro zenon_H25f ]. % 22.64/22.71 apply (zenon_L663_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H155 | zenon_intro zenon_H260 ]. % 22.64/22.71 apply (zenon_L2538_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H9e ]. % 22.64/22.71 apply (zenon_L347_); trivial. % 22.64/22.71 apply (zenon_L154_); trivial. % 22.64/22.71 (* end of lemma zenon_L2539_ *) % 22.64/22.71 assert (zenon_L2540_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H25e zenon_H115 zenon_H31 zenon_Ha0 zenon_H6e zenon_Ha9 zenon_H13a zenon_H1b4 zenon_H17c zenon_Hb9 zenon_H196. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H38 | zenon_intro zenon_H25f ]. % 22.64/22.71 apply (zenon_L1162_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H155 | zenon_intro zenon_H260 ]. % 22.64/22.71 apply (zenon_L2538_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H9e ]. % 22.64/22.71 apply (zenon_L347_); trivial. % 22.64/22.71 apply (zenon_L154_); trivial. % 22.64/22.71 (* end of lemma zenon_L2540_ *) % 22.64/22.71 assert (zenon_L2541_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 22.64/22.71 do 0 intro. intros zenon_H19a zenon_H26d zenon_Hf5 zenon_H196 zenon_Hb9 zenon_H1b4 zenon_H13a zenon_Ha9 zenon_H6e zenon_Ha0 zenon_H31 zenon_H25e zenon_H68 zenon_H17c. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.64/22.71 apply (zenon_L756_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.64/22.71 apply (zenon_L2539_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.64/22.71 apply (zenon_L2540_); trivial. % 22.64/22.71 apply (zenon_L295_); trivial. % 22.64/22.71 (* end of lemma zenon_L2541_ *) % 22.64/22.71 assert (zenon_L2542_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.64/22.71 do 0 intro. intros zenon_H1a8 zenon_H68 zenon_H25e zenon_H31 zenon_Ha0 zenon_Ha9 zenon_H13a zenon_H1b4 zenon_Hb9 zenon_H196 zenon_Hf5 zenon_H26d zenon_H19a zenon_H1b3 zenon_H1ba zenon_H17c zenon_H1b7. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.71 apply (zenon_L2541_); trivial. % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.71 exact (zenon_H1b3 zenon_Hef). % 22.64/22.71 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.71 exact (zenon_H1ba zenon_H6d). % 22.64/22.71 apply (zenon_L188_); trivial. % 22.64/22.71 (* end of lemma zenon_L2542_ *) % 22.64/22.71 assert (zenon_L2543_ : ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e1))) -> (((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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> False). % 22.64/22.72 do 0 intro. intros zenon_H31 zenon_H1d8 zenon_H16a zenon_H129 zenon_H8b zenon_H68 zenon_H201 zenon_Hb6 zenon_H77 zenon_H1cb zenon_H1cf zenon_H48 zenon_H139 zenon_H1b4 zenon_H271 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_Heb zenon_H15d zenon_Hf5 zenon_Ha9 zenon_H1c6 zenon_H6f zenon_H1fe zenon_H7d zenon_He2 zenon_H117 zenon_H26d zenon_H25e zenon_H196 zenon_Hb2 zenon_H19a zenon_H104 zenon_Ha0 zenon_H156 zenon_H158 zenon_H1a8 zenon_H1b7 zenon_H1b3 zenon_H13a zenon_H17c. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 22.64/22.72 exact (zenon_H181 zenon_H17c). % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.72 apply (zenon_L2_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.72 apply (zenon_L700_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.72 apply (zenon_L2520_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.72 apply (zenon_L784_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.72 apply (zenon_L2528_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.72 apply (zenon_L11_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.64/22.72 apply (zenon_L793_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.72 apply (zenon_L788_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.72 apply (zenon_L814_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.72 apply (zenon_L2537_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.72 apply (zenon_L37_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.72 apply (zenon_L790_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.72 apply (zenon_L791_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.72 apply (zenon_L361_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.72 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.64/22.72 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.72 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.72 apply (zenon_L2542_); trivial. % 22.64/22.72 apply (zenon_L1916_); trivial. % 22.64/22.72 apply (zenon_L51_); trivial. % 22.64/22.72 (* end of lemma zenon_L2543_ *) % 22.64/22.72 assert (zenon_L2544_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (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 (e0) (e1)) = (op (e0) (e3)))) -> (((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) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((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 (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (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) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (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 (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H204 zenon_H23d zenon_H236 zenon_H139 zenon_H240 zenon_H164 zenon_H17c zenon_H68 zenon_Hbb zenon_Ha0 zenon_H192 zenon_H179 zenon_H177 zenon_H77 zenon_H3d zenon_H1b3 zenon_H117 zenon_H48 zenon_H3c zenon_H173 zenon_Hfa zenon_H20f zenon_H1fb zenon_H25e zenon_H196 zenon_H1b4 zenon_Hf5 zenon_H13a zenon_H19a zenon_H4e zenon_H8b zenon_H1cb zenon_H1cf zenon_H13b zenon_H104 zenon_Ha9 zenon_H1b7 zenon_H1a8 zenon_H12e zenon_Hb6 zenon_H1fe zenon_H1f zenon_H6c zenon_H158 zenon_H156 zenon_Hb2 zenon_H26d zenon_He2 zenon_H7d zenon_H6f zenon_H1c6 zenon_H15d zenon_Heb zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H271 zenon_H201 zenon_H129 zenon_H16a zenon_H1d8 zenon_H23b. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.72 apply (zenon_L2529_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.72 exact (zenon_H1f zenon_H1e). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.72 exact (zenon_H205 zenon_H2a). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.72 apply (zenon_L2543_); trivial. % 22.64/22.72 apply (zenon_L1857_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.72 apply (zenon_L2529_); trivial. % 22.64/22.72 apply (zenon_L1861_); trivial. % 22.64/22.72 (* end of lemma zenon_L2544_ *) % 22.64/22.72 assert (zenon_L2545_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H139 zenon_H6c zenon_H77 zenon_H3d zenon_H196 zenon_Hb9 zenon_Ha9 zenon_H2a zenon_Ha0 zenon_H19a zenon_H1fb zenon_Hf5 zenon_H13a zenon_H25e zenon_H68 zenon_H17c zenon_H1b4. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.72 apply (zenon_L214_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.72 apply (zenon_L2523_); trivial. % 22.64/22.72 apply (zenon_L347_); trivial. % 22.64/22.72 (* end of lemma zenon_L2545_ *) % 22.64/22.72 assert (zenon_L2546_ : (((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)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H117 zenon_H65 zenon_H6d zenon_H104 zenon_Hbb zenon_H139 zenon_H6c zenon_H77 zenon_H3d zenon_H196 zenon_Ha9 zenon_H2a zenon_Ha0 zenon_H19a zenon_H1fb zenon_Hf5 zenon_H13a zenon_H25e zenon_H68 zenon_H17c zenon_H1b4. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.64/22.72 apply (zenon_L43_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.64/22.72 apply (zenon_L289_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.64/22.72 apply (zenon_L129_); trivial. % 22.64/22.72 apply (zenon_L2545_); trivial. % 22.64/22.72 (* end of lemma zenon_L2546_ *) % 22.64/22.72 assert (zenon_L2547_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_Hb2 zenon_H155 zenon_H17c zenon_Hb6 zenon_H3c zenon_Ha9 zenon_H65 zenon_Hbb zenon_Hbc. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.72 apply (zenon_L444_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.72 apply (zenon_L46_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.72 apply (zenon_L43_); trivial. % 22.64/22.72 apply (zenon_L48_); trivial. % 22.64/22.72 (* end of lemma zenon_L2547_ *) % 22.64/22.72 assert (zenon_L2548_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H82 zenon_H4c zenon_Hbc zenon_Hbb zenon_Ha9 zenon_Hb6 zenon_H17c zenon_H155 zenon_Hb2 zenon_H65 zenon_H77 zenon_H34 zenon_H48. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.72 exact (zenon_H4c zenon_H47). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.72 apply (zenon_L2547_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.72 apply (zenon_L30_); trivial. % 22.64/22.72 apply (zenon_L456_); trivial. % 22.64/22.72 (* end of lemma zenon_L2548_ *) % 22.64/22.72 assert (zenon_L2549_ : ((~((op (e0) (e1)) = (e0)))\/(~((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 (e0) (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 (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e1)) = (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (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) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H204 zenon_H164 zenon_Hbb zenon_H192 zenon_H179 zenon_H82 zenon_H6c zenon_H1fb zenon_H23d zenon_H236 zenon_H66 zenon_H68 zenon_H1f zenon_H65 zenon_H55 zenon_H17c zenon_H13a zenon_H1b3 zenon_H1b7 zenon_H1a8 zenon_H158 zenon_H156 zenon_Ha0 zenon_H104 zenon_H19a zenon_Hb2 zenon_H196 zenon_H25e zenon_H26d zenon_H117 zenon_He2 zenon_H7d zenon_H1fe zenon_H6f zenon_H1c6 zenon_Ha9 zenon_Hf5 zenon_H15d zenon_Heb zenon_H270 zenon_Hcc zenon_H1cd zenon_Hbc zenon_H111 zenon_H271 zenon_H1b4 zenon_H139 zenon_H48 zenon_H1cf zenon_H1cb zenon_H77 zenon_Hb6 zenon_H201 zenon_H8b zenon_H129 zenon_H16a zenon_H1d8 zenon_H23b. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.72 apply (zenon_L1866_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.72 exact (zenon_H1f zenon_H1e). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.72 exact (zenon_H205 zenon_H2a). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.72 apply (zenon_L2543_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.72 exact (zenon_Ha4 zenon_H9f). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.72 apply (zenon_L110_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.72 exact (zenon_H1b3 zenon_Hef). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.72 apply (zenon_L34_); trivial. % 22.64/22.72 apply (zenon_L188_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.72 apply (zenon_L193_); trivial. % 22.64/22.72 apply (zenon_L156_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.72 exact (zenon_H1f zenon_H1e). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.72 exact (zenon_H1f zenon_H1e). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.72 apply (zenon_L2517_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.72 apply (zenon_L27_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.72 exact (zenon_H4c zenon_H47). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.72 apply (zenon_L214_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.72 exact (zenon_H1b3 zenon_Hef). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.72 apply (zenon_L2546_); trivial. % 22.64/22.72 apply (zenon_L188_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.72 apply (zenon_L94_); trivial. % 22.64/22.72 apply (zenon_L2548_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.72 apply (zenon_L264_); trivial. % 22.64/22.72 exact (zenon_H238 zenon_H38). % 22.64/22.72 apply (zenon_L1861_); trivial. % 22.64/22.72 (* end of lemma zenon_L2549_ *) % 22.64/22.72 assert (zenon_L2550_ : (((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)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H139 zenon_H6c zenon_H6f zenon_H6d zenon_H153 zenon_H77 zenon_H17c zenon_H1b4. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.72 apply (zenon_L21_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.72 apply (zenon_L94_); trivial. % 22.64/22.72 apply (zenon_L347_); trivial. % 22.64/22.72 (* end of lemma zenon_L2550_ *) % 22.64/22.72 assert (zenon_L2551_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3))))))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H15c zenon_H15d zenon_Hf5 zenon_H6c zenon_H6f zenon_H1b4 zenon_H17c zenon_H139 zenon_Hb6 zenon_Ha9 zenon_H6d zenon_H1cd zenon_Hbb zenon_H1c6 zenon_H48 zenon_H158 zenon_H1b3 zenon_H173 zenon_H68 zenon_H72 zenon_H73 zenon_H236 zenon_H7a zenon_H40 zenon_H87 zenon_H77 zenon_Heb. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.64/22.72 apply (zenon_L344_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.72 apply (zenon_L13_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.72 apply (zenon_L1111_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.72 apply (zenon_L2550_); trivial. % 22.64/22.72 apply (zenon_L1082_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.72 apply (zenon_L304_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.72 apply (zenon_L2530_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.72 apply (zenon_L21_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.72 apply (zenon_L22_); trivial. % 22.64/22.72 apply (zenon_L165_); trivial. % 22.64/22.72 (* end of lemma zenon_L2551_ *) % 22.64/22.72 assert (zenon_L2552_ : (((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) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> ((op (e0) (e0)) = (e1)) -> (((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). % 22.64/22.72 do 0 intro. intros zenon_H125 zenon_H6c zenon_H4e zenon_Hbc zenon_Hbb zenon_Ha9 zenon_Heb zenon_Hb6 zenon_H40 zenon_H77 zenon_H72 zenon_Hec zenon_H47 zenon_Hb2 zenon_H17c zenon_H18a. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.72 apply (zenon_L83_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.72 apply (zenon_L253_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.72 apply (zenon_L66_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.72 apply (zenon_L43_); trivial. % 22.64/22.72 apply (zenon_L48_); trivial. % 22.64/22.72 apply (zenon_L268_); trivial. % 22.64/22.72 (* end of lemma zenon_L2552_ *) % 22.64/22.72 assert (zenon_L2553_ : (((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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H117 zenon_H65 zenon_Ha9 zenon_H6d zenon_H104 zenon_Hbb zenon_H25e zenon_H136 zenon_Hf5 zenon_H9f zenon_H1b4 zenon_H17c zenon_H196. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.64/22.72 apply (zenon_L43_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.64/22.72 apply (zenon_L289_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.64/22.72 apply (zenon_L129_); trivial. % 22.64/22.72 apply (zenon_L665_); trivial. % 22.64/22.72 (* end of lemma zenon_L2553_ *) % 22.64/22.72 assert (zenon_L2554_ : (((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) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (((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). % 22.64/22.72 do 0 intro. intros zenon_H125 zenon_H6c zenon_H4e zenon_H72 zenon_Hbc zenon_Hbb zenon_Ha9 zenon_H3c zenon_Hb6 zenon_H155 zenon_Hb2 zenon_H17c zenon_H18a. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.72 apply (zenon_L83_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.72 apply (zenon_L2547_); trivial. % 22.64/22.72 apply (zenon_L268_); trivial. % 22.64/22.72 (* end of lemma zenon_L2554_ *) % 22.64/22.72 assert (zenon_L2555_ : (((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) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H125 zenon_H6c zenon_H4e zenon_H72 zenon_H54 zenon_H77 zenon_H17c zenon_H18a. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.72 apply (zenon_L83_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.72 apply (zenon_L30_); trivial. % 22.64/22.72 apply (zenon_L268_); trivial. % 22.64/22.72 (* end of lemma zenon_L2555_ *) % 22.64/22.72 assert (zenon_L2556_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (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 (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H125 zenon_H4e zenon_H72 zenon_H1b4 zenon_H68 zenon_H25e zenon_H13a zenon_Hf5 zenon_H1fb zenon_H19a zenon_Ha0 zenon_H2a zenon_Ha9 zenon_H196 zenon_H3d zenon_H77 zenon_H6c zenon_H139 zenon_Hbb zenon_H104 zenon_H6d zenon_H117 zenon_H17c zenon_H18a. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.72 apply (zenon_L83_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.72 apply (zenon_L2546_); trivial. % 22.64/22.72 apply (zenon_L268_); trivial. % 22.64/22.72 (* end of lemma zenon_L2556_ *) % 22.64/22.72 assert (zenon_L2557_ : (((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 (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 22.64/22.72 do 0 intro. intros zenon_H164 zenon_H48 zenon_H7e zenon_H2a zenon_H192 zenon_Hbb zenon_Ha0 zenon_H68 zenon_H17c. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.64/22.72 apply (zenon_L456_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.64/22.72 apply (zenon_L292_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.64/22.72 apply (zenon_L80_); trivial. % 22.64/22.72 apply (zenon_L295_); trivial. % 22.64/22.72 (* end of lemma zenon_L2557_ *) % 22.64/22.72 assert (zenon_L2558_ : ((~((op (e1) (e3)) = (e1)))\/(~((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) (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) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((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))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H15c zenon_H156 zenon_H158 zenon_H15d zenon_H82 zenon_H6f zenon_H6d zenon_H13b zenon_H104 zenon_H25e zenon_H196 zenon_H1b4 zenon_Hf5 zenon_H117 zenon_H68 zenon_He3 zenon_H48 zenon_H13a zenon_H139 zenon_H6c zenon_H4e zenon_H72 zenon_Hb2 zenon_Hbb zenon_Hbc zenon_Ha9 zenon_H40 zenon_H77 zenon_Heb zenon_Hb6 zenon_H18a zenon_H17c zenon_H125 zenon_H164 zenon_H192 zenon_H1fb zenon_Ha0 zenon_H19a zenon_H1fe zenon_H1d8 zenon_H7d zenon_He2 zenon_H26d zenon_H236. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.72 apply (zenon_L2552_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.72 apply (zenon_L21_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.72 apply (zenon_L83_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.72 apply (zenon_L60_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.72 exact (zenon_He3 zenon_He7). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.72 apply (zenon_L62_); trivial. % 22.64/22.72 apply (zenon_L2553_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.72 apply (zenon_L55_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.72 apply (zenon_L193_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.64/22.72 apply (zenon_L43_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.64/22.72 apply (zenon_L289_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.64/22.72 apply (zenon_L129_); trivial. % 22.64/22.72 apply (zenon_L154_); trivial. % 22.64/22.72 apply (zenon_L268_); trivial. % 22.64/22.72 apply (zenon_L347_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.72 apply (zenon_L2550_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.72 apply (zenon_L13_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.72 apply (zenon_L2554_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.72 apply (zenon_L2555_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.72 apply (zenon_L83_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.72 apply (zenon_L444_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.72 apply (zenon_L66_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.72 apply (zenon_L43_); trivial. % 22.64/22.72 apply (zenon_L48_); trivial. % 22.64/22.72 apply (zenon_L71_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.72 apply (zenon_L2552_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.72 apply (zenon_L2556_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.72 apply (zenon_L2550_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.72 apply (zenon_L2552_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.72 apply (zenon_L2554_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.72 apply (zenon_L2555_); trivial. % 22.64/22.72 apply (zenon_L2557_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.72 apply (zenon_L2535_); trivial. % 22.64/22.72 apply (zenon_L2369_); trivial. % 22.64/22.72 apply (zenon_L101_); trivial. % 22.64/22.72 (* end of lemma zenon_L2558_ *) % 22.64/22.72 assert (zenon_L2559_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H1a8 zenon_H77 zenon_H3d zenon_H1b3 zenon_H1ba zenon_H17c zenon_H1b7. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.72 apply (zenon_L214_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.72 exact (zenon_H1b3 zenon_Hef). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.72 exact (zenon_H1ba zenon_H6d). % 22.64/22.72 apply (zenon_L188_); trivial. % 22.64/22.72 (* end of lemma zenon_L2559_ *) % 22.64/22.72 assert (zenon_L2560_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H139 zenon_H6c zenon_H129 zenon_H8b zenon_H6f zenon_H7b zenon_H16a zenon_H153 zenon_H77 zenon_H17c zenon_H1b4. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.72 apply (zenon_L1365_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.72 apply (zenon_L94_); trivial. % 22.64/22.72 apply (zenon_L347_); trivial. % 22.64/22.72 (* end of lemma zenon_L2560_ *) % 22.64/22.72 assert (zenon_L2561_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H1a8 zenon_Ha9 zenon_Hdb zenon_H1b3 zenon_H1ba zenon_H17c zenon_H1b7. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.72 apply (zenon_L110_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.72 exact (zenon_H1b3 zenon_Hef). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.72 exact (zenon_H1ba zenon_H6d). % 22.64/22.72 apply (zenon_L188_); trivial. % 22.64/22.72 (* end of lemma zenon_L2561_ *) % 22.64/22.72 assert (zenon_L2562_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H13a zenon_H155 zenon_H1b7 zenon_H17c zenon_H1ba zenon_H1b3 zenon_Ha9 zenon_H1a8 zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.72 apply (zenon_L444_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.72 apply (zenon_L2561_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.72 apply (zenon_L178_); trivial. % 22.64/22.72 apply (zenon_L154_); trivial. % 22.64/22.72 (* end of lemma zenon_L2562_ *) % 22.64/22.72 assert (zenon_L2563_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H139 zenon_H6c zenon_Hbb zenon_H177 zenon_H47 zenon_Hb6 zenon_H196 zenon_Hb9 zenon_Ha9 zenon_H2a zenon_Ha0 zenon_H19a zenon_H1fb zenon_Hf5 zenon_H13a zenon_H25e zenon_H68 zenon_H17c zenon_H1b4. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.72 apply (zenon_L986_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.72 apply (zenon_L2523_); trivial. % 22.64/22.72 apply (zenon_L347_); trivial. % 22.64/22.72 (* end of lemma zenon_L2563_ *) % 22.64/22.72 assert (zenon_L2564_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H13a zenon_H155 zenon_H17c zenon_Ha0 zenon_H2a zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.72 apply (zenon_L444_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.72 apply (zenon_L53_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.72 apply (zenon_L178_); trivial. % 22.64/22.72 apply (zenon_L154_); trivial. % 22.64/22.72 (* end of lemma zenon_L2564_ *) % 22.64/22.72 assert (zenon_L2565_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H15d zenon_Hb6 zenon_H68 zenon_H25e zenon_Hf5 zenon_H1fb zenon_H19a zenon_Ha9 zenon_H1b4 zenon_H77 zenon_H16a zenon_H7b zenon_H6f zenon_H8b zenon_H129 zenon_H6c zenon_H139 zenon_H13a zenon_H17c zenon_Ha0 zenon_H2a zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.72 apply (zenon_L2563_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.72 apply (zenon_L2545_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.72 apply (zenon_L2560_); trivial. % 22.64/22.72 apply (zenon_L2564_); trivial. % 22.64/22.72 (* end of lemma zenon_L2565_ *) % 22.64/22.72 assert (zenon_L2566_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((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)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((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). % 22.64/22.72 do 0 intro. intros zenon_H139 zenon_H6c zenon_H196 zenon_Hb9 zenon_Hbb zenon_H177 zenon_Ha0 zenon_H38 zenon_Ha9 zenon_H1a8 zenon_H1b3 zenon_H1ba zenon_H1b7 zenon_H47 zenon_Hb6 zenon_H13a zenon_H17c zenon_H1b4. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.72 apply (zenon_L986_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.72 apply (zenon_L253_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.72 apply (zenon_L2561_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.72 apply (zenon_L193_); trivial. % 22.64/22.72 apply (zenon_L156_); trivial. % 22.64/22.72 apply (zenon_L347_); trivial. % 22.64/22.72 (* end of lemma zenon_L2566_ *) % 22.64/22.72 assert (zenon_L2567_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H139 zenon_H6c zenon_H129 zenon_H17c zenon_H8b zenon_H6f zenon_H7b zenon_H16a zenon_H153 zenon_H77 zenon_H38 zenon_H68. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.72 apply (zenon_L1365_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.72 apply (zenon_L94_); trivial. % 22.64/22.72 apply (zenon_L165_); trivial. % 22.64/22.72 (* end of lemma zenon_L2567_ *) % 22.64/22.72 assert (zenon_L2568_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H13a zenon_H17c zenon_H68 zenon_Ha0 zenon_H25e zenon_Hf5 zenon_H1b4 zenon_H25b zenon_H186 zenon_H4d zenon_H20f zenon_H195 zenon_H19a zenon_Hb6 zenon_H3d zenon_Ha9 zenon_H66 zenon_Hb9 zenon_H196. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.72 apply (zenon_L666_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.72 apply (zenon_L55_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.72 apply (zenon_L193_); trivial. % 22.64/22.72 apply (zenon_L154_); trivial. % 22.64/22.72 (* end of lemma zenon_L2568_ *) % 22.64/22.72 assert (zenon_L2569_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (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) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.72 do 0 intro. intros zenon_H139 zenon_H6c zenon_H129 zenon_H8b zenon_H6f zenon_H7b zenon_H16a zenon_Hbb zenon_Hb6 zenon_H1bf zenon_H13a zenon_H68 zenon_Ha0 zenon_H25e zenon_Hf5 zenon_H25b zenon_H186 zenon_H20f zenon_H195 zenon_H19a zenon_H3d zenon_Ha9 zenon_Hb9 zenon_H196 zenon_H77 zenon_H201 zenon_H17c zenon_H1b4. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.72 exact (zenon_H6c zenon_H67). % 22.64/22.72 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.72 apply (zenon_L1365_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.72 apply (zenon_L94_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.72 apply (zenon_L2568_); trivial. % 22.64/22.72 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.72 exact (zenon_H1bf zenon_H105). % 22.64/22.72 apply (zenon_L363_); trivial. % 22.64/22.72 apply (zenon_L347_); trivial. % 22.64/22.72 (* end of lemma zenon_L2569_ *) % 22.64/22.72 assert (zenon_L2570_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 22.64/22.73 do 0 intro. intros zenon_H164 zenon_H1e zenon_H33 zenon_Hbc zenon_H18a zenon_H7d zenon_H7f zenon_H212 zenon_Hbb zenon_Ha0 zenon_H68 zenon_H17c. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H34 | zenon_intro zenon_H165 ]. % 22.64/22.73 apply (zenon_L7_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_He0 | zenon_intro zenon_H166 ]. % 22.64/22.73 apply (zenon_L1375_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H11d | zenon_intro zenon_H167 ]. % 22.64/22.73 apply (zenon_L80_); trivial. % 22.64/22.73 apply (zenon_L295_); trivial. % 22.64/22.73 (* end of lemma zenon_L2570_ *) % 22.64/22.73 assert (zenon_L2571_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 22.64/22.73 do 0 intro. intros zenon_He4 zenon_Hb6 zenon_Hdb zenon_H156 zenon_H4d zenon_H55 zenon_H54 zenon_H164 zenon_H1e zenon_H33 zenon_Hbc zenon_H18a zenon_H7d zenon_H212 zenon_Hbb zenon_Ha0 zenon_H68 zenon_H17c. % 22.64/22.73 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.64/22.73 apply (zenon_L55_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.64/22.73 apply (zenon_L486_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.64/22.73 apply (zenon_L15_); trivial. % 22.64/22.73 apply (zenon_L2570_); trivial. % 22.64/22.73 (* end of lemma zenon_L2571_ *) % 22.64/22.73 assert (zenon_L2572_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.73 do 0 intro. intros zenon_H16a zenon_H54 zenon_H77 zenon_H1ba zenon_H8b zenon_H17c zenon_H129. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.64/22.73 apply (zenon_L30_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.64/22.73 exact (zenon_H1ba zenon_H6d). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.64/22.73 exact (zenon_H8b zenon_H8a). % 22.64/22.73 apply (zenon_L126_); trivial. % 22.64/22.73 (* end of lemma zenon_L2572_ *) % 22.64/22.73 assert (zenon_L2573_ : (((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 (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 22.64/22.73 do 0 intro. intros zenon_H13f zenon_H129 zenon_H17c zenon_H8b zenon_H1ba zenon_H77 zenon_H16a zenon_Hdd zenon_H48 zenon_H153 zenon_H111 zenon_Hb6 zenon_Hb9. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.73 apply (zenon_L2572_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.73 apply (zenon_L111_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.73 apply (zenon_L148_); trivial. % 22.64/22.73 apply (zenon_L182_); trivial. % 22.64/22.73 (* end of lemma zenon_L2573_ *) % 22.64/22.73 assert (zenon_L2574_ : ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.73 do 0 intro. intros zenon_H17c zenon_H1b4 zenon_Hf5 zenon_H25e zenon_Hfa zenon_H1cb zenon_H8b zenon_H4e zenon_H13a zenon_H1fb zenon_H19a zenon_Ha9 zenon_H1cf zenon_H1b3 zenon_H68 zenon_H20f zenon_H173 zenon_H3c zenon_H48 zenon_H13b zenon_Ha0 zenon_H2a zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.73 apply (zenon_L2525_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.73 apply (zenon_L53_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.73 apply (zenon_L178_); trivial. % 22.64/22.73 apply (zenon_L154_); trivial. % 22.64/22.73 (* end of lemma zenon_L2574_ *) % 22.64/22.73 assert (zenon_L2575_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((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))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 22.64/22.73 do 0 intro. intros zenon_H91 zenon_H13d zenon_H104 zenon_Hbb zenon_H13e zenon_H68 zenon_H2d zenon_H8b zenon_H129 zenon_H17c zenon_H16a. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.73 apply (zenon_L2519_); trivial. % 22.64/22.73 apply (zenon_L196_); trivial. % 22.64/22.73 (* end of lemma zenon_L2575_ *) % 22.64/22.73 assert (zenon_L2576_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (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 (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> False). % 22.64/22.73 do 0 intro. intros zenon_H91 zenon_H13d zenon_H8b zenon_H104 zenon_Hbb zenon_H13e zenon_H19a zenon_H68 zenon_Hf5 zenon_H13a zenon_Hb9 zenon_H196 zenon_Ha0 zenon_Ha9 zenon_H17c zenon_H1b4 zenon_H25e zenon_H31 zenon_H26d zenon_H1b3 zenon_H1b7 zenon_H1a8. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.73 apply (zenon_L2542_); trivial. % 22.64/22.73 apply (zenon_L196_); trivial. % 22.64/22.73 (* end of lemma zenon_L2576_ *) % 22.64/22.73 assert (zenon_L2577_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (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) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 22.64/22.73 do 0 intro. intros zenon_H82 zenon_H1b4 zenon_H13a zenon_Hb6 zenon_H1b7 zenon_H1b3 zenon_H1a8 zenon_Ha9 zenon_Ha0 zenon_H177 zenon_Hbb zenon_H196 zenon_H6c zenon_H139 zenon_H195 zenon_Hb9 zenon_H20f zenon_H5d zenon_Hf5 zenon_H38 zenon_H25b zenon_H129 zenon_H17c zenon_H8b zenon_H1ba zenon_H77 zenon_H16a zenon_H34 zenon_H48. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 apply (zenon_L2566_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_L1297_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_L2572_); trivial. % 22.64/22.73 apply (zenon_L456_); trivial. % 22.64/22.73 (* end of lemma zenon_L2577_ *) % 22.64/22.73 assert (zenon_L2578_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.73 do 0 intro. intros zenon_H3a zenon_H139 zenon_H6c zenon_H77 zenon_H8a zenon_H111 zenon_H17c zenon_H1b4. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.73 apply (zenon_L785_); trivial. % 22.64/22.73 (* end of lemma zenon_L2578_ *) % 22.64/22.73 assert (zenon_L2579_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((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 (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((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))))) -> (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3))))))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 22.64/22.73 do 0 intro. intros zenon_H204 zenon_H4e zenon_H77 zenon_H164 zenon_H192 zenon_H48 zenon_H82 zenon_H23d zenon_H1d5 zenon_H236 zenon_H66 zenon_H68 zenon_H1f zenon_H117 zenon_Hf5 zenon_H186 zenon_H4d zenon_H20f zenon_H17c zenon_H195 zenon_H25b zenon_Hbb zenon_H104 zenon_H6f zenon_H65 zenon_Ha9 zenon_H177 zenon_Ha0 zenon_H13a zenon_H63 zenon_H23b. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.73 apply (zenon_L1866_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.73 exact (zenon_H1f zenon_H1e). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.73 exact (zenon_H205 zenon_H2a). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.73 apply (zenon_L814_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.73 exact (zenon_Ha4 zenon_H9f). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.64/22.73 apply (zenon_L43_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.64/22.73 apply (zenon_L205_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.64/22.73 apply (zenon_L129_); trivial. % 22.64/22.73 apply (zenon_L664_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.73 apply (zenon_L178_); trivial. % 22.64/22.73 apply (zenon_L156_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.73 exact (zenon_H1f zenon_H1e). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 exact (zenon_H4c zenon_H47). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_L14_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_L30_); trivial. % 22.64/22.73 apply (zenon_L2557_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.73 apply (zenon_L264_); trivial. % 22.64/22.73 exact (zenon_H238 zenon_H38). % 22.64/22.73 apply (zenon_L601_); trivial. % 22.64/22.73 (* end of lemma zenon_L2579_ *) % 22.64/22.73 assert (zenon_L2580_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (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))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 22.64/22.73 do 0 intro. intros zenon_H15d zenon_H1b4 zenon_H25e zenon_Hf5 zenon_H25b zenon_H186 zenon_H20f zenon_H195 zenon_H19a zenon_Ha9 zenon_H6c zenon_H139 zenon_H73 zenon_H82 zenon_H48 zenon_H94 zenon_Hb2 zenon_H55 zenon_H164 zenon_H1e zenon_H33 zenon_Hbc zenon_H18a zenon_H212 zenon_Ha0 zenon_H68 zenon_H13a zenon_H7d zenon_H16a zenon_H7b zenon_H77 zenon_H8b zenon_H17c zenon_H129 zenon_H4d zenon_H156 zenon_Hb6 zenon_He4 zenon_H177 zenon_Hbb zenon_Hb9 zenon_H196. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.73 exact (zenon_H6c zenon_H67). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.73 apply (zenon_L214_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.73 apply (zenon_L2568_); trivial. % 22.64/22.73 apply (zenon_L347_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_L184_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_L2366_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.73 apply (zenon_L444_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.73 apply (zenon_L2571_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.73 apply (zenon_L178_); trivial. % 22.64/22.73 apply (zenon_L154_); trivial. % 22.64/22.73 apply (zenon_L942_); trivial. % 22.64/22.73 (* end of lemma zenon_L2580_ *) % 22.64/22.73 assert (zenon_L2581_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (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) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 22.64/22.73 do 0 intro. intros zenon_H139 zenon_H6c zenon_H20f zenon_H4d zenon_H77 zenon_H173 zenon_H1cf zenon_H4e zenon_H8b zenon_H1cb zenon_Hfa zenon_H196 zenon_Hb9 zenon_Ha9 zenon_H2a zenon_Ha0 zenon_H19a zenon_H1fb zenon_Hf5 zenon_H13a zenon_H25e zenon_H68 zenon_H17c zenon_H1b4. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.73 exact (zenon_H6c zenon_H67). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.73 apply (zenon_L2524_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.73 apply (zenon_L226_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.73 apply (zenon_L59_); trivial. % 22.64/22.73 apply (zenon_L570_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.73 apply (zenon_L2523_); trivial. % 22.64/22.73 apply (zenon_L347_); trivial. % 22.64/22.73 (* end of lemma zenon_L2581_ *) % 22.64/22.73 assert (zenon_L2582_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3))))))))) -> (~((op (e1) (e2)) = (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) (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)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (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) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (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) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (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) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 22.64/22.73 do 0 intro. intros zenon_Hc0 zenon_H131 zenon_H104 zenon_H13e zenon_H15d zenon_Hb2 zenon_Hbc zenon_H94 zenon_H177 zenon_H156 zenon_H55 zenon_H164 zenon_H7d zenon_H18a zenon_H212 zenon_H33 zenon_He4 zenon_H16a zenon_H129 zenon_H8b zenon_H82 zenon_H73 zenon_H6c zenon_H77 zenon_H13a zenon_Ha9 zenon_Hb6 zenon_H25b zenon_H195 zenon_H17c zenon_H20f zenon_H4d zenon_H186 zenon_Hf5 zenon_H25e zenon_H196 zenon_H1b4 zenon_Ha0 zenon_H68 zenon_H19a zenon_H139 zenon_H48 zenon_H1cf zenon_H1cb zenon_H4e zenon_H1fb zenon_H173 zenon_Hfa zenon_H236. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.73 apply (zenon_L2580_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.73 apply (zenon_L2581_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.73 apply (zenon_L781_); trivial. % 22.64/22.73 apply (zenon_L664_); trivial. % 22.64/22.73 apply (zenon_L130_); trivial. % 22.64/22.73 (* end of lemma zenon_L2582_ *) % 22.64/22.73 assert (zenon_L2583_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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 (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((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)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((op (e3) (e3)) = (e2)) -> False). % 22.64/22.73 do 0 intro. intros zenon_H271 zenon_H179 zenon_H192 zenon_Ha0 zenon_H68 zenon_H164 zenon_H48 zenon_H1cf zenon_H1cb zenon_H77 zenon_Hb6 zenon_H201 zenon_H8b zenon_H129 zenon_H16a zenon_H4d zenon_H4e zenon_H13e zenon_H104 zenon_H131 zenon_H82 zenon_H23d zenon_H1d5 zenon_H236 zenon_H117 zenon_Hf5 zenon_H186 zenon_H20f zenon_H195 zenon_H25b zenon_H6f zenon_Ha9 zenon_H177 zenon_H13a zenon_Hbc zenon_H1cd zenon_Hfa zenon_H173 zenon_H1fb zenon_H139 zenon_H19a zenon_H1b4 zenon_H196 zenon_H25e zenon_H6c zenon_H73 zenon_He4 zenon_H33 zenon_H212 zenon_H18a zenon_H7d zenon_H55 zenon_H156 zenon_H94 zenon_Hb2 zenon_H15d zenon_Hcc zenon_H17c. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 22.64/22.73 exact (zenon_H181 zenon_H17c). % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.73 apply (zenon_L2_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.73 apply (zenon_L2518_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.73 apply (zenon_L2521_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.73 apply (zenon_L784_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.73 apply (zenon_L758_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.73 apply (zenon_L11_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.73 apply (zenon_L132_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.73 apply (zenon_L788_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.73 apply (zenon_L2579_); trivial. % 22.64/22.73 apply (zenon_L2579_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.73 apply (zenon_L343_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.73 apply (zenon_L37_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.73 apply (zenon_L790_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.73 apply (zenon_L791_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.73 apply (zenon_L361_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.73 apply (zenon_L2582_); trivial. % 22.64/22.73 apply (zenon_L51_); trivial. % 22.64/22.73 (* end of lemma zenon_L2583_ *) % 22.64/22.73 assert (zenon_L2584_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e1))) -> (((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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 22.64/22.73 do 0 intro. intros zenon_H277 zenon_H31 zenon_H1d8 zenon_H16a zenon_H129 zenon_H68 zenon_H201 zenon_Hb6 zenon_H77 zenon_H1cb zenon_H1cf zenon_H48 zenon_H139 zenon_H1b4 zenon_H271 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_Heb zenon_H15d zenon_Hf5 zenon_Ha9 zenon_H1c6 zenon_H6f zenon_H1fe zenon_H7d zenon_He2 zenon_H117 zenon_H26d zenon_H25e zenon_H196 zenon_Hb2 zenon_H19a zenon_H104 zenon_Ha0 zenon_H156 zenon_H158 zenon_H1a8 zenon_H1b7 zenon_H13a zenon_H17c zenon_H131. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H4d ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ]. % 22.64/22.73 apply (zenon_L2543_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 22.64/22.73 exact (zenon_H181 zenon_H17c). % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.73 apply (zenon_L2_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.73 apply (zenon_L700_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.73 apply (zenon_L782_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.73 apply (zenon_L784_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.73 apply (zenon_L786_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.73 apply (zenon_L11_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.73 apply (zenon_L787_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.73 apply (zenon_L788_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.73 apply (zenon_L789_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.73 apply (zenon_L88_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.73 apply (zenon_L37_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.73 apply (zenon_L790_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.73 apply (zenon_L791_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.73 apply (zenon_L361_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.73 apply (zenon_L792_); trivial. % 22.64/22.73 apply (zenon_L51_); trivial. % 22.64/22.73 apply (zenon_L793_); trivial. % 22.64/22.73 (* end of lemma zenon_L2584_ *) % 22.64/22.73 assert (zenon_L2585_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (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 (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((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) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (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) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 22.64/22.73 do 0 intro. intros zenon_H20b zenon_H1b7 zenon_H1a8 zenon_H158 zenon_H26d zenon_He2 zenon_H1fe zenon_H1c6 zenon_Heb zenon_H270 zenon_H111 zenon_H1d8 zenon_H277 zenon_H17c zenon_Hcc zenon_H15d zenon_Hb2 zenon_H94 zenon_H156 zenon_H55 zenon_H7d zenon_H18a zenon_H212 zenon_H33 zenon_He4 zenon_H73 zenon_H6c zenon_H25e zenon_H196 zenon_H1b4 zenon_H19a zenon_H139 zenon_H1fb zenon_H173 zenon_Hfa zenon_H1cd zenon_Hbc zenon_H13a zenon_H177 zenon_Ha9 zenon_H6f zenon_H25b zenon_H195 zenon_H20f zenon_H186 zenon_Hf5 zenon_H117 zenon_H236 zenon_H1d5 zenon_H23d zenon_H82 zenon_H131 zenon_H104 zenon_H13e zenon_H4e zenon_H4d zenon_H16a zenon_H129 zenon_H201 zenon_Hb6 zenon_H77 zenon_H1cb zenon_H1cf zenon_H48 zenon_H164 zenon_H68 zenon_Ha0 zenon_H192 zenon_H179 zenon_H271. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ]. % 22.64/22.73 apply (zenon_L2583_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 22.64/22.73 exact (zenon_H181 zenon_H17c). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H31 | zenon_intro zenon_H20c ]. % 22.64/22.73 apply (zenon_L2584_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H153 | zenon_intro zenon_H20d ]. % 22.64/22.73 apply (zenon_L184_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H66 | zenon_intro zenon_Hfe ]. % 22.64/22.73 apply (zenon_L258_); trivial. % 22.64/22.73 apply (zenon_L178_); trivial. % 22.64/22.73 (* end of lemma zenon_L2585_ *) % 22.64/22.73 assert (zenon_L2586_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((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 (e3) (e0)) = (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 (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (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) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(((~((op (e0) (e0)) = (e0)))\/(~((op (e0) (e0)) = (e0))))/\(((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1))))/\(((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2))))/\((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))))))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0))))/\(((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1))))/\(((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2))))/\((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))))))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0))))/\(((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1))))/\(((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2))))/\((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))))))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0))))/\(((~((op (e3) (e1)) = (e3)))\/(~((op (e3) (e3)) = (e1))))/\(((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2))))/\((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e0) (e3)) = (op (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 (e0) (e1)) = (op (e0) (e3)))) -> (~((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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (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 (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 22.64/22.73 do 0 intro. intros zenon_H291 zenon_H17c zenon_H140 zenon_H5d zenon_H141 zenon_H25b zenon_H195 zenon_H186 zenon_H212 zenon_H33 zenon_He4 zenon_H13f zenon_H18a zenon_H125 zenon_H73 zenon_H55 zenon_H82 zenon_H131 zenon_H13e zenon_H1d8 zenon_H271 zenon_H111 zenon_Hbc zenon_H1cd zenon_Hcc zenon_H270 zenon_Heb zenon_H15d zenon_H1c6 zenon_H6f zenon_H7d zenon_He2 zenon_H26d zenon_Hb2 zenon_H156 zenon_H158 zenon_H1fe zenon_H12e zenon_H1a8 zenon_H1b7 zenon_Ha9 zenon_H104 zenon_H13b zenon_H4e zenon_H19a zenon_H13a zenon_Hf5 zenon_H1b4 zenon_H196 zenon_H25e zenon_H1fb zenon_H20f zenon_Hfa zenon_H173 zenon_H117 zenon_H177 zenon_H139 zenon_H236 zenon_H23d zenon_H16a zenon_H129 zenon_H201 zenon_Hb6 zenon_H77 zenon_H1cb zenon_H1cf zenon_H48 zenon_H164 zenon_H68 zenon_Ha0 zenon_H192 zenon_H179 zenon_H20b zenon_H277 zenon_H94 zenon_H1d5. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H6c | zenon_intro zenon_H31 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H4d ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 22.64/22.73 exact (zenon_H181 zenon_H17c). % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.73 apply (zenon_L2_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.73 apply (zenon_L2518_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.73 apply (zenon_L2521_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.73 apply (zenon_L784_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.73 apply (zenon_L2544_); trivial. % 22.64/22.73 apply (zenon_L2544_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.73 apply (zenon_L11_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.73 apply (zenon_L131_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.73 apply (zenon_L788_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.73 apply (zenon_L2549_); trivial. % 22.64/22.73 apply (zenon_L2549_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.73 apply (zenon_L2551_); trivial. % 22.64/22.73 apply (zenon_L2551_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.73 apply (zenon_L2558_); trivial. % 22.64/22.73 apply (zenon_L2558_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.73 apply (zenon_L37_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.73 apply (zenon_L790_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.73 apply (zenon_L791_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.73 apply (zenon_L361_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_L2559_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_L2560_); trivial. % 22.64/22.73 apply (zenon_L2562_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.73 apply (zenon_L2565_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.73 apply (zenon_L2542_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L2566_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_L2559_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_L2567_); trivial. % 22.64/22.73 apply (zenon_L246_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_L2569_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_L2560_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.73 exact (zenon_H6c zenon_H67). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.73 apply (zenon_L1365_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.73 apply (zenon_L444_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.73 apply (zenon_L110_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.73 exact (zenon_H1b3 zenon_Hef). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.73 apply (zenon_L94_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.73 apply (zenon_L2571_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.73 exact (zenon_H1bf zenon_H105). % 22.64/22.73 apply (zenon_L363_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.73 apply (zenon_L56_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.73 exact (zenon_H1bf zenon_H105). % 22.64/22.73 apply (zenon_L182_); trivial. % 22.64/22.73 apply (zenon_L188_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.73 apply (zenon_L193_); trivial. % 22.64/22.73 apply (zenon_L154_); trivial. % 22.64/22.73 apply (zenon_L347_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.73 apply (zenon_L2565_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.73 apply (zenon_L1916_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.73 apply (zenon_L2567_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.73 apply (zenon_L664_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.73 exact (zenon_H1bf zenon_H105). % 22.64/22.73 apply (zenon_L363_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_L2559_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.73 apply (zenon_L2519_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.73 apply (zenon_L2573_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.73 exact (zenon_H13d zenon_H14c). % 22.64/22.73 apply (zenon_L77_); trivial. % 22.64/22.73 apply (zenon_L2562_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_L2574_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_L2572_); trivial. % 22.64/22.73 apply (zenon_L2557_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.73 apply (zenon_L2517_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.73 apply (zenon_L2575_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 apply (zenon_L2563_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_L2574_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_L2572_); trivial. % 22.64/22.73 apply (zenon_L456_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.73 apply (zenon_L2576_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_L2559_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.73 apply (zenon_L2519_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.73 apply (zenon_L2573_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.73 exact (zenon_H13d zenon_H14c). % 22.64/22.73 apply (zenon_L1162_); trivial. % 22.64/22.73 apply (zenon_L246_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.73 apply (zenon_L1385_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.73 apply (zenon_L2575_); trivial. % 22.64/22.73 apply (zenon_L2577_); trivial. % 22.64/22.73 apply (zenon_L196_); trivial. % 22.64/22.73 apply (zenon_L51_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 22.64/22.73 exact (zenon_H181 zenon_H17c). % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.73 apply (zenon_L2_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.73 apply (zenon_L2518_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.73 apply (zenon_L782_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.73 apply (zenon_L784_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.73 apply (zenon_L2578_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.73 apply (zenon_L11_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.73 apply (zenon_L787_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.73 apply (zenon_L788_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.73 apply (zenon_L789_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.73 apply (zenon_L88_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.73 apply (zenon_L37_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.73 apply (zenon_L790_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.73 apply (zenon_L791_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.73 apply (zenon_L361_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.73 apply (zenon_L792_); trivial. % 22.64/22.73 apply (zenon_L51_); trivial. % 22.64/22.73 apply (zenon_L2585_); trivial. % 22.64/22.73 apply (zenon_L2584_); trivial. % 22.64/22.73 (* end of lemma zenon_L2586_ *) % 22.64/22.73 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H23d. zenon_intro zenon_H292. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H292). zenon_intro zenon_H288. zenon_intro zenon_H293. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H293). zenon_intro zenon_H20b. zenon_intro zenon_H294. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H294). zenon_intro zenon_H25e. zenon_intro zenon_H295. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H295). zenon_intro zenon_H297. zenon_intro zenon_H296. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H296). zenon_intro zenon_H158. zenon_intro zenon_H298. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H298). zenon_intro zenon_H1ec. zenon_intro zenon_H299. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H25b. zenon_intro zenon_H29a. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H22d. zenon_intro zenon_H29b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H29b). zenon_intro zenon_H266. zenon_intro zenon_H29c. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H13e. zenon_intro zenon_H29d. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H29d). zenon_intro zenon_H27e. zenon_intro zenon_H29e. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H29e). zenon_intro zenon_H212. zenon_intro zenon_H29f. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H29f). zenon_intro zenon_H24e. zenon_intro zenon_H2a0. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2a0). zenon_intro zenon_H231. zenon_intro zenon_H1bb. % 22.64/22.73 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H236. zenon_intro zenon_H2a1. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2a1). zenon_intro zenon_H1fe. zenon_intro zenon_H2a2. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2a2). zenon_intro zenon_H15d. zenon_intro zenon_H2a3. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2a3). zenon_intro zenon_H82. zenon_intro zenon_H2a4. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2a4). zenon_intro zenon_H139. zenon_intro zenon_H2a5. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2a5). zenon_intro zenon_H125. zenon_intro zenon_H2a6. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2a6). zenon_intro zenon_H13a. zenon_intro zenon_H2a7. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_Hb2. zenon_intro zenon_H2a8. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H13b. zenon_intro zenon_H2a9. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_He2. zenon_intro zenon_H2aa. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2aa). zenon_intro zenon_Heb. zenon_intro zenon_H2ab. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2ab). zenon_intro zenon_He4. zenon_intro zenon_H2ac. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2ac). zenon_intro zenon_Hfa. zenon_intro zenon_H2ad. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2ad). zenon_intro zenon_H1a8. zenon_intro zenon_H2ae. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H13c. zenon_intro zenon_H2af. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H1c6. zenon_intro zenon_H2b0. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H141. zenon_intro zenon_H2b1. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b1). zenon_intro zenon_H140. zenon_intro zenon_H2b2. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H13f. zenon_intro zenon_H2b3. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b3). zenon_intro zenon_H201. zenon_intro zenon_H2b4. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b4). zenon_intro zenon_H16a. zenon_intro zenon_H2b5. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b5). zenon_intro zenon_H1cf. zenon_intro zenon_H2b6. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b6). zenon_intro zenon_H117. zenon_intro zenon_H2b7. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b7). zenon_intro zenon_H1a2. zenon_intro zenon_H2b8. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b8). zenon_intro zenon_H164. zenon_intro zenon_H2b9. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b9). zenon_intro zenon_H19a. zenon_intro zenon_H2ba. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2ba). zenon_intro zenon_H12e. zenon_intro zenon_H2bb. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2bb). zenon_intro zenon_H18d. zenon_intro zenon_H2bc. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2bc). zenon_intro zenon_H183. zenon_intro zenon_H2bd. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2bd). zenon_intro zenon_H1c3. zenon_intro zenon_H2be. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2be). zenon_intro zenon_H121. zenon_intro zenon_H26a. % 22.64/22.73 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H24. zenon_intro zenon_H2bf. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2bf). zenon_intro zenon_H2c. zenon_intro zenon_H2c0. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2c0). zenon_intro zenon_H33. zenon_intro zenon_H2c1. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2c1). zenon_intro zenon_H100. zenon_intro zenon_H2c2. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2c2). zenon_intro zenon_H179. zenon_intro zenon_H2c3. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2c3). zenon_intro zenon_H109. zenon_intro zenon_H2c4. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2c4). zenon_intro zenon_H173. zenon_intro zenon_H2c5. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2c5). zenon_intro zenon_H6f. zenon_intro zenon_H2c6. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2c6). zenon_intro zenon_H192. zenon_intro zenon_H2c7. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2c7). zenon_intro zenon_Hf0. zenon_intro zenon_H2c8. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2c8). zenon_intro zenon_H11a. zenon_intro zenon_H2c9. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2c9). zenon_intro zenon_H1f1. zenon_intro zenon_H2ca. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2ca). zenon_intro zenon_H73. zenon_intro zenon_H2cb. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2cb). zenon_intro zenon_H111. zenon_intro zenon_H2cc. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2cc). zenon_intro zenon_H177. zenon_intro zenon_H2cd. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2cd). zenon_intro zenon_H131. zenon_intro zenon_H2ce. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2ce). zenon_intro zenon_H163. zenon_intro zenon_H2cf. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2cf). zenon_intro zenon_H104. zenon_intro zenon_H2d0. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2d0). zenon_intro zenon_Hf5. zenon_intro zenon_H2d1. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2d1). zenon_intro zenon_H196. zenon_intro zenon_H2d2. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2d2). zenon_intro zenon_H1b4. zenon_intro zenon_H2d3. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2d3). zenon_intro zenon_H195. zenon_intro zenon_H2d4. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2d4). zenon_intro zenon_H20f. zenon_intro zenon_H2d5. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2d5). zenon_intro zenon_H129. zenon_intro zenon_H2d6. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2d6). zenon_intro zenon_H19d. zenon_intro zenon_H2d7. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2d7). zenon_intro zenon_H1d5. zenon_intro zenon_H2d8. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2d8). zenon_intro zenon_H2da. zenon_intro zenon_H2d9. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2d9). zenon_intro zenon_H1d8. zenon_intro zenon_H2db. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2db). zenon_intro zenon_H1fb. zenon_intro zenon_H2dc. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H26d. zenon_intro zenon_H2dd. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2dd). zenon_intro zenon_H23c. zenon_intro zenon_H2de. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H4e. zenon_intro zenon_H2df. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2df). zenon_intro zenon_H5d. zenon_intro zenon_H2e0. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2e0). zenon_intro zenon_H156. zenon_intro zenon_H2e1. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2e1). zenon_intro zenon_H234. zenon_intro zenon_H2e2. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2e2). zenon_intro zenon_H186. zenon_intro zenon_H2e3. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2e3). zenon_intro zenon_H55. zenon_intro zenon_H2e4. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2e4). zenon_intro zenon_H1ef. zenon_intro zenon_H2e5. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2e5). zenon_intro zenon_H94. zenon_intro zenon_H2e6. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2e6). zenon_intro zenon_H190. zenon_intro zenon_H2e7. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2e7). zenon_intro zenon_H189. zenon_intro zenon_H2e8. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2e8). zenon_intro zenon_H1c2. zenon_intro zenon_H2e9. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2e9). zenon_intro zenon_H7d. zenon_intro zenon_H2ea. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2ea). zenon_intro zenon_Hbc. zenon_intro zenon_H2eb. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2eb). zenon_intro zenon_H18a. zenon_intro zenon_H2ec. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H1cd. zenon_intro zenon_H2ed. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2ed). zenon_intro zenon_H1b7. zenon_intro zenon_H1cb. % 22.64/22.73 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H48. zenon_intro zenon_H2ee. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H68. zenon_intro zenon_H2ef. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_Ha0. zenon_intro zenon_H2f0. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H77. zenon_intro zenon_H2f1. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_Hb6. zenon_intro zenon_Ha9. % 22.64/22.73 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H2f2. zenon_intro zenon_Hcc. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H2f2); [ zenon_intro zenon_H2f4 | zenon_intro zenon_H2f3 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H1e. zenon_intro zenon_H2f5. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2f5). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2f6). zenon_intro zenon_H28f. zenon_intro zenon_H2f8. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2f8). zenon_intro zenon_H1ca. zenon_intro zenon_H1c0. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_He3 | zenon_intro zenon_H3c ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H13d | zenon_intro zenon_H65 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.73 apply (zenon_L2_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.73 apply (zenon_L4_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.73 apply (zenon_L6_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.73 apply (zenon_L8_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.73 apply (zenon_L9_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.73 apply (zenon_L11_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.73 apply (zenon_L145_); trivial. % 22.64/22.73 apply (zenon_L145_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.73 apply (zenon_L204_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.73 apply (zenon_L212_); trivial. % 22.64/22.73 apply (zenon_L212_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.73 apply (zenon_L19_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.73 apply (zenon_L213_); trivial. % 22.64/22.73 apply (zenon_L213_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.73 apply (zenon_L37_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_L215_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_L225_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_L105_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_L235_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.73 apply (zenon_L20_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.73 apply (zenon_L20_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.73 apply (zenon_L41_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.73 apply (zenon_L110_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.73 apply (zenon_L171_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.73 exact (zenon_He3 zenon_He7). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.73 apply (zenon_L24_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.73 apply (zenon_L230_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.73 apply (zenon_L117_); trivial. % 22.64/22.73 apply (zenon_L192_); trivial. % 22.64/22.73 apply (zenon_L234_); trivial. % 22.64/22.73 apply (zenon_L115_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.73 apply (zenon_L203_); trivial. % 22.64/22.73 apply (zenon_L71_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.73 apply (zenon_L122_); trivial. % 22.64/22.73 apply (zenon_L167_); trivial. % 22.64/22.73 apply (zenon_L238_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.73 apply (zenon_L40_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.73 apply (zenon_L108_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.73 apply (zenon_L244_); trivial. % 22.64/22.73 apply (zenon_L244_); trivial. % 22.64/22.73 apply (zenon_L197_); trivial. % 22.64/22.73 apply (zenon_L51_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.73 apply (zenon_L2_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.73 apply (zenon_L4_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.73 apply (zenon_L6_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.73 apply (zenon_L8_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.73 apply (zenon_L9_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.73 apply (zenon_L11_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.73 apply (zenon_L198_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.73 exact (zenon_H209 zenon_H9d). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_L146_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_L109_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.73 apply (zenon_L20_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.73 apply (zenon_L160_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.73 apply (zenon_L94_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.73 apply (zenon_L20_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.73 apply (zenon_L245_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.73 apply (zenon_L174_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.73 apply (zenon_L95_); trivial. % 22.64/22.73 apply (zenon_L92_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.73 apply (zenon_L32_); trivial. % 22.64/22.73 apply (zenon_L91_); trivial. % 22.64/22.73 apply (zenon_L31_); trivial. % 22.64/22.73 apply (zenon_L192_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.73 apply (zenon_L19_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.73 apply (zenon_L200_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.73 apply (zenon_L37_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.73 exact (zenon_H209 zenon_H9d). % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_L215_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_L225_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 apply (zenon_L13_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_L223_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.73 apply (zenon_L20_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.73 apply (zenon_L20_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.73 apply (zenon_L245_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.73 apply (zenon_L110_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.73 apply (zenon_L249_); trivial. % 22.64/22.73 apply (zenon_L115_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.73 apply (zenon_L30_); trivial. % 22.64/22.73 apply (zenon_L91_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.73 apply (zenon_L122_); trivial. % 22.64/22.73 apply (zenon_L98_); trivial. % 22.64/22.73 apply (zenon_L134_); trivial. % 22.64/22.73 apply (zenon_L238_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.73 apply (zenon_L40_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.73 apply (zenon_L221_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.73 apply (zenon_L201_); trivial. % 22.64/22.73 apply (zenon_L51_); trivial. % 22.64/22.73 apply (zenon_L203_); trivial. % 22.64/22.73 apply (zenon_L223_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H2fa | zenon_intro zenon_H2f9 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2fa). zenon_intro zenon_H47. zenon_intro zenon_H2fb. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2fb). zenon_intro zenon_H2fd. zenon_intro zenon_H2fc. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2fc). zenon_intro zenon_H290. zenon_intro zenon_H2fe. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2fe). zenon_intro zenon_H264. zenon_intro zenon_H230. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H2fd); [ zenon_intro zenon_H4c | zenon_intro zenon_H2a ]. % 22.64/22.73 exact (zenon_H4c zenon_H47). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1bf | zenon_intro zenon_H6d ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.73 apply (zenon_L2_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.64/22.73 apply (zenon_L250_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.73 apply (zenon_L147_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.73 apply (zenon_L252_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.73 apply (zenon_L171_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.73 apply (zenon_L253_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.73 apply (zenon_L116_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.73 apply (zenon_L43_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.73 exact (zenon_H7a zenon_H3c). % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.73 exact (zenon_H40 zenon_H3f). % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.73 exact (zenon_H1d4 zenon_H4d). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.73 apply (zenon_L123_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.73 exact (zenon_H159 zenon_H10c). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.73 apply (zenon_L53_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.73 exact (zenon_H159 zenon_H10c). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.73 apply (zenon_L261_); trivial. % 22.64/22.73 apply (zenon_L44_); trivial. % 22.64/22.73 apply (zenon_L263_); trivial. % 22.64/22.73 apply (zenon_L271_); trivial. % 22.64/22.73 apply (zenon_L277_); trivial. % 22.64/22.73 apply (zenon_L305_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.64/22.73 apply (zenon_L250_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.73 apply (zenon_L306_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.73 apply (zenon_L252_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.73 apply (zenon_L171_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.73 apply (zenon_L253_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.73 apply (zenon_L116_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.73 apply (zenon_L43_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.73 apply (zenon_L25_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.73 exact (zenon_H40 zenon_H3f). % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.73 exact (zenon_H1d4 zenon_H4d). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.73 apply (zenon_L123_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.73 exact (zenon_H159 zenon_H10c). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.73 apply (zenon_L53_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.73 exact (zenon_H159 zenon_H10c). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.73 apply (zenon_L261_); trivial. % 22.64/22.73 apply (zenon_L313_); trivial. % 22.64/22.73 apply (zenon_L314_); trivial. % 22.64/22.73 apply (zenon_L312_); trivial. % 22.64/22.73 apply (zenon_L277_); trivial. % 22.64/22.73 apply (zenon_L305_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.73 apply (zenon_L315_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.73 apply (zenon_L317_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.73 apply (zenon_L318_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.73 apply (zenon_L11_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.73 apply (zenon_L322_); trivial. % 22.64/22.73 apply (zenon_L322_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.73 apply (zenon_L330_); trivial. % 22.64/22.73 apply (zenon_L330_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.73 apply (zenon_L147_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.73 apply (zenon_L253_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.73 apply (zenon_L333_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.73 apply (zenon_L334_); trivial. % 22.64/22.73 exact (zenon_H209 zenon_H9d). % 22.64/22.73 apply (zenon_L336_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.73 apply (zenon_L147_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.73 apply (zenon_L252_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.73 apply (zenon_L337_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.73 apply (zenon_L338_); trivial. % 22.64/22.73 apply (zenon_L340_); trivial. % 22.64/22.73 apply (zenon_L336_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.73 apply (zenon_L342_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.73 apply (zenon_L351_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.73 apply (zenon_L37_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.73 apply (zenon_L353_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.73 apply (zenon_L354_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.73 apply (zenon_L375_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.73 apply (zenon_L377_); trivial. % 22.64/22.73 apply (zenon_L51_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.73 apply (zenon_L2_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.64/22.73 apply (zenon_L250_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.73 apply (zenon_L358_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.73 apply (zenon_L252_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.73 apply (zenon_L171_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.73 apply (zenon_L307_); trivial. % 22.64/22.73 apply (zenon_L271_); trivial. % 22.64/22.73 apply (zenon_L277_); trivial. % 22.64/22.73 apply (zenon_L372_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.64/22.73 apply (zenon_L250_); trivial. % 22.64/22.73 apply (zenon_L313_); trivial. % 22.64/22.73 apply (zenon_L373_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.73 apply (zenon_L315_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.73 apply (zenon_L317_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.73 apply (zenon_L318_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.73 apply (zenon_L11_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.73 apply (zenon_L381_); trivial. % 22.64/22.73 apply (zenon_L381_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.73 apply (zenon_L383_); trivial. % 22.64/22.73 apply (zenon_L383_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.73 apply (zenon_L358_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.73 apply (zenon_L384_); trivial. % 22.64/22.73 apply (zenon_L336_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.73 apply (zenon_L342_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.73 apply (zenon_L386_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.73 apply (zenon_L37_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.73 apply (zenon_L353_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.73 apply (zenon_L387_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.73 apply (zenon_L375_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.73 apply (zenon_L388_); trivial. % 22.64/22.73 apply (zenon_L51_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 22.64/22.73 apply (zenon_L481_); trivial. % 22.64/22.73 apply (zenon_L394_); trivial. % 22.64/22.73 apply (zenon_L699_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_H300 | zenon_intro zenon_H2ff ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H300). zenon_intro zenon_H67. zenon_intro zenon_H301. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H301). zenon_intro zenon_H291. zenon_intro zenon_H302. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H302). zenon_intro zenon_H277. zenon_intro zenon_H303. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H303). zenon_intro zenon_H270. zenon_intro zenon_H271. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H6c | zenon_intro zenon_H31 ]. % 22.64/22.73 exact (zenon_H6c zenon_H67). % 22.64/22.73 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H4d ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.73 apply (zenon_L2_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.73 apply (zenon_L700_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_L713_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_L217_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.73 apply (zenon_L701_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.73 apply (zenon_L55_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.73 apply (zenon_L68_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.73 apply (zenon_L713_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.73 apply (zenon_L716_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.73 apply (zenon_L723_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.73 apply (zenon_L706_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.73 exact (zenon_H1b3 zenon_Hef). % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.73 apply (zenon_L217_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.73 apply (zenon_L378_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.73 apply (zenon_L727_); trivial. % 22.64/22.73 apply (zenon_L149_); trivial. % 22.64/22.73 apply (zenon_L206_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_L239_); trivial. % 22.64/22.73 apply (zenon_L728_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.73 apply (zenon_L701_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.73 apply (zenon_L730_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.73 apply (zenon_L68_); trivial. % 22.64/22.73 apply (zenon_L733_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_L217_); trivial. % 22.64/22.73 apply (zenon_L736_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_L239_); trivial. % 22.64/22.73 apply (zenon_L737_); trivial. % 22.64/22.73 apply (zenon_L1071_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_L713_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_L217_); trivial. % 22.64/22.73 apply (zenon_L1075_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_L239_); trivial. % 22.64/22.73 apply (zenon_L728_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.73 apply (zenon_L701_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.73 apply (zenon_L1076_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.73 apply (zenon_L68_); trivial. % 22.64/22.73 apply (zenon_L733_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_L217_); trivial. % 22.64/22.73 apply (zenon_L1077_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.73 apply (zenon_L239_); trivial. % 22.64/22.73 apply (zenon_L737_); trivial. % 22.64/22.73 apply (zenon_L1071_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.73 apply (zenon_L757_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.73 apply (zenon_L1078_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.73 apply (zenon_L11_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.73 apply (zenon_L1079_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.73 apply (zenon_L1080_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.73 apply (zenon_L814_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.73 apply (zenon_L1086_); trivial. % 22.64/22.73 apply (zenon_L1086_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.73 apply (zenon_L1088_); trivial. % 22.64/22.73 apply (zenon_L1088_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.73 apply (zenon_L37_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.73 apply (zenon_L706_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.73 exact (zenon_H1b3 zenon_Hef). % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.73 apply (zenon_L227_); trivial. % 22.64/22.73 apply (zenon_L228_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.73 apply (zenon_L922_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.73 apply (zenon_L1093_); trivial. % 22.64/22.73 apply (zenon_L1093_); trivial. % 22.64/22.73 apply (zenon_L374_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.64/22.73 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.73 apply (zenon_L1108_); trivial. % 22.64/22.73 apply (zenon_L51_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.73 apply (zenon_L2_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.73 apply (zenon_L700_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.73 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.73 apply (zenon_L251_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.73 apply (zenon_L1109_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.73 apply (zenon_L217_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.73 apply (zenon_L701_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.73 apply (zenon_L55_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.73 apply (zenon_L68_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.73 apply (zenon_L701_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.73 apply (zenon_L46_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.73 apply (zenon_L716_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.73 apply (zenon_L721_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.73 apply (zenon_L706_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.73 exact (zenon_H1b3 zenon_Hef). % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.73 apply (zenon_L217_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.73 apply (zenon_L832_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.73 apply (zenon_L727_); trivial. % 22.64/22.73 apply (zenon_L149_); trivial. % 22.64/22.73 apply (zenon_L206_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.73 apply (zenon_L67_); trivial. % 22.64/22.73 apply (zenon_L48_); trivial. % 22.64/22.73 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_L239_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.74 apply (zenon_L701_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.74 apply (zenon_L705_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.74 apply (zenon_L178_); trivial. % 22.64/22.74 apply (zenon_L115_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_L251_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L251_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_L1109_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_L217_); trivial. % 22.64/22.74 apply (zenon_L736_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_L239_); trivial. % 22.64/22.74 apply (zenon_L737_); trivial. % 22.64/22.74 apply (zenon_L1103_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L251_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_L1109_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_L217_); trivial. % 22.64/22.74 apply (zenon_L1110_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L251_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_L1109_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_L217_); trivial. % 22.64/22.74 apply (zenon_L1077_); trivial. % 22.64/22.74 apply (zenon_L197_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.74 apply (zenon_L757_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.74 apply (zenon_L1078_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.74 apply (zenon_L11_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.74 apply (zenon_L1079_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.74 apply (zenon_L1080_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.74 apply (zenon_L814_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.74 apply (zenon_L1112_); trivial. % 22.64/22.74 apply (zenon_L1112_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.74 apply (zenon_L1114_); trivial. % 22.64/22.74 apply (zenon_L1114_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.74 apply (zenon_L37_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 exact (zenon_H1a3 zenon_Hbb). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L1116_); trivial. % 22.64/22.74 apply (zenon_L1116_); trivial. % 22.64/22.74 apply (zenon_L1121_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.74 apply (zenon_L791_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.74 apply (zenon_L361_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.74 apply (zenon_L1108_); trivial. % 22.64/22.74 apply (zenon_L51_); trivial. % 22.64/22.74 apply (zenon_L1142_); trivial. % 22.64/22.74 apply (zenon_L1145_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H2ff); [ zenon_intro zenon_H305 | zenon_intro zenon_H304 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H305). zenon_intro zenon_H9f. zenon_intro zenon_H306. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H306). zenon_intro zenon_H283. zenon_intro zenon_H307. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H307). zenon_intro zenon_H282. zenon_intro zenon_H308. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H308). zenon_intro zenon_H281. zenon_intro zenon_H284. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H38 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H159 | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H191 | zenon_intro zenon_H93 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.74 apply (zenon_L2_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.74 apply (zenon_L1146_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.74 apply (zenon_L1147_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_L253_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L1149_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_L1163_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L100_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1164_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L436_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.74 apply (zenon_L1443_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.74 apply (zenon_L1403_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1444_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_L1446_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_L1449_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L1461_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_L1443_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.74 apply (zenon_L317_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L1448_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_L1469_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_L1416_); trivial. % 22.64/22.74 apply (zenon_L1436_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.74 apply (zenon_L1242_); trivial. % 22.64/22.74 apply (zenon_L543_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L1472_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_L456_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L1284_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L25_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.64/22.74 apply (zenon_L738_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.64/22.74 apply (zenon_L492_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_L1405_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_L1473_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L1474_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L1455_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L56_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L111_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.64/22.74 apply (zenon_L1476_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.64/22.74 apply (zenon_L56_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.64/22.74 apply (zenon_L1169_); trivial. % 22.64/22.74 apply (zenon_L1171_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_L1484_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_L1265_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L1409_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L94_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_L1485_); trivial. % 22.64/22.74 apply (zenon_L456_); trivial. % 22.64/22.74 apply (zenon_L246_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_L253_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L253_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L25_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L1497_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L14_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1414_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L1501_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L117_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1414_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.74 apply (zenon_L252_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_L1506_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.74 apply (zenon_L65_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.74 apply (zenon_L1506_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.74 apply (zenon_L1460_); trivial. % 22.64/22.74 apply (zenon_L802_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_L291_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L69_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L186_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1164_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L1533_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L1534_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_L1537_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_L1539_); trivial. % 22.64/22.74 apply (zenon_L414_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.74 apply (zenon_L317_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L69_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L186_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1164_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L1467_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_L1537_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_L186_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_L62_); trivial. % 22.64/22.74 apply (zenon_L1468_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_L117_); trivial. % 22.64/22.74 apply (zenon_L1627_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.74 apply (zenon_L1500_); trivial. % 22.64/22.74 apply (zenon_L802_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.74 apply (zenon_L252_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L171_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L186_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1164_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L1471_); trivial. % 22.64/22.74 apply (zenon_L1628_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_L1539_); trivial. % 22.64/22.74 apply (zenon_L414_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.74 apply (zenon_L65_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L69_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L186_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1164_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L162_); trivial. % 22.64/22.74 apply (zenon_L1628_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_L1539_); trivial. % 22.64/22.74 apply (zenon_L1627_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.74 apply (zenon_L1242_); trivial. % 22.64/22.74 apply (zenon_L802_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.74 apply (zenon_L30_); trivial. % 22.64/22.74 apply (zenon_L291_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_L456_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L1284_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_L1497_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_L1501_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L25_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_L1494_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_L1631_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H3d | zenon_intro zenon_He8 ]. % 22.64/22.74 apply (zenon_L1632_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3f | zenon_intro zenon_He9 ]. % 22.64/22.74 apply (zenon_L492_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H53 | zenon_intro zenon_H7f ]. % 22.64/22.74 apply (zenon_L1474_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_L226_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L1491_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L110_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L27_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L1634_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_L1492_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_L1629_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_L291_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L94_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L69_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L1636_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L186_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L217_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L929_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H66 | zenon_intro zenon_H1d0 ]. % 22.64/22.74 apply (zenon_L1470_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_H72 | zenon_intro zenon_H1d1 ]. % 22.64/22.74 apply (zenon_L436_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H160 ]. % 22.64/22.74 apply (zenon_L366_); trivial. % 22.64/22.74 apply (zenon_L1480_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_L1637_); trivial. % 22.64/22.74 apply (zenon_L1639_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_L186_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L1640_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L100_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1481_); trivial. % 22.64/22.74 apply (zenon_L1639_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L1635_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L1455_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1641_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L1638_); trivial. % 22.64/22.74 apply (zenon_L299_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_L184_); trivial. % 22.64/22.74 apply (zenon_L414_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.74 apply (zenon_L316_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L1499_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_L1642_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_L117_); trivial. % 22.64/22.74 apply (zenon_L1627_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.74 apply (zenon_L1500_); trivial. % 22.64/22.74 apply (zenon_L802_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L1640_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L94_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_L456_); trivial. % 22.64/22.74 apply (zenon_L246_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_L253_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L253_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L25_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_L1163_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L100_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L436_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L929_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.74 apply (zenon_L1644_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.74 apply (zenon_L1403_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1066_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L46_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L436_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.74 apply (zenon_L1644_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.74 apply (zenon_L1403_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1444_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_L371_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L1455_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L929_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.74 apply (zenon_L1663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.74 apply (zenon_L1665_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1066_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.74 apply (zenon_L1666_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.74 apply (zenon_L113_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L1668_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L124_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1651_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_L371_); trivial. % 22.64/22.74 apply (zenon_L299_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L1673_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L1161_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_L62_); trivial. % 22.64/22.74 apply (zenon_L1447_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L1461_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_L1663_); trivial. % 22.64/22.74 apply (zenon_L456_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L1284_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L25_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_L1668_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_L1265_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_L1649_); trivial. % 22.64/22.74 apply (zenon_L456_); trivial. % 22.64/22.74 apply (zenon_L246_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_L253_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L253_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L25_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L929_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L1680_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.74 apply (zenon_L65_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L46_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L1454_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_L1681_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.74 apply (zenon_L1743_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.74 apply (zenon_L1498_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.74 apply (zenon_L1669_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L1439_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L117_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L1669_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.64/22.74 apply (zenon_L180_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.64/22.74 apply (zenon_L1152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.64/22.74 apply (zenon_L1674_); trivial. % 22.64/22.74 apply (zenon_L218_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_L62_); trivial. % 22.64/22.74 apply (zenon_L1468_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.74 apply (zenon_L1673_); trivial. % 22.64/22.74 apply (zenon_L802_); trivial. % 22.64/22.74 apply (zenon_L422_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.74 apply (zenon_L252_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L1450_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L27_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L929_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L1744_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L1459_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L1439_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L379_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L687_); trivial. % 22.64/22.74 apply (zenon_L415_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_L22_); trivial. % 22.64/22.74 apply (zenon_L1458_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L1460_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L365_); trivial. % 22.64/22.74 apply (zenon_L415_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_L291_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_L1743_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_L1660_); trivial. % 22.64/22.74 apply (zenon_L422_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.74 apply (zenon_L252_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L171_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L69_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L186_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1647_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L94_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L965_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L1650_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.64/22.74 apply (zenon_L30_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.64/22.74 apply (zenon_L1646_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.64/22.74 apply (zenon_L1679_); trivial. % 22.64/22.74 apply (zenon_L1159_); trivial. % 22.64/22.74 apply (zenon_L415_); trivial. % 22.64/22.74 apply (zenon_L371_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L1244_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L217_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L1741_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_L379_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1661_); trivial. % 22.64/22.74 apply (zenon_L965_); trivial. % 22.64/22.74 apply (zenon_L414_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_L1660_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.74 apply (zenon_L30_); trivial. % 22.64/22.74 apply (zenon_L291_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_L456_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_L1677_); trivial. % 22.64/22.74 apply (zenon_L246_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_L253_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L1149_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_L1407_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L1407_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1164_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L46_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L436_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.74 apply (zenon_L1746_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.74 apply (zenon_L1755_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1444_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L1455_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1164_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.74 apply (zenon_L1666_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.74 apply (zenon_L113_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L1756_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L124_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1651_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_L299_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_L1449_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L1766_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_L1746_); trivial. % 22.64/22.74 apply (zenon_L456_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_L1756_); trivial. % 22.64/22.74 apply (zenon_L246_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_L253_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L253_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L25_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L46_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L1454_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L1769_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L14_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1414_); trivial. % 22.64/22.74 apply (zenon_L886_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L100_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1164_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L436_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.74 apply (zenon_L1772_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.74 apply (zenon_L1473_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1444_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L1701_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L1455_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1164_); trivial. % 22.64/22.74 apply (zenon_L1774_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.74 apply (zenon_L317_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L46_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L1768_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L1539_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1414_); trivial. % 22.64/22.74 apply (zenon_L886_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.74 apply (zenon_L1775_); trivial. % 22.64/22.74 apply (zenon_L802_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.74 apply (zenon_L252_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_L1765_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.74 apply (zenon_L65_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.74 apply (zenon_L1765_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.74 apply (zenon_L1775_); trivial. % 22.64/22.74 apply (zenon_L802_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_L291_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L69_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L1701_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L186_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1770_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_L1772_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_L1539_); trivial. % 22.64/22.74 apply (zenon_L1556_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H2a | zenon_intro zenon_He5 ]. % 22.64/22.74 apply (zenon_L317_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L69_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L186_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1770_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L1467_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L217_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L1535_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L965_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.64/22.74 apply (zenon_L1437_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.64/22.74 apply (zenon_L368_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H155 | zenon_intro zenon_H18e ]. % 22.64/22.74 apply (zenon_L246_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H5c | zenon_intro zenon_H18f ]. % 22.64/22.74 apply (zenon_L1777_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H128 | zenon_intro zenon_H11f ]. % 22.64/22.74 apply (zenon_L1444_); trivial. % 22.64/22.74 apply (zenon_L964_); trivial. % 22.64/22.74 apply (zenon_L1159_); trivial. % 22.64/22.74 apply (zenon_L886_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_L186_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_L62_); trivial. % 22.64/22.74 apply (zenon_L1468_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_L117_); trivial. % 22.64/22.74 apply (zenon_L1556_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hdd | zenon_intro zenon_He0 ]. % 22.64/22.74 apply (zenon_L1242_); trivial. % 22.64/22.74 apply (zenon_L802_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L1701_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.74 apply (zenon_L252_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L171_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L69_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L1778_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L486_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.64/22.74 apply (zenon_L1779_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.64/22.74 apply (zenon_L289_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.64/22.74 apply (zenon_L258_); trivial. % 22.64/22.74 apply (zenon_L1159_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L1244_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.64/22.74 apply (zenon_L1779_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.64/22.74 apply (zenon_L1090_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.64/22.74 apply (zenon_L258_); trivial. % 22.64/22.74 apply (zenon_L1780_); trivial. % 22.64/22.74 apply (zenon_L886_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_L1661_); trivial. % 22.64/22.74 apply (zenon_L965_); trivial. % 22.64/22.74 apply (zenon_L414_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L217_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L365_); trivial. % 22.64/22.74 apply (zenon_L886_); trivial. % 22.64/22.74 exact (zenon_H1c7 zenon_Hac). % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.74 apply (zenon_L30_); trivial. % 22.64/22.74 apply (zenon_L291_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_L211_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_L1778_); trivial. % 22.64/22.74 apply (zenon_L246_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_L253_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L253_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L25_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L900_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L1454_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L929_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L1781_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L100_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L46_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L436_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L54_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L1782_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L59_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L1784_); trivial. % 22.64/22.74 apply (zenon_L1152_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_L1790_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a9 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Hef | zenon_intro zenon_H1aa ]. % 22.64/22.74 apply (zenon_L1455_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H6d | zenon_intro zenon_H171 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_L289_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L929_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L1782_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L14_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L255_); trivial. % 22.64/22.74 apply (zenon_L1153_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_L1790_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.74 apply (zenon_L46_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.74 apply (zenon_L162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L359_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L1672_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L1781_); trivial. % 22.64/22.74 apply (zenon_L1162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_L62_); trivial. % 22.64/22.74 apply (zenon_L1447_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L1766_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L297_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_L1785_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_L1660_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.74 apply (zenon_L252_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L171_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L69_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_L1653_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_L1662_); trivial. % 22.64/22.74 apply (zenon_L1551_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.74 apply (zenon_L24_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.74 apply (zenon_L1659_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.74 apply (zenon_L117_); trivial. % 22.64/22.74 apply (zenon_L1555_); trivial. % 22.64/22.74 apply (zenon_L663_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.74 apply (zenon_L30_); trivial. % 22.64/22.74 apply (zenon_L291_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_L456_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L1284_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_L1789_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_L1649_); trivial. % 22.64/22.74 apply (zenon_L456_); trivial. % 22.64/22.74 apply (zenon_L246_); trivial. % 22.64/22.74 apply (zenon_L434_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.74 apply (zenon_L1712_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.74 apply (zenon_L11_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.74 apply (zenon_L1792_); trivial. % 22.64/22.74 apply (zenon_L1792_); trivial. % 22.64/22.74 apply (zenon_L176_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_L1567_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.74 apply (zenon_L1569_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.74 apply (zenon_L1795_); trivial. % 22.64/22.74 apply (zenon_L1795_); trivial. % 22.64/22.74 apply (zenon_L102_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.74 apply (zenon_L37_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_L1734_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.74 apply (zenon_L1353_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.74 apply (zenon_L1799_); trivial. % 22.64/22.74 apply (zenon_L1799_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.74 apply (zenon_L1800_); trivial. % 22.64/22.74 apply (zenon_L1800_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.74 apply (zenon_L1739_); trivial. % 22.64/22.74 apply (zenon_L51_); trivial. % 22.64/22.74 apply (zenon_L1205_); trivial. % 22.64/22.74 apply (zenon_L1740_); trivial. % 22.64/22.74 apply (zenon_L1794_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H30a | zenon_intro zenon_H309 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H30a). zenon_intro zenon_He7. zenon_intro zenon_H2f5. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H2f5). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H2f6). zenon_intro zenon_H28f. zenon_intro zenon_H2f8. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H2f8). zenon_intro zenon_H1ca. zenon_intro zenon_H1c0. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_He3 | zenon_intro zenon_H3c ]. % 22.64/22.74 exact (zenon_He3 zenon_He7). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H13d | zenon_intro zenon_H65 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.74 apply (zenon_L2_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.74 apply (zenon_L26_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.74 apply (zenon_L1838_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.74 apply (zenon_L1840_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.74 apply (zenon_L487_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 exact (zenon_H1f zenon_H1e). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 exact (zenon_H205 zenon_H2a). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 exact (zenon_H237 zenon_H31). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 exact (zenon_H1f zenon_H1e). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L25_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.74 apply (zenon_L46_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.74 apply (zenon_L67_); trivial. % 22.64/22.74 apply (zenon_L1890_); trivial. % 22.64/22.74 apply (zenon_L1873_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L1868_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_L1839_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.74 apply (zenon_L1891_); trivial. % 22.64/22.74 apply (zenon_L1858_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.74 apply (zenon_L487_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 exact (zenon_H1f zenon_H1e). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 apply (zenon_L318_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 exact (zenon_H237 zenon_H31). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 exact (zenon_H1f zenon_H1e). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L25_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.74 apply (zenon_L46_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.74 apply (zenon_L67_); trivial. % 22.64/22.74 apply (zenon_L1894_); trivial. % 22.64/22.74 apply (zenon_L1839_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.74 apply (zenon_L1891_); trivial. % 22.64/22.74 apply (zenon_L1861_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.74 apply (zenon_L11_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.74 apply (zenon_L16_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.74 apply (zenon_L18_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.74 apply (zenon_L1870_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.74 apply (zenon_L1872_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.74 apply (zenon_L37_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L1901_); trivial. % 22.64/22.74 apply (zenon_L1901_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L1902_); trivial. % 22.64/22.74 apply (zenon_L1902_); trivial. % 22.64/22.74 apply (zenon_L238_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.74 apply (zenon_L1903_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.74 apply (zenon_L1878_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.74 apply (zenon_L1907_); trivial. % 22.64/22.74 apply (zenon_L1907_); trivial. % 22.64/22.74 apply (zenon_L197_); trivial. % 22.64/22.74 apply (zenon_L51_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.74 apply (zenon_L2_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.74 apply (zenon_L26_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.74 apply (zenon_L1838_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.74 apply (zenon_L1840_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.74 apply (zenon_L487_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 exact (zenon_H1f zenon_H1e). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 exact (zenon_H205 zenon_H2a). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 exact (zenon_H237 zenon_H31). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 exact (zenon_H1f zenon_H1e). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L25_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.74 apply (zenon_L55_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.74 apply (zenon_L1890_); trivial. % 22.64/22.74 apply (zenon_L1873_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L214_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L1867_); trivial. % 22.64/22.74 apply (zenon_L165_); trivial. % 22.64/22.74 apply (zenon_L1839_); trivial. % 22.64/22.74 apply (zenon_L1881_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.74 apply (zenon_L487_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 exact (zenon_H1f zenon_H1e). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 apply (zenon_L65_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 exact (zenon_H237 zenon_H31). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 exact (zenon_H1f zenon_H1e). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L25_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_L1894_); trivial. % 22.64/22.74 apply (zenon_L1839_); trivial. % 22.64/22.74 apply (zenon_L611_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.74 apply (zenon_L11_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.74 apply (zenon_L16_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.74 apply (zenon_L18_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.74 apply (zenon_L1888_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.74 apply (zenon_L1872_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.74 apply (zenon_L37_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.74 exact (zenon_H209 zenon_H9d). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L1913_); trivial. % 22.64/22.74 apply (zenon_L1913_); trivial. % 22.64/22.74 apply (zenon_L238_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.74 apply (zenon_L1903_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.74 apply (zenon_L221_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.74 apply (zenon_L201_); trivial. % 22.64/22.74 apply (zenon_L51_); trivial. % 22.64/22.74 apply (zenon_L1889_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_He3 | zenon_intro zenon_H3c ]. % 22.64/22.74 exact (zenon_He3 zenon_He7). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.74 apply (zenon_L2_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.74 apply (zenon_L26_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.74 apply (zenon_L6_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.74 apply (zenon_L8_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.74 apply (zenon_L9_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.74 apply (zenon_L11_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.74 apply (zenon_L16_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.74 apply (zenon_L18_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.74 apply (zenon_L19_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.74 apply (zenon_L1872_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.74 apply (zenon_L37_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.74 apply (zenon_L106_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.74 apply (zenon_L40_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.74 apply (zenon_L1878_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.74 apply (zenon_L49_); trivial. % 22.64/22.74 apply (zenon_L51_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H30c | zenon_intro zenon_H30b ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H30c). zenon_intro zenon_H3f. zenon_intro zenon_H2fb. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H2fb). zenon_intro zenon_H2fd. zenon_intro zenon_H2fc. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H2fc). zenon_intro zenon_H290. zenon_intro zenon_H2fe. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H2fe). zenon_intro zenon_H264. zenon_intro zenon_H230. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H2fd); [ zenon_intro zenon_H4c | zenon_intro zenon_H2a ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1bf | zenon_intro zenon_H6d ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.74 apply (zenon_L2_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.74 apply (zenon_L482_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.74 apply (zenon_L1944_); trivial. % 22.64/22.74 apply (zenon_L1944_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 apply (zenon_L1948_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L1958_); trivial. % 22.64/22.74 apply (zenon_L1958_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 apply (zenon_L1948_); trivial. % 22.64/22.74 apply (zenon_L434_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.74 apply (zenon_L513_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.74 apply (zenon_L11_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.74 apply (zenon_L483_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.74 apply (zenon_L485_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.74 apply (zenon_L1959_); trivial. % 22.64/22.74 apply (zenon_L1959_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.74 apply (zenon_L522_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.74 apply (zenon_L37_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L1960_); trivial. % 22.64/22.74 apply (zenon_L1960_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L1961_); trivial. % 22.64/22.74 apply (zenon_L1961_); trivial. % 22.64/22.74 apply (zenon_L238_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.74 apply (zenon_L1962_); trivial. % 22.64/22.74 apply (zenon_L1962_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.74 apply (zenon_L531_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.74 apply (zenon_L1965_); trivial. % 22.64/22.74 apply (zenon_L1965_); trivial. % 22.64/22.74 apply (zenon_L197_); trivial. % 22.64/22.74 apply (zenon_L51_); trivial. % 22.64/22.74 apply (zenon_L1942_); trivial. % 22.64/22.74 apply (zenon_L1956_); trivial. % 22.64/22.74 apply (zenon_L699_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H30b); [ zenon_intro zenon_H30e | zenon_intro zenon_H30d ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H30e). zenon_intro zenon_Hef. zenon_intro zenon_H301. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H301). zenon_intro zenon_H291. zenon_intro zenon_H302. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H302). zenon_intro zenon_H277. zenon_intro zenon_H303. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H303). zenon_intro zenon_H270. zenon_intro zenon_H271. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H6c | zenon_intro zenon_H31 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H4d ]. % 22.64/22.74 exact (zenon_H1b3 zenon_Hef). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H181 | zenon_intro zenon_Hbb ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.74 apply (zenon_L2_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.74 apply (zenon_L1966_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.74 apply (zenon_L974_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L1980_); trivial. % 22.64/22.74 apply (zenon_L1980_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.74 apply (zenon_L758_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.74 apply (zenon_L11_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.64/22.74 apply (zenon_L378_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 apply (zenon_L1987_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 apply (zenon_L1987_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L1995_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_L1008_); trivial. % 22.64/22.74 apply (zenon_L1998_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 apply (zenon_L777_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 apply (zenon_L1999_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L2004_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_L973_); trivial. % 22.64/22.74 apply (zenon_L2008_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.64/22.74 apply (zenon_L779_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 apply (zenon_L1987_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 apply (zenon_L161_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L1995_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_L2009_); trivial. % 22.64/22.74 apply (zenon_L1998_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 apply (zenon_L800_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 apply (zenon_L1999_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L2004_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_L2009_); trivial. % 22.64/22.74 apply (zenon_L2008_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.64/22.74 apply (zenon_L2013_); trivial. % 22.64/22.74 apply (zenon_L176_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.74 apply (zenon_L335_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.74 apply (zenon_L2022_); trivial. % 22.64/22.74 apply (zenon_L2022_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.74 apply (zenon_L343_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.74 apply (zenon_L37_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L2024_); trivial. % 22.64/22.74 apply (zenon_L2024_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L2025_); trivial. % 22.64/22.74 apply (zenon_L2025_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L2027_); trivial. % 22.64/22.74 apply (zenon_L2027_); trivial. % 22.64/22.74 apply (zenon_L434_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.74 apply (zenon_L2028_); trivial. % 22.64/22.74 apply (zenon_L2028_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.74 apply (zenon_L985_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.74 apply (zenon_L2052_); trivial. % 22.64/22.74 apply (zenon_L51_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.74 apply (zenon_L2_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.74 apply (zenon_L1966_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.74 apply (zenon_L1009_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L2053_); trivial. % 22.64/22.74 apply (zenon_L2053_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.74 apply (zenon_L758_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.74 apply (zenon_L11_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.64/22.74 apply (zenon_L378_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 apply (zenon_L2057_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 apply (zenon_L2058_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 apply (zenon_L778_); trivial. % 22.64/22.74 apply (zenon_L2059_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H16b | zenon_intro zenon_H191 ]. % 22.64/22.74 apply (zenon_L779_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 apply (zenon_L2057_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 apply (zenon_L2058_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 apply (zenon_L800_); trivial. % 22.64/22.74 apply (zenon_L2059_); trivial. % 22.64/22.74 apply (zenon_L130_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.74 apply (zenon_L335_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.74 apply (zenon_L2062_); trivial. % 22.64/22.74 apply (zenon_L2062_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.74 apply (zenon_L343_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.74 apply (zenon_L37_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 exact (zenon_H1a3 zenon_Hbb). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L2064_); trivial. % 22.64/22.74 apply (zenon_L2064_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 exact (zenon_H1a3 zenon_Hbb). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L2065_); trivial. % 22.64/22.74 apply (zenon_L2065_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 exact (zenon_H1a3 zenon_Hbb). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.74 apply (zenon_L2067_); trivial. % 22.64/22.74 apply (zenon_L2067_); trivial. % 22.64/22.74 apply (zenon_L895_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.74 apply (zenon_L791_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.74 apply (zenon_L361_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.74 apply (zenon_L2052_); trivial. % 22.64/22.74 apply (zenon_L51_); trivial. % 22.64/22.74 apply (zenon_L2109_); trivial. % 22.64/22.74 apply (zenon_L1045_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H30d); [ zenon_intro zenon_H310 | zenon_intro zenon_H30f ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H310). zenon_intro zenon_H10c. zenon_intro zenon_H306. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H306). zenon_intro zenon_H283. zenon_intro zenon_H307. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H307). zenon_intro zenon_H282. zenon_intro zenon_H308. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H308). zenon_intro zenon_H281. zenon_intro zenon_H284. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H38 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H159 | zenon_intro zenon_H5c ]. % 22.64/22.74 exact (zenon_H159 zenon_H10c). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H191 | zenon_intro zenon_H93 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.74 apply (zenon_L2_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.74 apply (zenon_L2110_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.64/22.74 apply (zenon_L2115_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_L1333_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.74 apply (zenon_L1206_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.74 apply (zenon_L11_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.74 apply (zenon_L1207_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 apply (zenon_L2223_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 apply (zenon_L2225_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 apply (zenon_L2225_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L2215_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_L2216_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_L251_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L147_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.74 apply (zenon_L120_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.74 apply (zenon_L193_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.74 apply (zenon_L2210_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.74 apply (zenon_L272_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L2216_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H54 | zenon_intro zenon_H14f ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L2228_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L117_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L2217_); trivial. % 22.64/22.74 apply (zenon_L331_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H53 | zenon_intro zenon_H150 ]. % 22.64/22.74 apply (zenon_L111_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H105 | zenon_intro zenon_H128 ]. % 22.64/22.74 apply (zenon_L2217_); trivial. % 22.64/22.74 apply (zenon_L149_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L365_); trivial. % 22.64/22.74 apply (zenon_L209_); trivial. % 22.64/22.74 apply (zenon_L157_); trivial. % 22.64/22.74 apply (zenon_L2211_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_L65_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L2212_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_L18_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_L2228_); trivial. % 22.64/22.74 apply (zenon_L456_); trivial. % 22.64/22.74 apply (zenon_L192_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 apply (zenon_L2128_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L2221_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_L2115_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_L251_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.74 apply (zenon_L120_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.74 apply (zenon_L393_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L731_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H153 | zenon_intro zenon_H202 ]. % 22.64/22.74 apply (zenon_L239_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H4d | zenon_intro zenon_H203 ]. % 22.64/22.74 apply (zenon_L335_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H105 | zenon_intro zenon_H106 ]. % 22.64/22.74 apply (zenon_L2229_); trivial. % 22.64/22.74 apply (zenon_L331_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L2124_); trivial. % 22.64/22.74 apply (zenon_L209_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L264_); trivial. % 22.64/22.74 apply (zenon_L2112_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_L146_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_L239_); trivial. % 22.64/22.74 apply (zenon_L192_); trivial. % 22.64/22.74 apply (zenon_L414_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 apply (zenon_L2223_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 apply (zenon_L2225_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 apply (zenon_L161_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L2215_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_L2216_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_L423_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_L65_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.74 apply (zenon_L53_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.74 apply (zenon_L95_); trivial. % 22.64/22.74 apply (zenon_L419_); trivial. % 22.64/22.74 apply (zenon_L192_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 apply (zenon_L2128_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L2221_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_L2115_); trivial. % 22.64/22.74 apply (zenon_L1940_); trivial. % 22.64/22.74 apply (zenon_L414_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_L13_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_L146_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L13_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_L17_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_L20_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.74 apply (zenon_L110_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.74 apply (zenon_L95_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L731_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L2232_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L2124_); trivial. % 22.64/22.74 apply (zenon_L648_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L94_); trivial. % 22.64/22.74 apply (zenon_L598_); trivial. % 22.64/22.74 apply (zenon_L31_); trivial. % 22.64/22.74 apply (zenon_L192_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 apply (zenon_L2233_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_L251_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.74 apply (zenon_L120_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.74 apply (zenon_L68_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L2111_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_L2232_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L2124_); trivial. % 22.64/22.74 apply (zenon_L2219_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L264_); trivial. % 22.64/22.74 apply (zenon_L2112_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_L146_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_L239_); trivial. % 22.64/22.74 apply (zenon_L192_); trivial. % 22.64/22.74 apply (zenon_L1347_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_L13_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_L146_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.74 apply (zenon_L120_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.74 apply (zenon_L95_); trivial. % 22.64/22.74 apply (zenon_L210_); trivial. % 22.64/22.74 apply (zenon_L192_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 apply (zenon_L161_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.74 apply (zenon_L251_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.74 apply (zenon_L147_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.74 apply (zenon_L2234_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H67 | zenon_intro zenon_H126 ]. % 22.64/22.74 apply (zenon_L251_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H76 | zenon_intro zenon_H127 ]. % 22.64/22.74 apply (zenon_L171_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H65 | zenon_intro zenon_H102 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.74 apply (zenon_L116_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.74 apply (zenon_L43_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H76 | zenon_intro zenon_Hfb ]. % 22.64/22.74 apply (zenon_L171_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L2235_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H118 ]. % 22.64/22.74 apply (zenon_L73_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H10d | zenon_intro zenon_H119 ]. % 22.64/22.74 apply (zenon_L152_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H110 | zenon_intro zenon_Hb9 ]. % 22.64/22.74 exact (zenon_H191 zenon_H110). % 22.64/22.74 apply (zenon_L166_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L2236_); trivial. % 22.64/22.74 apply (zenon_L2218_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H72 | zenon_intro zenon_Hf7 ]. % 22.64/22.74 apply (zenon_L407_); trivial. % 22.64/22.74 apply (zenon_L63_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.74 apply (zenon_L116_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L2238_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.64/22.74 apply (zenon_L2209_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.64/22.74 apply (zenon_L274_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.64/22.74 apply (zenon_L2236_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.64/22.74 apply (zenon_L43_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.64/22.74 apply (zenon_L54_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H38 | zenon_intro zenon_H19b ]. % 22.64/22.74 apply (zenon_L1259_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H136 | zenon_intro zenon_H19c ]. % 22.64/22.74 apply (zenon_L157_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H115 | zenon_intro zenon_H167 ]. % 22.64/22.74 apply (zenon_L2239_); trivial. % 22.64/22.74 exact (zenon_H162 zenon_H167). % 22.64/22.74 apply (zenon_L2162_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L2123_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.64/22.74 apply (zenon_L254_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.64/22.74 apply (zenon_L274_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.64/22.74 apply (zenon_L2123_); trivial. % 22.64/22.74 apply (zenon_L2239_); trivial. % 22.64/22.74 apply (zenon_L91_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_L146_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_L2214_); trivial. % 22.64/22.74 apply (zenon_L192_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_L2238_); trivial. % 22.64/22.74 apply (zenon_L1767_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.74 apply (zenon_L2128_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.74 apply (zenon_L2221_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.74 apply (zenon_L2115_); trivial. % 22.64/22.74 apply (zenon_L1767_); trivial. % 22.64/22.74 apply (zenon_L414_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.74 apply (zenon_L13_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.74 apply (zenon_L146_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.74 apply (zenon_L13_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.74 apply (zenon_L18_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.74 exact (zenon_Ha4 zenon_H9f). % 22.64/22.74 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.74 apply (zenon_L120_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.74 apply (zenon_L95_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H2d | zenon_intro zenon_H14a ]. % 22.64/22.74 apply (zenon_L731_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hdd | zenon_intro zenon_H14b ]. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H31 | zenon_intro zenon_H14d ]. % 22.64/22.74 apply (zenon_L2240_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H14e ]. % 22.64/22.74 apply (zenon_L1265_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H14c | zenon_intro zenon_H11d ]. % 22.64/22.74 apply (zenon_L2124_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H65 | zenon_intro zenon_H16c ]. % 22.64/22.74 apply (zenon_L2117_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H6d | zenon_intro zenon_H16d ]. % 22.64/22.74 apply (zenon_L54_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H8a | zenon_intro zenon_H93 ]. % 22.64/22.74 apply (zenon_L155_); trivial. % 22.64/22.74 apply (zenon_L267_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H115 ]. % 22.64/22.74 apply (zenon_L2124_); trivial. % 22.64/22.74 apply (zenon_L2219_); trivial. % 22.64/22.74 apply (zenon_L31_); trivial. % 22.64/22.74 apply (zenon_L192_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.74 apply (zenon_L2233_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.74 apply (zenon_L2240_); trivial. % 22.64/22.74 apply (zenon_L2243_); trivial. % 22.64/22.74 apply (zenon_L434_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.74 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.74 apply (zenon_L2245_); trivial. % 22.64/22.74 apply (zenon_L2245_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.74 apply (zenon_L1351_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.74 apply (zenon_L37_); trivial. % 22.64/22.74 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.74 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.75 apply (zenon_L2195_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.75 apply (zenon_L2250_); trivial. % 22.64/22.75 apply (zenon_L2250_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_L1354_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hbb. zenon_intro zenon_Hc1. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hb9. zenon_intro zenon_H32. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H89. zenon_intro zenon_H92. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H7b | zenon_intro zenon_H13d ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.75 apply (zenon_L2253_); trivial. % 22.64/22.75 apply (zenon_L2253_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 apply (zenon_L1355_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 apply (zenon_L2251_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_L2252_); trivial. % 22.64/22.75 apply (zenon_L1384_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8b ]. % 22.64/22.75 apply (zenon_L2254_); trivial. % 22.64/22.75 apply (zenon_L2254_); trivial. % 22.64/22.75 apply (zenon_L1389_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_L1233_); trivial. % 22.64/22.75 apply (zenon_L2203_); trivial. % 22.64/22.75 apply (zenon_L1391_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H312 | zenon_intro zenon_H311 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H312). zenon_intro zenon_H14c. zenon_intro zenon_H2f5. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2f5). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2f6). zenon_intro zenon_H28f. zenon_intro zenon_H2f8. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2f8). zenon_intro zenon_H1ca. zenon_intro zenon_H1c0. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_He3 | zenon_intro zenon_H3c ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H13d | zenon_intro zenon_H65 ]. % 22.64/22.75 exact (zenon_H13d zenon_H14c). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_L2236_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L28_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.75 apply (zenon_L2267_); trivial. % 22.64/22.75 apply (zenon_L2267_); trivial. % 22.64/22.75 apply (zenon_L2269_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.75 apply (zenon_L2273_); trivial. % 22.64/22.75 apply (zenon_L2273_); trivial. % 22.64/22.75 apply (zenon_L434_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.75 apply (zenon_L2276_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L2278_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L1336_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.75 apply (zenon_L1866_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 exact (zenon_H205 zenon_H2a). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 exact (zenon_H237 zenon_H31). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.75 exact (zenon_Ha4 zenon_H9f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.75 exact (zenon_Ha4 zenon_H9f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.75 apply (zenon_L116_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.75 apply (zenon_L43_); trivial. % 22.64/22.75 apply (zenon_L2281_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.75 apply (zenon_L193_); trivial. % 22.64/22.75 apply (zenon_L1873_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_L405_); trivial. % 22.64/22.75 apply (zenon_L2265_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.75 apply (zenon_L1866_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 exact (zenon_H205 zenon_H2a). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_L814_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.75 exact (zenon_Ha4 zenon_H9f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.75 apply (zenon_L116_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.75 apply (zenon_L43_); trivial. % 22.64/22.75 apply (zenon_L2283_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_L27_); trivial. % 22.64/22.75 apply (zenon_L2265_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_L2236_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_L405_); trivial. % 22.64/22.75 apply (zenon_L501_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 exact (zenon_H237 zenon_H31). % 22.64/22.75 exact (zenon_H238 zenon_H38). % 22.64/22.75 apply (zenon_L601_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_L2236_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_L27_); trivial. % 22.64/22.75 apply (zenon_L2287_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_L264_); trivial. % 22.64/22.75 exact (zenon_H238 zenon_H38). % 22.64/22.75 apply (zenon_L1861_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L35_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L39_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L2329_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.75 apply (zenon_L2339_); trivial. % 22.64/22.75 apply (zenon_L2339_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L2340_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.75 apply (zenon_L2341_); trivial. % 22.64/22.75 apply (zenon_L2341_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L28_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.75 exact (zenon_H209 zenon_H9d). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc4 ]. % 22.64/22.75 apply (zenon_L2342_); trivial. % 22.64/22.75 apply (zenon_L2342_); trivial. % 22.64/22.75 apply (zenon_L2269_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.75 apply (zenon_L2343_); trivial. % 22.64/22.75 apply (zenon_L434_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_L1884_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L2278_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L1336_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.75 apply (zenon_L1866_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 exact (zenon_H205 zenon_H2a). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 exact (zenon_H237 zenon_H31). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.75 exact (zenon_Ha4 zenon_H9f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.75 apply (zenon_L2281_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.75 apply (zenon_L193_); trivial. % 22.64/22.75 apply (zenon_L1873_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_L405_); trivial. % 22.64/22.75 apply (zenon_L2265_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.75 apply (zenon_L1866_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 exact (zenon_H205 zenon_H2a). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_L264_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_L2283_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_L27_); trivial. % 22.64/22.75 apply (zenon_L2265_); trivial. % 22.64/22.75 apply (zenon_L1886_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L35_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L39_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L2329_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_L221_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L201_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H13d | zenon_intro zenon_H65 ]. % 22.64/22.75 exact (zenon_H13d zenon_H14c). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L26_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L28_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H34. zenon_intro zenon_H39. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.75 apply (zenon_L1754_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.75 apply (zenon_L2276_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L16_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L18_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.64/22.75 apply (zenon_L1868_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_L25_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_L27_); trivial. % 22.64/22.75 apply (zenon_L500_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 exact (zenon_H237 zenon_H31). % 22.64/22.75 exact (zenon_H238 zenon_H38). % 22.64/22.75 apply (zenon_L601_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_L25_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_L405_); trivial. % 22.64/22.75 apply (zenon_L2286_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_L814_); trivial. % 22.64/22.75 exact (zenon_H238 zenon_H38). % 22.64/22.75 apply (zenon_L601_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L35_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L39_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L2345_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.75 exact (zenon_H7a zenon_H3c). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H40 ]. % 22.64/22.75 apply (zenon_L2347_); trivial. % 22.64/22.75 apply (zenon_L2347_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L2340_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L26_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L28_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 apply (zenon_L1475_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.75 apply (zenon_L180_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.75 apply (zenon_L214_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.75 apply (zenon_L1294_); trivial. % 22.64/22.75 apply (zenon_L165_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_L1880_); trivial. % 22.64/22.75 apply (zenon_L246_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_L1884_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L2278_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L18_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H4c ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H237 | zenon_intro zenon_H6c ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.75 apply (zenon_L1866_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 exact (zenon_H205 zenon_H2a). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 exact (zenon_H237 zenon_H31). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.75 exact (zenon_Ha4 zenon_H9f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.75 apply (zenon_L1293_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.75 apply (zenon_L193_); trivial. % 22.64/22.75 apply (zenon_L1873_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H238 | zenon_intro zenon_Ha4 ]. % 22.64/22.75 apply (zenon_L1866_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 exact (zenon_H1f zenon_H1e). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 exact (zenon_H205 zenon_H2a). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_L264_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.75 exact (zenon_Ha4 zenon_H9f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.75 apply (zenon_L2282_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.75 apply (zenon_L193_); trivial. % 22.64/22.75 apply (zenon_L156_); trivial. % 22.64/22.75 apply (zenon_L1886_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L35_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L39_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L2345_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_L221_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L201_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H13d | zenon_intro zenon_H65 ]. % 22.64/22.75 exact (zenon_H13d zenon_H14c). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L4_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L6_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L8_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_L9_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L2278_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L33_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L19_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L35_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L39_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L40_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_L45_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L2340_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_H314 | zenon_intro zenon_H313 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H314). zenon_intro zenon_H105. zenon_intro zenon_H2fb. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2fb). zenon_intro zenon_H2fd. zenon_intro zenon_H2fc. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2fc). zenon_intro zenon_H290. zenon_intro zenon_H2fe. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2fe). zenon_intro zenon_H264. zenon_intro zenon_H230. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H2fd); [ zenon_intro zenon_H4c | zenon_intro zenon_H2a ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1bf | zenon_intro zenon_H6d ]. % 22.64/22.75 exact (zenon_H1bf zenon_H105). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L2348_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L2349_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L2351_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.75 apply (zenon_L2355_); trivial. % 22.64/22.75 apply (zenon_L2355_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L319_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L2356_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L435_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.75 apply (zenon_L2364_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 apply (zenon_L2365_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 apply (zenon_L451_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 apply (zenon_L2365_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_L250_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_L2368_); trivial. % 22.64/22.75 apply (zenon_L1087_); trivial. % 22.64/22.75 apply (zenon_L2369_); trivial. % 22.64/22.75 apply (zenon_L101_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_Hec | zenon_intro zenon_H159 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 apply (zenon_L2365_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 apply (zenon_L457_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 exact (zenon_H4c zenon_H47). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.75 apply (zenon_L20_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.75 apply (zenon_L214_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.75 apply (zenon_L22_); trivial. % 22.64/22.75 apply (zenon_L2370_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_L148_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.75 exact (zenon_H4c zenon_H47). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.75 apply (zenon_L20_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.75 apply (zenon_L21_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.75 apply (zenon_L264_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.75 apply (zenon_L303_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.75 exact (zenon_He3 zenon_He7). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.75 apply (zenon_L64_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H148 ]. % 22.64/22.75 apply (zenon_L46_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H10c | zenon_intro zenon_H149 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1a4 ]. % 22.64/22.75 apply (zenon_L68_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H133 | zenon_intro zenon_H1a5 ]. % 22.64/22.75 apply (zenon_L436_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H110 | zenon_intro zenon_Hbb ]. % 22.64/22.75 apply (zenon_L400_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H9e | zenon_intro zenon_H26b ]. % 22.64/22.75 apply (zenon_L115_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H26c ]. % 22.64/22.75 apply (zenon_L90_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc3 ]. % 22.64/22.75 apply (zenon_L2367_); trivial. % 22.64/22.75 apply (zenon_L622_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H133 | zenon_intro zenon_Ha5 ]. % 22.64/22.75 apply (zenon_L436_); trivial. % 22.64/22.75 apply (zenon_L90_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.75 apply (zenon_L70_); trivial. % 22.64/22.75 apply (zenon_L84_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_L60_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_L2368_); trivial. % 22.64/22.75 apply (zenon_L1087_); trivial. % 22.64/22.75 apply (zenon_L2369_); trivial. % 22.64/22.75 apply (zenon_L1113_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L458_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L2372_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.75 apply (zenon_L2388_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L467_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L2348_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L2349_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L2389_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.75 apply (zenon_L2390_); trivial. % 22.64/22.75 apply (zenon_L2390_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L319_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L2356_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L435_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.75 apply (zenon_L2364_); trivial. % 22.64/22.75 apply (zenon_L385_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L458_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L387_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.75 apply (zenon_L2388_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L388_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1bf | zenon_intro zenon_H6d ]. % 22.64/22.75 exact (zenon_H1bf zenon_H105). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L482_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L2349_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L2351_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_L513_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L319_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L485_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L435_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L522_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L458_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L2372_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_L531_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L467_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L482_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L2349_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L2389_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_L513_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L483_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L485_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L435_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L522_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L458_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L387_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_L531_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L388_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_L2352_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H316 | zenon_intro zenon_H315 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H316). zenon_intro zenon_H8a. zenon_intro zenon_H301. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H301). zenon_intro zenon_H291. zenon_intro zenon_H302. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H302). zenon_intro zenon_H277. zenon_intro zenon_H303. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H303). zenon_intro zenon_H270. zenon_intro zenon_H271. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H6c | zenon_intro zenon_H31 ]. % 22.64/22.75 apply (zenon_L2109_); trivial. % 22.64/22.75 apply (zenon_L2081_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H318 | zenon_intro zenon_H317 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H318). zenon_intro zenon_H110. zenon_intro zenon_H306. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H306). zenon_intro zenon_H283. zenon_intro zenon_H307. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H307). zenon_intro zenon_H282. zenon_intro zenon_H308. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H308). zenon_intro zenon_H281. zenon_intro zenon_H284. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H159 | zenon_intro zenon_H5c ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H191 | zenon_intro zenon_H93 ]. % 22.64/22.75 exact (zenon_H191 zenon_H110). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H25. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 apply (zenon_L2392_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_L65_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_L2394_); trivial. % 22.64/22.75 apply (zenon_L596_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L2396_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L2397_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.75 apply (zenon_L2400_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L2401_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H5c. zenon_intro zenon_H62. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H7f. zenon_intro zenon_H39. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.75 apply (zenon_L2406_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L1208_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L1209_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H93. zenon_intro zenon_H9a. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H160. zenon_intro zenon_H39. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_Hc2. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_H209 | zenon_intro zenon_H162 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.75 apply (zenon_L815_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H181 ]. % 22.64/22.75 apply (zenon_L2415_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 apply (zenon_L2408_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 apply (zenon_L352_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_L215_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_L2136_); trivial. % 22.64/22.75 apply (zenon_L596_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_L2129_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 apply (zenon_L352_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_L65_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.75 apply (zenon_L2150_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.75 apply (zenon_L2409_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.75 apply (zenon_L217_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.75 exact (zenon_Ha4 zenon_H9f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.75 apply (zenon_L53_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.75 apply (zenon_L75_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.75 exact (zenon_Ha4 zenon_H9f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H25 | zenon_intro zenon_H146 ]. % 22.64/22.75 apply (zenon_L116_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_He7 | zenon_intro zenon_H147 ]. % 22.64/22.75 apply (zenon_L272_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H136 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hed ]. % 22.64/22.75 apply (zenon_L46_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H3f | zenon_intro zenon_Hee ]. % 22.64/22.75 apply (zenon_L219_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4d | zenon_intro zenon_H5c ]. % 22.64/22.75 apply (zenon_L117_); trivial. % 22.64/22.75 apply (zenon_L2152_); trivial. % 22.64/22.75 apply (zenon_L422_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.75 apply (zenon_L67_); trivial. % 22.64/22.75 exact (zenon_H209 zenon_H9d). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.75 apply (zenon_L147_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.75 apply (zenon_L94_); trivial. % 22.64/22.75 apply (zenon_L167_); trivial. % 22.64/22.75 apply (zenon_L596_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 apply (zenon_L352_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_L2417_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.75 exact (zenon_Ha4 zenon_H9f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.75 apply (zenon_L53_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.75 apply (zenon_L95_); trivial. % 22.64/22.75 apply (zenon_L2416_); trivial. % 22.64/22.75 apply (zenon_L2418_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 apply (zenon_L2411_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_L2129_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 apply (zenon_L2413_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.75 apply (zenon_L818_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.75 apply (zenon_L2409_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.75 apply (zenon_L217_); trivial. % 22.64/22.75 apply (zenon_L866_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_L239_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H47 | zenon_intro zenon_H83 ]. % 22.64/22.75 apply (zenon_L2414_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H3c | zenon_intro zenon_H84 ]. % 22.64/22.75 apply (zenon_L2409_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H54 | zenon_intro zenon_H7e ]. % 22.64/22.75 apply (zenon_L217_); trivial. % 22.64/22.75 apply (zenon_L2420_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.75 apply (zenon_L251_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.75 exact (zenon_Ha4 zenon_H9f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.75 apply (zenon_L110_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.75 apply (zenon_L68_); trivial. % 22.64/22.75 apply (zenon_L2416_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.75 apply (zenon_L264_); trivial. % 22.64/22.75 apply (zenon_L167_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_L2417_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_L239_); trivial. % 22.64/22.75 apply (zenon_L2418_); trivial. % 22.64/22.75 apply (zenon_L555_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H120 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.75 apply (zenon_L20_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.75 apply (zenon_L2421_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.75 apply (zenon_L122_); trivial. % 22.64/22.75 apply (zenon_L167_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.75 apply (zenon_L53_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.75 exact (zenon_H159 zenon_H10c). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.75 apply (zenon_L163_); trivial. % 22.64/22.75 exact (zenon_H1c7 zenon_Hac). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.75 apply (zenon_L251_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.75 apply (zenon_L2421_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.75 apply (zenon_L264_); trivial. % 22.64/22.75 apply (zenon_L167_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1c8 ]. % 22.64/22.75 apply (zenon_L55_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H10c | zenon_intro zenon_H1c9 ]. % 22.64/22.75 exact (zenon_H159 zenon_H10c). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H10d | zenon_intro zenon_Hac ]. % 22.64/22.75 apply (zenon_L163_); trivial. % 22.64/22.75 exact (zenon_H1c7 zenon_Hac). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_L239_); trivial. % 22.64/22.75 apply (zenon_L2423_); trivial. % 22.64/22.75 apply (zenon_L2427_); trivial. % 22.64/22.75 apply (zenon_L237_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_L2393_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9f | zenon_intro zenon_Hb4 ]. % 22.64/22.75 exact (zenon_Ha4 zenon_H9f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hb5 ]. % 22.64/22.75 apply (zenon_L42_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H9d ]. % 22.64/22.75 apply (zenon_L282_); trivial. % 22.64/22.75 apply (zenon_L221_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L2428_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_L1222_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H191 | zenon_intro zenon_H93 ]. % 22.64/22.75 exact (zenon_H191 zenon_H110). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 22.64/22.75 apply (zenon_L2473_); trivial. % 22.64/22.75 apply (zenon_L1234_); trivial. % 22.64/22.75 apply (zenon_L2454_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H317); [ zenon_intro zenon_H31a | zenon_intro zenon_H319 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H31a). zenon_intro zenon_H167. zenon_intro zenon_H2f5. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2f5). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2f6). zenon_intro zenon_H28f. zenon_intro zenon_H2f8. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2f8). zenon_intro zenon_H1ca. zenon_intro zenon_H1c0. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 22.64/22.75 apply (zenon_L2324_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_He3 | zenon_intro zenon_H3c ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H13d | zenon_intro zenon_H65 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 22.64/22.75 exact (zenon_H162 zenon_H167). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L4_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L6_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L8_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_L9_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L2305_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L2306_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L19_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L2313_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L1831_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L40_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_L221_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L201_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 22.64/22.75 exact (zenon_H162 zenon_H167). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L4_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L28_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L8_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_L9_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L2322_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L2306_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L19_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L35_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L39_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L40_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_L221_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L201_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H162 | zenon_intro zenon_H9d ]. % 22.64/22.75 exact (zenon_H162 zenon_H167). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L26_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L6_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L8_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_L9_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L16_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L18_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L19_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L1830_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L1831_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L40_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_L221_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L201_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H31c | zenon_intro zenon_H31b ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H31c). zenon_intro zenon_H11f. zenon_intro zenon_H2fb. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2fb). zenon_intro zenon_H2fd. zenon_intro zenon_H2fc. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2fc). zenon_intro zenon_H290. zenon_intro zenon_H2fe. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2fe). zenon_intro zenon_H264. zenon_intro zenon_H230. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H2fd); [ zenon_intro zenon_H4c | zenon_intro zenon_H2a ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1bf | zenon_intro zenon_H6d ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 22.64/22.75 exact (zenon_H120 zenon_H11f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L2476_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L2478_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L2480_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.75 apply (zenon_L2492_); trivial. % 22.64/22.75 apply (zenon_L2492_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H4d. zenon_intro zenon_H5b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H53. zenon_intro zenon_H32. % 22.64/22.75 apply (zenon_L2491_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L2483_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L2495_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.75 apply (zenon_L2496_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L2487_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L387_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H3e. zenon_intro zenon_H45. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H169. zenon_intro zenon_H15c. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.75 apply (zenon_L2373_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 exact (zenon_H4c zenon_H47). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_L2382_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_L2497_); trivial. % 22.64/22.75 apply (zenon_L187_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1b3 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 exact (zenon_H4c zenon_H47). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.75 apply (zenon_L20_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.75 apply (zenon_L214_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.75 apply (zenon_L2498_); trivial. % 22.64/22.75 apply (zenon_L2499_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.75 apply (zenon_L1601_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.75 apply (zenon_L1602_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.75 apply (zenon_L2488_); trivial. % 22.64/22.75 apply (zenon_L262_); trivial. % 22.64/22.75 apply (zenon_L187_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 apply (zenon_L2490_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 exact (zenon_H4c zenon_H47). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.75 apply (zenon_L20_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.75 apply (zenon_L214_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.75 apply (zenon_L2498_); trivial. % 22.64/22.75 apply (zenon_L2500_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_L239_); trivial. % 22.64/22.75 apply (zenon_L187_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_L2501_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_L2477_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 exact (zenon_H4c zenon_H47). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_L2503_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_L239_); trivial. % 22.64/22.75 apply (zenon_L187_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H1e | zenon_intro zenon_H1ff ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H67 | zenon_intro zenon_H142 ]. % 22.64/22.75 apply (zenon_L20_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H6e | zenon_intro zenon_H143 ]. % 22.64/22.75 apply (zenon_L2504_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H66 | zenon_intro zenon_Hf6 ]. % 22.64/22.75 apply (zenon_L2498_); trivial. % 22.64/22.75 apply (zenon_L165_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 22.64/22.75 apply (zenon_L2474_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2d | zenon_intro zenon_H34 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 exact (zenon_H4c zenon_H47). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.75 apply (zenon_L2444_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.75 apply (zenon_L55_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.75 apply (zenon_L2488_); trivial. % 22.64/22.75 apply (zenon_L262_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_L1603_); trivial. % 22.64/22.75 apply (zenon_L187_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 22.64/22.75 exact (zenon_H4c zenon_H47). % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H3d | zenon_intro zenon_H15f ]. % 22.64/22.75 apply (zenon_L2503_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H153 | zenon_intro zenon_H155 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H9f | zenon_intro zenon_H144 ]. % 22.64/22.75 apply (zenon_L2505_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hdb | zenon_intro zenon_H145 ]. % 22.64/22.75 apply (zenon_L1602_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hfe | zenon_intro zenon_H9e ]. % 22.64/22.75 apply (zenon_L2488_); trivial. % 22.64/22.75 apply (zenon_L156_); trivial. % 22.64/22.75 apply (zenon_L246_); trivial. % 22.64/22.75 apply (zenon_L373_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L388_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 22.64/22.75 exact (zenon_H120 zenon_H11f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L2476_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_L2478_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L2480_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_L2509_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L319_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L2483_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L435_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H6d. zenon_intro zenon_H88. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H72. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.75 apply (zenon_L2496_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L458_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L387_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb1). zenon_intro zenon_Hac. zenon_intro zenon_Hb3. % 22.64/22.75 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Ha5. zenon_intro zenon_H2b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H44. zenon_intro zenon_H43. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H7a | zenon_intro zenon_He3 ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e | zenon_intro zenon_H239 ]. % 22.64/22.75 apply (zenon_L2512_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H2a | zenon_intro zenon_H23a ]. % 22.64/22.75 apply (zenon_L2506_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H31 | zenon_intro zenon_H38 ]. % 22.64/22.75 apply (zenon_L2513_); trivial. % 22.64/22.75 apply (zenon_L925_); trivial. % 22.64/22.75 apply (zenon_L385_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L388_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_H1bf | zenon_intro zenon_H6d ]. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 22.64/22.75 exact (zenon_H120 zenon_H11f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L482_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.64/22.75 apply (zenon_L2514_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L2480_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H22. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1d. zenon_intro zenon_H23. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H204. zenon_intro zenon_H206. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H206). zenon_intro zenon_H240. zenon_intro zenon_H23b. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1f ]. % 22.64/22.75 apply (zenon_L2516_); trivial. % 22.64/22.75 apply (zenon_L2516_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L483_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L2483_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L2495_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L522_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L2487_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L387_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_L531_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L388_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H120 | zenon_intro zenon_Hac ]. % 22.64/22.75 exact (zenon_H120 zenon_H11f). % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H20 | zenon_intro zenon_Hcd ]. % 22.64/22.75 apply (zenon_L2_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_H28 | zenon_intro zenon_Hce ]. % 22.64/22.75 apply (zenon_L482_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H2f | zenon_intro zenon_Hcf ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H2d. zenon_intro zenon_H32. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bf ]. % 22.64/22.75 exact (zenon_H1ba zenon_H6d). % 22.64/22.75 apply (zenon_L2514_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H36 | zenon_intro zenon_Hd0 ]. % 22.64/22.75 apply (zenon_L2480_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd1 ]. % 22.64/22.75 apply (zenon_L2509_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H41 | zenon_intro zenon_Hd2 ]. % 22.64/22.75 apply (zenon_L11_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_H5a | zenon_intro zenon_Hd3 ]. % 22.64/22.75 apply (zenon_L483_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_H61 | zenon_intro zenon_Hd4 ]. % 22.64/22.75 apply (zenon_L2483_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H63 | zenon_intro zenon_Hd5 ]. % 22.64/22.75 apply (zenon_L435_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H87 | zenon_intro zenon_Hd6 ]. % 22.64/22.75 apply (zenon_L522_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H8c | zenon_intro zenon_Hd7 ]. % 22.64/22.75 apply (zenon_L37_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H99 | zenon_intro zenon_Hd8 ]. % 22.64/22.75 apply (zenon_L458_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_H9b | zenon_intro zenon_Hd9 ]. % 22.64/22.75 apply (zenon_L387_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hda ]. % 22.64/22.75 apply (zenon_L531_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hc5 ]. % 22.64/22.75 apply (zenon_L388_); trivial. % 22.64/22.75 apply (zenon_L51_); trivial. % 22.64/22.75 apply (zenon_L2506_); trivial. % 22.64/22.75 apply (zenon_or_s _ _ zenon_H31b); [ zenon_intro zenon_H31e | zenon_intro zenon_H31d ]. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H31e). zenon_intro zenon_H17c. zenon_intro zenon_H301. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H301). zenon_intro zenon_H291. zenon_intro zenon_H302. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H302). zenon_intro zenon_H277. zenon_intro zenon_H303. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H303). zenon_intro zenon_H270. zenon_intro zenon_H271. % 22.64/22.75 apply (zenon_L2586_); trivial. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H31d). zenon_intro zenon_Hc3. zenon_intro zenon_H306. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H306). zenon_intro zenon_H283. zenon_intro zenon_H307. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H307). zenon_intro zenon_H282. zenon_intro zenon_H308. % 22.64/22.75 apply (zenon_and_s _ _ zenon_H308). zenon_intro zenon_H281. zenon_intro zenon_H284. % 22.64/22.75 apply (zenon_L1235_); trivial. % 22.64/22.75 Qed. % 22.64/22.75 % SZS output end Proof % 22.64/22.75 (* END-PROOF *) % 22.64/22.75 nodes searched: 164071 % 22.64/22.75 max branch formulas: 303 % 22.64/22.75 proof nodes created: 16079 % 22.64/22.75 formulas created: 81233 % 22.64/22.75 %------------------------------------------------------------------------------